So I will turn it over to him. All right, well, thanks very much, Eric. And thank you guys very much for the opportunity to talk with you this morning. So in any case, in the spirit of Eric's chronicling, the number of council meetings and so forth, actually the intramural program of NHGRI is now in its 21st year, having marked its 20th anniversary last year. And actually, my own tenure at the NIH is a little bit longer than that. I actually started at the NIH in 1985, although it may seem incredible to you that someone looking like me could actually have been here for that long, but it's true. I started actually in the Arthritis Institute and had an interest in the positional cloning of various genes that are involved in the regulation of inflammation. And certainly one of the things that was very exciting to us in the rest of the intramural program of the NIH was the advent of the intramural program of NHGRI, because that really did bring genomic technology, and it created really a critical mass of people who are interested in genetics and genomics to the NIH campus in Bethesda. And so this really was, I thought, a wonderful thing and something that really catalyzed the transformation, really, of the intramural campus. And so when I had the opportunity to join NHGRI in 2010, and actually I joined NHGRI on the auspicious date of 10, 10, 10, October 10, 2010, it's really been just a fantastic time getting to work with people in NHGRI since then. So in any case, I'm going to talk to you a little bit about the NHGRI intramural program. And just to give you an overview of the things that we will be talking about, first of all, I'll give you at least a little bit of a raise-owned debt for intramural research at the NIH. Secondly, I'll talk to you a little bit about the NHGRI intramural vision and what we do in our particular intramural program. Thirdly, I'll talk with you a little bit about the intramural faculty of NHGRI and its organization and recent reorganization. Fourthly, we'll talk about at least a few of the scientific accomplishments of the intramural program, at least a little bit adding to some of the things that Eric talked about a couple minutes ago. Fifth, we'll talk a little bit about how NHGRI intramural science is evaluated, both in the context of the blue ribbon panel review that we underwent back in 2011 and 2012, which, by the way, was chaired by David Page sitting over across from me in the corner, trying to look inconspicuous with this. And then also a little bit about our Board of Scientific Counselors' Review of Scientific Programs. I'll also talk a little bit about the budget of the intramural program and the vicissitudes that we've had to go through with the various sequestrations and shutdowns and so forth. And then finally, I'll end with a little bit in terms of new initiatives in the intramural program. So to get started, let's just talk first a little bit about what are the distinctive features of research at the intramural program of the NIH. And there are nine things that I've identified here on this slide that I think are important. One is that the intramural program tends to have an institutional commitment to researchers over projects more like the Hughes Institute. Secondly, there's a quadrennial heavily retrospective review, which is different from the prospective review that is seen most prevalently in the intramural program. Thirdly, because of the fact that usually funding is relatively stable, it allows for long-term studies that require this kind of stability of funding. And this lends itself, then, we hope, and we certainly strive for, high-risk, high-reward projects that would be difficult to do with R01 funding. Certainly, in the intramural program of the NIH, there's critical mass in certain key areas. Certainly, genomics now is one of them. Immunology, I would say, is certainly another that is world-class in the intramural program of the NIH. The structural biology, I guess, would be another to single out. Certainly, one of the justifications for having an intramural program is the idea that researchers at the NIH, currently sometimes, turn on a dime, changing their research focus to respond to public health crises, such as what was seen in the 1980s with the HIV crisis, for example. And the intramural program really took a leadership role in getting things going in that area. It's also an intellectual home for institute directors and extramural program staff. And so we want to have a vibrant intellectual community for these people to be able to take part in. It's close to the seat of government. And as Eric pointed out, sometimes we, in fact, host various people from Congress and the administration. And so it's very important to have really cutting-edge science that's going on here. And then finally, there are specialized resources that are available in the intramural program. And probably the one that comes to mind most prominently is that of the NIH Clinical Center. And this is really a unique hospital in the sense that it is a hospital where every single patient who is admitted is on a research protocol and where, in fact, there's no cost to the patient or to the investigator for the patient to be admitted. And so this really does then lend itself to doing clinical investigation in a very intensive way. And so the Clinical Center really has been the hub around which a lot of the research at the NIH intramural program has been done. In terms of the NHGRI's intramural research program, I'd just like to talk about five things that our faculty identified as being very important in the process of developing a vision statement back in 2012 as part of the Blue Ribbon Panel review process. First of all, the NHGRI intramural research program really aims to lead the way on the NIH campus in the genetics, genomics, pathophysiology, and treatment of human disease, fostering a deeper understanding of human biology. And as I said, that certainly has been my experience as first an outsider to the Genome Institute. And then certainly this is something that we want to continue. Certainly the intramural program also wishes to conduct transformative science, to develop collaborations among basic clinical and social and behavioral scientists, to take full advantage of the intramural environment and the critical mass that we have in certain areas, and to catalyze change across the NIH campus. Certainly in terms of this heat map that Eric had in his paper in Nature back a couple of years ago, whereas the overall genetics and genomics community is perhaps more focused in the biology of genomes and the biology of disease right now. The intramural program, partly because of the accessibility of the resources of the clinical center, perhaps is focused a little bit more in terms of understanding the biology of disease and the science of medicine. So in any case, just a little overview in terms of the faculty in the NHGRI intramural program. Altogether, we have 45 investigators who are our research faculty. Of them, 25 are tenured senior investigators. Four are tenure track investigators. And this is actually a reduction in the numbers. When I started as the scientific director, we actually had eight tenure track investigators. And over time, some have left, some have graduated to tenured positions. And certainly given budgetary constraints, this is an issue that we'll come back to a little bit later in terms of the future of the intramural program is just being able to set aside the resources for younger investigators. And then finally, we have 16 associate investigators who are more like research adjunct faculty at a medical school. Eight of them have some independent resources of their own, eight work primarily for other tenured investigators. And then in addition to that, we have 10 adjunct investigators shown here who actually hold their primary appointments in other institutes but have a affiliation with the NHGRI intramural program. So in any case, this is just a pictorial showing all of the faculty that I just summarized on the previous slide. Two major events this past year in 2013 with regard to the faculty. First of all, we had the joining of the faculty of Gary Gibbons, who many of you know is the director of NHLBI. He, of course, recently came to the NIH campus. He's an expert on cardiovascular genetics and health disparities. And he chose to locate his lab and NHGRI's intramural program. And I think that just the fact that we have not only Gary Gibbons as one of our faculty members, but also Harold Varmas at his request and Francis Collins is just a vindication of the quality of the intellectual environment in NHGRI's intramural program and says something about the administrative support that NHGRI is able to provide as well. We did have one of our investigators, a tenure track investigator, Yardena Samuels, who took a tenured position at the Weizmann Institute in Rehoboth during this last year as well. So one new tenured member of the faculty and one person leaving. In any case, over the last year, just as Eric has reorganized the overall structure of the NHGRI writ large, our intramural program has also undergone a reorganization, which was at least in part recommended by some of the outside advisory bodies that we have. The goals, basically, of doing this reorganization were to increase scientific synergy amongst investigators to advance the careers of some of our mid-level faculty, certainly some element of succession planning as well. And as Eric mentioned a little while ago, Larry Brody has taken on the position of division director for the Division of Genomics and Society. And because of that, the Genome Technology Branch has been phased out, and the members of the Genome Technology Branch have been located in other branches. We have now two new, rather three new branch chiefs in the institute, Julie Segre, whom Eric mentioned with regard to the Service to America Award that she received this last year. Pam Schwartzberg, who is an expert on the genetics of various immune diseases, and Charles Rotimi, whose work concentrates on health disparities research and the genetics of cardiovascular and metabolic disease in the African and African-American populations. Certainly in this process, we tried to more clearly delineate the role of the branch chief in terms of scientific leadership and mentorship. And we have an expanded leadership group with now nine branches in terms of seven, as we had before. I'll just mention briefly that we have eight cores within the NHGRI intramural program. And certainly these cores have taken a leadership role on campus in terms of disseminated genomic thinking and genomic technology. For example, the Bioethics Core certainly has taken a leadership role in terms of helping investigators and other institutes to think about issues of informed consent in genomic studies, whether it be genome-wide association studies or whole exome sequencing. The Bioinformatics and Scientific Programming Core has a number of courses that they offer for the broader community, including one that is currently starting, at least the most recent edition of which had over 1,000 people signed up on campus. And videos of that course are kept on YouTube. And there are literally hundreds of thousands of views of the lectures in this course. So it really is something that disseminates genomic thinking and technology, not just to the NIH campus, but in fact to the broader community. And several of these other cores, of course, have had a major role in terms of disseminating these technologies to others at the NIH campus. Another feature of the intramural program is NISC, the NIH Intramural Sequencing Center, which was founded several years ago as a medium-sized genome sequencing center that provides, at least at this point, next-gen DNA sequencing and sequence analysis. It has a budget of around $7 million a year. And Jim Mulliken is the director. As you can see, there's a number of different sequencers that are available. And last year, NISC produced about 45 terabases of high-seq output to 55 principal investigators and 11 different institutes. Again, underscoring the fact that NHGRI really does serve a broad role for a number of intramural programs at the NIH. Eric also mentioned the undiagnosed diseases network and, of course, the undiagnosed diseases program was the progenitor of that. This was established by NHGRI clinical director Bill Gall back in 2008. And Bill had the vision of attracting patients to the NIH with seemingly inexplicable conditions referred throughout the country, performing comprehensive both clinical and molecular genetic analyses of these patients and discovering a number of heretofore unknown molecular lesions defining new genetic diseases. And, of course, it is now the parent, if you will, of the undiagnosed diseases network of the common fund. So just a few highlights, some of which Eric has talked about, but others not, just to give you a flavor for some of the things that are going on scientifically in the intramural program. Here is a paper that was published in the New England Journal of Medicine last summer from Bill Gall's group on a gene VPS45, which encodes a transporter molecule that transports, among other things, adhesion molecules to the cell surfaces of white blood cells. Patients who have loss of function mutations in this gene have an immunodeficiency, have a problem with neutrophil function and, in particular, neutrophil adherence and migration. And so these patients have an immune deficiency. A second clinically related paper is one that Les Beeseker co-authored. It was a opinion piece in JAMA dealing with reporting incidental findings in the clinical setting. And of course, Les Beeseker has had a major leadership role in this area through the ClinSeq initiative that he started, and certainly has participated in a number of the approaches to this, including the American College of Medical Genetics list of actionable variants that should be reported. Another important paper from the intramural program is one from Julie Sigrae's group that was published in Nature last year dealing with the fungal microbiome on the human skin. And then, as Eric pointed out in his comments, Julie and Evan Snitkin in her lab, as well as Tara Palmer and David Henderson from the Clinical Center were involved in a very important study, identifying basically the transmission of a resistant organism through the Clinical Center and effectively dealt with that and really established a paradigm for how to do this in clinical practice. Other important papers from the intramural program here is one from Pam Schwartzberg's group defining a new immunodeficiency disease caused by mutations in PI3 kinase. These patients have EBV and CMV infections and have a problem with the formation of the immunologic synapse. A paper from Inza Yang's group dealing with heterotopic ossification. This is actually a very important problem in some of the returning veterans from the Middle East who have had amputations. And actually, at least some of these individuals develop calcifications at the stump of their amputation, which can be then very, very painful to them with their prostheses. And Inza has had a major interest in identifying the molecular pathways that lead to heterotopic ossification. A couple of papers from the husband-wife team of Joan Bailey Wilson and Alec Wilson dealing with various genome-wide association studies that they've done over the course of the last year on myopia and on craniosynostosis. Couple of papers from Charles Rotimi's group dealing with body mass index in individuals of African ancestry and Charles's continuing contribution to the 1000 Genomes Project. A couple of papers from tenure-track investigators, one of them Chuck Venditti, who's done really incredible work developing a cohort of patients with various metabolic acidemias and identifying the molecular basis of those diseases. And then Daphne Bell, another tenure-track investigator in the Institute who's been looking at whole exome and whole genome sequencing of endometrial tumors. And then here, a paper from Steve Parker, a postdoc in Francis Collins Group, identifying a group of enhancers, stretch enhancers similar to the super-enhancers that Rick Young's group has been looking at and identifying their role in gene regulation and human disease. And a paper that Eric alluded to from Andy Baxavanis' group on the comb jelly and its sequence. And then here, a set of three papers from NISC, and these are just some of a whole host of papers from Jim Mulliken and the group at the Sequencing Center collaboratively identifying sequence in various non-human primates, the neanderthal. And then in some cases, actually looking at other subjects, such as HIV antibodies and co-evolution of the virus itself. Unabashedly, I'm showing three highlights of work from my own research group, one of them a paper that we published in Nature a little over a year ago dealing with the biology of NLRP3, which is a gene that we found mutated in a particular kind of inflammatory disease a number of years ago in the role of calcium encyclical AMP in signaling through this pathway. This is a very important pathway, both in a number of rare hereditary disorders of inflammation and also seems to play an important role in more common diseases, such as gout and cardiovascular disease. Here, a paper that we published in Nature Genetics last spring on a genome-wide association study in Betchette's disease. The interesting thing about that paper is that we found variants of ERAP1, which is a molecule in the endoplasmic reticulum that trims peptides for loading onto HLA Class 1 molecules, and there's actually an epistatic interaction between variants in ERAP1 and a particular HLA Class 1 molecule. And then finally, the one that we're most excited about, and this is a paper that will be coming out online in the New England Journal of Medicine next week, and basically it is a paper that describes a new disease, Dada2, deficiency of ADA2, in children with recurrent fevers and strokes, and at least in some cases, polyarteritis nidosum. And ADA2 is actually a protein that's at least in function similar to ADA1, which many of you know of, is the gene that's mutated in at least some cases of severe combined immunodeficiency. But ADA2 actually is a growth factor that's involved both in endothelial integrity and also in the differentiation of certain subsets of monocytes and macrophages. So in any case, just to turn to a very important topic and that is evaluating intramural science, I'll talk about just a little bit about two things. One, the blue ribbon panel process that occurred in 2011 and 2012, chaired by David Page, and I will just give a couple of slides summarizing some of their findings. Certainly the panel did look fairly broadly at the science that's being conducted in the intramural program. This is a review that occurs every 10 years, roughly, and is intended both to take stock of what's going on in the intramural program and make sure that appropriate types and quality of research is being done and also to think about the future. And so in their report, the blue ribbon panel did say that the IRP remains an outstanding research enterprise and this is reflected by its scientific productivity, an excellent record of educating and mentoring, enhancement of the broader NIH IRP through the dissemination of genomic technologies, the development of an impressive research in clinical faculty, the establishment of a robust research infrastructure, and a spirit of collaboration and collegiality. The panel refrained from being prescriptive in terms of exactly what kinds of things the intramural program should be doing over 10 years, wisely believing that it's very hard to know what kind of science is going to be practiced 10 years from now, but at least in terms of general principles exhorted us to embrace, to continue to embrace a risk-taking culture, to insist on excellence, to continue to be a change agent on the NIH campus and beyond and did know one area of need, and that is the interpretation of the volume of genome information that's being captured and its integration with other clinical data, and I'll actually come back to that in a little bit when we start talking about initiatives that we're currently undertaking. On a more granular basis, the Board of Scientific Counselors, as Eric pointed out, is the body that actually evaluates the science that's going on in the intramural program on a year-to-year basis. Currently, our BSC is chaired by Tom Hudson, who is the president of the Ontario Institute for Cancer Research, and then there are eight other individuals who are on the Board as well. Each branch within the NHGRI intramural program is evaluated every four years, and certainly we have made this process a little bit more standardized and we hope have made it even more rigorous over the course of the last couple of years, at least in part because of the suggestions of our Board of Scientific Counselors and in part because of suggestions of the blue ribbon panel. And so when I meet with the BSC and the ad hoc reviewers, I do tell them that we're really looking for great science and in particular, I ask them to think of five questions in evaluating the scientists and their programs. First, does the work fundamentally change the way that we think about or understand relevant areas of biomedical science? Second, through the development of new methods, does it change the way that we do science? Third, for clinical research, does it change the way that we practice medicine? Fourth, whether clinical or basic, how would the field look if the intramural investigator had not been active for the last five years? And then finally, is the research worth studying with the special resources associated with the IRP? In any case, since I've been scientific director, we have implemented a summative rating system of outstanding, excellent, and very good for each of the investigators who is reviewed and over the course of the last three years that we've been using this system. 17 out of 25 faculty got ratings of outstanding, one got a rating of outstanding to excellent, five excellent and two very good. And certainly one of the things that the Blue Ribbon Panel asked us to do is to have some sort of process in place if someone did get very good ratings and we certainly do have that in place now and investigators are up for re-review actually a year after their very good rating and then are totally re-reviewed two years later. And so we really have taken this very seriously. Turning for a moment to the subject of budget, I will just on one slide summarize at least the current budgetary circumstances of the intramural program. From fiscal year 2010 to 2012, FY 2010 was Eric's last year as scientific director and then the first two years from my scientific directorship. We had a flat budget of $104 million a year and from that $32 million are taken off the top for the maintenance of the clinical center and other central costs associated with the intramural program. In fiscal year 2013 because of sequestration, that figure was cut from 104 million to 100 million again with the same amount taken off the top in terms of overhead. In 2014, we budgeted for $98 million expecting that there would be a second wave of sequestration. Fortunately that has not happened, as Eric said. Over this period of time, we've converted the way that we do budgeting for individual investigators from a capitated centrally supported budget model to a bottom line approach where basically investigators are given a set amount of money per year and then they get to choose whether they spend it in personnel or services and supplies, figuring that that gives them more latitude to wisely spend their money in times of shortage. Overall we've done 15% across the board cuts in individual investigators since 2010 meaning everyone has been cut by that much and once we have these descriptors associated with each investigator then the budgeting will be based on their evaluations but of course we want to have it fair where everyone has been evaluated in the same way first. The actual fiscal year 2014 budget at least from what we understand will be about 102.5 million dollars. There are certain mandated expenditures like the 1% pay increase for GS employees and certain capital expenses that have been deferred but we do hope to be able to do at least one recruitment in bioinformatics during this year with some of the extra money that we have. Now turning to new initiatives just for a short time I'd like to highlight a couple of things. One of them is a sequencing project, the NHGRI clinical center sequencing project that actually a group of leadership the branch chiefs came up with that a meeting in August and Les Beeseker and Jim Mulliken have taken the lead on. So in any case what basically we're planning to do is to offer investigators in other institutes besides NHGRI whole exome sequencing at NISC on clinical center patients that reagent only cost and that's roughly half of the cost that investigators in other institutes would be charged otherwise if they were charged for the overhead cost of the sequencing. This is being further subsidized by competitive awards from Michael Goddusman's office so that essentially for those individuals that win one of these competitive awards they will have whole exome sequencing for their project at no cost. The sequencing we are implementing CLIA certified sequencing and Jim Mulliken is setting that up at NISC now. We do plan to return incidental findings to subjects and the genetic counseling service will be providing support for patients that receive those findings. The first year we're going to do this as a pilot with a thousand exomes offered although we hope to expand this as hopefully it is widely appreciated on campus and as funds permit so that it may expand eventually to all clinical center patients and would be integrated with some of the deep phenotyping capabilities that are available in other parts of the NIH such as the Center for Human Immunology and some of the neurology groups who have really top notch imaging capabilities. Second thing that I'll just mention briefly is the U01, Extramural Intramural Collaboration Mechanism. This is something that has been developed over the course of the last couple of years and it's basically a program that allows extramural investigators to partner with intramural investigators to write a grant application that involves patients that would be seen at the clinical center and the idea is that the extramural investigator might be conducting laboratory based research while the NIH investigator would be seeing patients phenotyping them and hopefully there would be then some integration between the two. The grants are for $500,000 a year for three years and basically our intramural program will be funding one new application a year so that eventually we'll be funding three at a time and simply because of the overall orientation of NHGRI's extramural funding, these applications should have a strong genomics orientation in order to be funded by NHGRI. There are a number of immediate challenges that we're facing here in the intramural program. Certainly one of them is just one that everyone has to face in these constrained budgetary times and that's maintaining a vibrant research enterprise in an area of flat budgets. Funding the NIH clinical center is particularly an important one because as I mentioned it really does have a central role in a lot of the research that's being done in the intramural program and unfortunately the costs of healthcare go up regardless of whether the federal budget is flat or not and so of course the concern is that the clinical center budget then takes up a larger and larger proportion of intramural funds. Certainly we also need to stay at the cutting edge of genomic technology and bioinformatics and that's part of the reason why our first recruit that we'll be doing with some extra money is in these areas. We wanna continue to catalyze genomic medicine in the intramural program and of course we need to in some way identify a way of liberating resources for new recruitments since really the age of our faculty is something that's really of significant concern to me in terms of the future of our intramural program. Michael Goddusman's office and Francis Collins have also just within the last couple of weeks initiated a 10 year planning initiative for the intramural program of the NIH. So each institute with an intramural program is going to review its intramural program and develop a strategic plan. The main question is what should the IRP look like both at the institute level and across institutes in 10 years and how can we get there? Each institute will constitute a review committee of prominent extramural and intramural scientists for institutes with a recent blue ribbon panel review. The current review may be an addendum to the blue ribbon panel review or maybe we'll have a reunion of the blue ribbon panel or something like that. What did you write? The review should address both scientific priorities and operational issues and institute reports are due at the end of July. A combined report from the institutes is supposed to be transmitted to the advisory committee to the director in September and the ACD would be rendering recommendations for the future of the intramural program on December the 12th, 2014. So anyway, that's basically what I have to say. I did manage to do it in 40 minutes which is what Eric had asked. And so anyway, with that, Excelsior onward and upward. So questions for Dan? Well, I have a question about how you actually implement the high risk, high reward strategy. I mean, unlike venture capital where they spread the risk and they know many of their investments are gonna go extinct. I hear you have kind of a fixed body. You want scientists to produce results and yet you should almost strive for some reasonable rate of failure as an indication that the high risk strategy is paying off. So I'm wondering how you. Oh, it's a very, very thorny or tricky question in terms of how to do this because you're quite right. And certainly as we scrutinize investigators more with the Board of Scientific Counselors and look more carefully at what their level of productivity is, it certainly does encourage people to go for sort of incremental quantum kinds of approaches rather than higher risk, longer term kinds of projects. I guess that really the only answer that I can give is in talking with investigators and thinking about as we have reviews and discussions of people's work in the intramural program of encouraging them with the bully pulpit that I have of taking on sometimes longer term things. Certainly it's an important thing with the tenure track investigators to encourage them to do that kind of thing. Certainly one my own personal experience with this which I think Bob can probably remember because he was one of my reviewers back many, many years ago. Is that I took on a positional cloning project as what I was doing as a tenure track investigator. And so it was very much a high risk, high reward, long term project. And that certainly is my point of view as to what people should do is to try to identify things that are really important and bold and to go for them. But it is, you're quite right, hard to actually get them to do it. Bob. Actually Dan, that was a very, very wonderful presentation. Thank you. I wanted to ask you for a comment and then ask you a question. So the comment is I've heard from other people not in your institute, but in other institutes in intramural program of real problems with morale. And not just from the sequestration but also from an onslaught of regulations coming down that really restrict the ability of scientists to participate in meetings and requests for that they're PowerPoints, that they're gonna give it scientific meetings, be put up in the public domain and all sorts of things like that. So I wanted to ask you about how you're able to maintain morale because it looks like people are working hard and doing well. And my question for you is have you been approached by the FDA about the NISC Next Generation Sequencing Center, not only having to be CLEA approved but also requiring investigational device exemptions if any other information is gonna go back to patients? Well, with regard to your first question, I guess the, I don't know if that's the easy question or the second one is the easy question. So maintaining morale, I mean it is something that is really one of the most important things that one can do right now with the intramural program. And I think that part of the dealings with that have to do with the fact that we have a very, very flexible and understanding administrative staff in NHGRI who really do put the investigator first. That's not to say breaking rules but at least being flexible to the extent that they can with regard to these kinds of things. And I think that with regard to the particular issues that you're raising has been very, very important. With regard to the budgetary constraints, the way that I've tried to handle that is by being totally transparent and by engaging the faculty in whatever decisions we make with regard to cutting programs or budgets or whatever so that it's not something that's coming down from on high but rather something that everybody's engaged in as a common response to an outside threat in a way. With regard to the FDA approaching NISC, well, no, so far we haven't heard that but that may just, maybe because we're not into it far enough for that to have happened. It might be worth while having a conversation with Anastasia-wise because the extramural newborn sequencing group has been approached by them. Really? Yeah. And we've been required to put in pre-IDE applications and they are looking very seriously at any next generation sequencing platforms including software that are used to generate information that's going back to patients. Wow. Okay, well, that's so boring. Actually, before we take another question, I mean, I should weigh in on the issue about morale a little, I guess, I mean, Bob, and coming from you is of relevance because of your longstanding presence in our intramural program and have seen various waves of phenomena. You know, and I also have my own vantage point. I mean, Dan's much closer to one on a day-by-day basis. I mean, I think there's no question that recent years, handful of years have just brought a constellation of stresses and strains to intramural investigators. I mean, budgetarily as part of it but some rather invasive attempts at requirements as well as other constraints around travel and et cetera, et cetera. No question. That said, I'd make two comments. One, I know it's also pretty stressful on the outside. So I think morale in general across biomedical research is not at all time high by any means. When I talk to people, I know lots of funding stress in particular. So I think it's there as well. I mean, the second comment to make is I also think that it's exactly what Dan said. I think the negative impact's gonna probably be last at NHGRI and I'm probably very biased in saying that. I do think we have an administrative approach to how we handle some of these things to try to make it as good as possible. I think fundamentally, morale has always been higher in our intramural program compared to a lot of other ones for a variety of reasons. So I think it's absolutely a case that it's an issue. I think it's probably more severe in other institutes than it is at ours for probably many reasons. But it's not just the intramural program. I think there's been morale issues across the whole Institute and across all of NIH for budgetary reasons, for restrictions on things like travel and so forth and then shut down, pay freezes, everything else. But I do think that we work very hard at the leadership and that's not just Dan and I, it's a whole suite of people to really try our best to buffer that as best we can. Tony, I know you had a question. Looking at the blue ribbon criteria for excellence in the intramural program, it talks about productivity, risk-taking excellence, but no one has mentioned innovation, which is one of the main criteria for the review of external grants. You may say that's inherent in risk-taking, but the example you give of positional cloning, you may just use standard technology and the risk is that someone else identifies the gene before you. So I just wanted to know how important innovation was in the way internal investigators are approaching their problems to add new value to the general field if they find a new way to do it or a new technology. No, it's a very good point and certainly, although it wasn't listed on those slides, it is something that we very much value and that is emphasized in the evaluations as we currently do them for people. I would say just with regard to going back to the positional cloning, I was doing that in the early 1990s, which was at a time when the approach was, well, you were involved in it too. It was not totally a standard approach at least at that time. But anyway, I certainly hear your point and I think that it is something that, although not mentioned, is very much a part of what we want to encourage. So great report and I want to congratulate you on actually following through on some of the things that we all suggested, it makes it feel worthwhile. And coming back to Marty's question about the risk-taking, I mean, I think that the having real, something we talked a lot about, having real rigor in that, in those every four-year reviews and actually having that be constantly reiterated and sort of conveyed by the advisors along the way, obviously risk-taking is in the eye of the beholder. It's actually bad. But then coming back to the question of morale and such and thinking about, I guess my sense is that the morale of a faculty is there's the underlying issues involved both reality and perception. And I think it's worth your conveying back to your colleagues that it's funny, the term flat funding would have an extremely positive ring in the extramural world. I can think of many institutions, it would be delighted to project flat federal funding. And it may be, and also thinking about the fact that many of your colleagues are spending rather less of their time obtaining that flat federal funding than their extramural brethren. But, and that leads me back to a question that we, at the end of the Blue Ribbon Report that we raised somewhat delicately and it's not one that you can really, well, I don't know how you'd like to address it, but of course a particular vulnerability for the intramural program at NHGRI, and now seeing the new numbers, I would, you know, back at the envelope suggests that you're now approaching 21% of NHGRI's budget. And that compares with what I understand to be generally speaking about a 13% perhaps on average across the other intramural programs. And we also highlighted the strong contrast as much as we loved it and supported it, the extraordinarily investigator driven nature of the intramural program stands in such stark contrast to the relatively top down nature, strongly top down nature of the extramural program at NHGRI. And so if you juxtapose those two things, is this actually a question that's floating across the campus, one that you have to answer to? I'd just be curious to your take on that 21% question. Well, certainly it's a question that I've had to think about ever since I started as scientific director and certainly we are, if not at the top, close to the top in terms of percentages of the total institute budget that's dedicated to the intramural program. So in terms of my own take on this, certainly I think that it's absolutely critical for us to justify ourselves through the excellence of what we do. And that probably beyond anything else is probably the most important justification for whatever level of funding the intramural program has. I think that one can talk about the long-term, high-risk, high-reward kinds of things, and those certainly are good, but as was noted, it is hard to in practice implement that across the whole intramural program. So I think that excellence, at least to me, is the most important aspect of all this. Certainly with regard to the overall percentage that the NHGRI intramural program is of the total, we are very aware of that, and I think that at least in conversations that Eric and I have had about this, we recognize that it certainly can go no higher than that and that with time, perhaps if the overall NIH budget starts to go up a little bit, that it would adjust downwards as a percentage if the intramural program were kept relatively fixed while the rest of the institute was allowed to expand. As far as the, across the NIH campus component to your question for sure, that is something that is part of the discussion, it's part of the discussion in Michael and Francis's 10-year plan is thinking about what is the right size for the intramural program and if it is to change how to get there in a reasonable way. Eric, you may want to- I have a couple of comments. I mean, first thing I would say is the direct answer to your question, David, is no. It really hasn't been asked of us very much. I mean, we've not, or else not to me, directly not that I've heard. So we've not gotten that criticism or there not have been cries for us to decrease it. If anything, I would point out that if anything, our intramural program is increasingly asked to do more and more in the intramural program because of the desire to grow genomics and especially medical application of genomics in the clinical center. So I think there's, if anything, I've only heard a cry that only we could do more, that would be better for the enterprise. So that said, it's something we keep an eye on. I mean, we talked about this at multiple levels when the blue ribbon panel report came through, both to this council, to our Board of Scientific Counselors. It is no question it's something very visible. It's why we keep a very close eye on these reviews. I mean, a fourth of our investigators are rigorously reviewed once a year because they get it every four years and you can see they're doing really quite well and if that trend would change, we might look at things a little bit differently. So, and there's a lot of reasons why I still feel comfortable. I don't think the program legitimately should grow or could grow. There's really no resources to allow it to grow at least as a percentage, but I don't have strong reasons to think it shouldn't be the current size that it is. Howard? Just curious whether you use the five categories from the 2001 strategic plan as ways of looking at your portfolio and if so, how are you doing in each of those five bins? Well, we do look at it at least to some extent and certainly given the resources that we have for doing clinical investigations, as I was mentioning, we really are skewing more towards the biology of human disease and the science of medicine categories there, which is a little bit to the right of at least where the overall heat map is supposed to be at the present time. Of course, if you go back, if you go back before that strategic plan, the difference between intramural and extramural was striking. I mean, it was very little, very little, especially in the more clinically oriented domains going on extramurally and a lot of that was going on. Again, because the clinical center, the nature of it. So, but I think if you actually look at it now, I think they're overlapping much more than previously. Any other questions for Dan? Okay, thank you, Dan. Pleasure. All right, you've earned lunch. So I think most of you know the drill, it's one floor up. Please be back. We're a little behind schedule. Please be back no later than 1.30. Let's start promptly then.


Hello, this is Damir Samiric and I'm commenting on life under corona in Bosnia and Herzegovina. Now since Bosnia and Herzegovina after the Dayton Peace Agreement is really chopped up administratively, it's very difficult to get a clear sense of what's going on but what people are commenting on mainly is that with the natural catastrophe that was announced and proclaimed there is only prohibition on the freedom of movement happening with very little support for the population. There is very few data on available tests and how testing are done. What gives us actually courage in this situation which is very reminiscent of the wartime and many people are commenting about fears and anxieties that are returning of the wartime is that what gives courage are the doctors, the nurses, the cleaners and actually all those who amidst all of this provide the food, treat us and keep us safe. What has been proven is that actually nepotism is lethal, that the incompetence of ethnic elites endangers us all. For small bribes they're willing to sacrifice a lot and the political civility as opposed to expertise is a hazard and now more than ever do we need to actually kind of come together as a society to remember when we look back that what managed to get us through was us coming together and being much kinder to each other and people organise individually to help the elderly, the sick, those who don't have anybody and that is the lesson that we learned during the war and during the floods in 2014 that the elites who are in charge have squandered all the reserves, that there are no reserves, there is no proper structure in place and that's you know people are just having to rely on themselves and actually that's not a bad thing after all but after all of this I think everybody's feeling there is a lot of anger and that some sort of reckoning will have to take place and what we will learn possibly out of this is that what we value the doctors, the nurses, the cleaners, the police officers will have to be re-evaluated and people are asking so why in the time of crisis socialism and the idea of welfare state comes back only then


For anybody that's been low carb as long as we have been we've noticed a weird trend that's happening in the last year or so. Hey there, NJRoot22.com here with another low carb keto carnivore chat. Chat. I like saying chat because it's I'm only chatting to myself here. Anyway, I've noticed a weird trend especially in videos and like influencer videos over the last six to 12 months. And that's about people that are like, you know, fitness gurus and they're all in good shape and so on. And they're talking about, you know, eating sugar is not bad. And there's this weird thing. There's something going on here. They're trying to coerce or convince or tell people that eating sugar and raising your blood sugar level and insulin and all this is not so bad. And I guess in depending on your lifestyle, eating sugar is probably not as detrimental as it is if you're not like a high activity person. If you're a sedentary person, eating sugar is just plain bad 100% of the time. And I suspect a lot of these fitness gurus who are mostly millennial and under 30 years old and they're in that phase of their life where they can almost do anything and not have any physical detriment, you know, like gaining weight and so on. If you're working out six days a week and burning, you know, tens of thousands of calories, lifting weights and doing cardio and crossfit and whatever it may be mountain biking, you have a lot more. It's a combination of being extra fit and young. You have so much forgiveness in terms of your physical appearance. You may look, you may have the abs, you may have the muscles and so on. But putting sugar in your body, in our opinion, long term, even when you're young is just setting you up for disaster when you're older. And a lot of people might not care.  I'll just adjust my lifestyle when I'm older. No, eating sugar is truly, there was a, there's a website I read called, I think the Sugar Summit or whatever, they say a lifetime of eating or eating sugar in general is worse than a lifetime of smoking cigarettes. And it's just not good for you.  When you put sugar in your body and your insulin level goes up and down. So I'm just wondering, excuse me, why, why is this new trend of people like, like saying sugar is not so bad? It's either two things. They're either just so blinded by the fact that they're in good shape and they can eat sugar and not get, you know, obese or fall into a bad trap. Or they're probably, there's a good chance that they're getting paid or coerced. You know, a lot of people are easily coerced by money. You know, if you just set them up to, if they're a big influencer and say they have million followers on certain social media channels and they're coerced to, to spread a bad message. And there's a lot of people out there, a lot of companies, entities, businesses that benefit from you being unhealthy.  Who benefits from sick people? Just find, find that dotted line and go down that rabbit hole and you'll see who would benefit from people being sick, unhealthy and in need of medical care and pills and, and so on and so forth. So you have to really wonder, and I would feel bad if these, these healthy kids who are promoting, you know, don't, don't worry about sugar or carbs and maybe they're, they're being taken and they, and they're just uneducated. I would feel really bad if they, they were spreading bad information, not knowing. And I would feel even worse, I would feel actually angry if they did it knowing, knowingly that I, I'm on the side that they, they're just dumb. I mean, any, any kid that's 25 years old and has a six pack abs and feels great, everybody feels great at 25. Even when you're, you know, doing shots and eating pizza. So I guess the more important thing is the long-term aspect of eating healthy and eating sugar is your worst decision you would ever make.  So if you like my little video here, please hit the subscribe and the bell and all that other stuff and look at my other channels, please. We've done, been doing this for several years now and we would like to get our subscriber count up. So thank you very much and I appreciate you watching.


Assalamu alaikum, Bismillahirrahmanirrahim, Asalaamu alaikum, Asalaamu alaikum wa rahmatullahi wa rahmatullahi wa sahbih, Just a few words insha'Allah to Allah and then we'll pray it for a week insha'Allah to Allah. Just being in prayer and being filled with incredible gratitude to Allah Subhanahu wa Ta'ala for being in the Masjid, the Masajid, or the most beloved places to Allah Subhanahu wa Ta'ala to be with the company of the righteous, many of my teachers, many of my beloved ones. This is a tremendous ni'mah and sometimes we don't stop and think about these ni'mah. Allah SWT tells us in the Qur'an that if you were to even try to enumerate the blessing of Allah SWT, one blessing of Allah SWT, you would not be able to do so. And above that, I mean, we're listening to the beautiful recitation of Qari Amr, may Allah SWT preserve him, the story of Musa A.S. and it reminded me of something I read in a book called The Lives of Man by Imam Abdullah ibn Ali al-Haddad, Rahim Allah SWT, in which he said that, he said on the authority of Ibn Abbas, may Allah SWT, he said the Prophet Muhammad SAW, he once came to a group of Sahaba and he said to them, what do you say about this ayah? That you were not at the side of Mount Sinai when we called out and the Sahaba said, Allah SWT, Allah in his messenger, no best. And then the Prophet SAW, he said, this was when Allah SWT, he revealed the alwah, the tablets to Musa A.S. and he described the Ummah of the Prophet Muhammad SAW in the alwah and Musa A.S. was so absolutely mesmerized by what he was reading that he requested to Allah SWT, oh Allah, make this my Ummah, make the Ummah of Ahmad SAW my Ummah and Allah SWT said to him, no, your Ummah is many Israel and then Allah SWT continued to describe the virtues of this Ummah in the scripture of Ahlul Kitab and there are many, many descriptions of the Prophet Muhammad SAW to this day in their books and Musa A.S. he was so smitten by what he was reading and at one point according to the Hadith, Musa A.S. said to Allah SWT, oh Allah, make me a man of that Ummah just a believer, a Muslim in the Ummah of Ahmad SAW Musa A.S. wanted to become just one of us we were the envy, good envy, this is a good envy we were the envy of prophets this is the ni'mah that Allah SWT has given us and then Allah SWT said to Musa A.S. he said, no, your Ummah is many Israel but you can hear their voice if you wish you can hear the voice of this great Ummah and Musa A.S. he said, I wish to hear their voice and then Allah SWT said, oh Ummah of Ahmad, in all of us, all of us, we said, Allah bake, Allah bake at your service and Allah SWT said, praise me and we said, Subhanallah and Allah SWT said, give me praise and we said, Alhamdulillah, La ilaha illa Allah and Musa A.S. heard our praise, heard our tasbih and our tahmeed and our tahleed he heard us say, Subhanallah and Alhamdulillah, La ilaha illa Allah and the Prophet SAW said, this is the meaning that you are not at the side of Sinai when we called out, when we called out to the Ummah of the Prophet SAW and Musa A.S. heard our voice this is a tremendous ni'mah we have to think about these things may Allah SWT increase us in this beautiful virtue, it's called a theological virtue Imam Al Ghazali and Rahim Allah Ta'ala he enumerates 19 theological virtues and towards the top of the list is Shukr gratitude to Allah SWT this is the epitome of the Akhlaq Nabawiyah the Prophet SAW when he is praying all night long and his feet were swollen red or his heels were cracking and his beloved wife, our mother Aisha she said, why do you do this Allah SWT has forgiven your past and future transgressions and the transgression of a prophet is completely different than our transgression a transgression of a prophet is leaving his master virtue but he's always virtuous what was his response what was his response shall I not be a grateful servant shall I not be a grateful servant he was Shakurah which is different than the Shakir the Shakir is the one who praises Allah in times of prosperity but the Shakur is the one who continues to praise Allah SWT whether in prosperity or in times of deprivation Allah SWT because he knows, he has the wisdom that Allah SWT if someone is asking Allah SWT for something and he doesn't get it the wise person knows that Allah SWT is insha'Allah he is taking something possibly dangerous or harmful away from me I don't deserve this thing, it's not good for me and he continues to praise Allah SWT this takes spiritual majority Allah SWT increases in Shakur to him peace be upon you


I want to summarize the past 60 years of molecular biology, a very new science and illustrate the growing importance of this science in society and an example of its translation to treat disease. Recall that molecular biology had its origins in the discovery of structure of DNA by Watson and Crick in 1953. For the first time, mankind understood the chemical basis of inheritance, of all life forms, including himself. Three decades later, the science advanced with the ability to synthesize sequence and recombine DNA, creating synthetic biology. In the mid-70s, a number of biotech companies were started to translate this science into the society and treatment of disease. One of these was Biogen, organized in 1978, and the first to open a laboratory near MIT. Biotech has generated new treatment for previously untreatable diseases, hundreds of thousands of new jobs, small and large biotech companies in blue, are now clustered around MIT in yellow, creating a unique biotech innovation cluster in Cambridge, Massachusetts. Through the 90s, molecular biology advanced through the genomic revolution, with completion of the human genome sequence in 2003, 50 years after the discovery of Watson and Crick. This has revealed the genetic basis of many diseases and is leading biotechnology forward. Further, the decreasing cost of DNA sequencing is allowing determination of the genetic makeup of all life forms, microorganisms, the plant kingdom. This vast body of information will drive science and molecular biology and biotech rapidly forward. The rate of this decrease is faster than that of Moore's law, which drove the IT revolution over the last 50 years. Molecular biology, cell biology with engineering, computational science, physical science will be necessary to take advantage of all this molecular biology and genomic information. The new Koch Institute at MIT is a convergent institute. As you've heard from two engineers working there, there's 12 engineers and 12 biologists in this institute. Examples of convergent science in the Koch is the inclusion of nanotechnology in the study and treatment of cancer, the creation of small devices to monitor body fluids, and new sensors to image normal and disease processes. The Koch is only part of the convergent movement at MIT. Today, more than a third of all MIT engineers are involved in life science. In addition, mathematicians, computer science, physicists, ecologists are all addressing fundamental problems in molecular biology using genomic information and convergent-type technology and thinking. As an example of convergent science, I will briefly summarize the translation of a Nobel Prize, the discovery of RNA interference by Andy Farr and Craig Mellow, and Andy was a graduate student at MIT. They discovered in 1998 that double-strand RNA from a gene would silence a gene when introduced into cells. Including S-I-R-N-A as shown here, knowing the sequence of a disease-causing gene would translate directly into treatment, a radical advance in medical science. The gene-to-disease relationship is similar to the current treatment therapies where oral drugs intercells to inhibit a gene protein, and antibodies bind to proteins on the surface of a cell to either activate the cell or kill the cell. Both gene-specific approaches. Thirteen years of convergent research has shown that linking this small RNA to a complex sugar that binds to the receptor on the surface of a human liver cell will facilitate the small RNA to transport into the cell and yield silencing of a disease gene. Knowing this delivery technology is shown here, it is now possible to give a patient one injection, sub-Q, and silence the activity of a disease gene for five months. Thus, the convergence of molecular biology, chemistry, engineering, clinical science has led to the innovation of a whole new class of drugs, small RNAs, that if you know the structure of a gene, you can design a drug almost directly from it. You can design medicine at the bench, and therefore convergent science is an increasingly important part of our future in biomedical science. And my question for you is if you have this tool of being able to silence a gene by designing a small RNA, what diseases would you apply it to?


As we raise the flag today for the very first time on this building, we celebrate the history, progress, and resilience of the Black community. We reflect on Juneteenth as a profound, significant day in the lives of the former enslaved Black Americans. This day has emerged as a day of Black freedom, Black liberation, and Black resilience. Let us celebrate the progress that has been made in the Black community and let us embrace the opportunities that we have to flourish. We celebrate Juneteenth as a day in history that we triumph over oppression. Juneteenth is American history.


So, we were talking about dimension and I had introduced finite morphisms which we wanted to use to study dimension. So if I, this was first finite morphisms were morphisms of a fine variety. So if x and y are fine varieties and f from x to y is finite is defined to be finite if and only if the, if I take the pull back. So the coordinate ring of x is a finite. So f star of a of y algebra. And I had introduced what this means. So it means that, so if f a and b k algebras then, so one is a sub-algebra of the other then we say that b is a finite as an a algebra if, well it's the analog of a finite dimensional vector space over a. So if there exist some elements finite in many b1 to be n in b such that b can be written as linear combinations of these elements with coefficients in a, we had given some characterizations of that. If b over, or some property, so if c over b is finite and b over a is finite and c over a is finite and we had some similar results and we had seen that being finite also has something to do with, so if, so one result that we had that if b over a is finite then every element of b satisfies a monic equation with coefficients, so it's a zero of a monic equation with coefficients in a. And so, yeah maybe that is, and then we finally, then we had come back to, now that we had studied this we had then come back to this definition and we had proven that finite morphisms are closed. So now we want to go forward, so maybe I, we want to, we want to study these finite morphisms to somehow study dimension, so it's somehow important that we have enough finite morphisms and so that we, for instance if we want a n to have dimension n, we will prove that in a moment and then we want to use this to compute the dimension of any variety, so if we can use finite morphisms to compare the dimensions then it would be good if we know that every, say a fine variety has a finite morphism to some a n and that's actually what is called the neutral normalization theorem, so that we can compare, so up to a finite, so there's always a finite morphism from any a fine variety to some a n, so let's, this is, and this will be a very important tool for us, so we have a theorem which is the neutral normalization theorem, so we prove a little bit more, so let z f in a n is a hypersurface, so f is a polynomial in x1 to xn, maybe irreducible, then there exists a finite subjective morphism from z of f to a n minus 1. Okay, so if later we prove that finite subjective morphisms preserve dimension and then this will hopefully show that the dimension of hypersurface in a n is the same as the dimension of a n minus 1 and that will maybe help us to show that the dimension of a n minus 1 also is n minus 1, we'll see that later today, so and more generally if x is in a fine variety, so then there exists a finite subjective morphism from say p from maybe also called p, p from x to ak for some k. Okay, so we want to prove that, it requires some work, first we will prove some very simple remark which we'll use in the proof of the first part, which is so obvious that maybe we don't even need to prove it, but anyway, so let f be a non-zero polynomial x1 to xn and so then, well then there exists a point p in a n with f of p different from 0. Now in some sense that's pretty obvious, but I still want to prove it because it actually does even take a little bit of effort. So if n is equal to 0, this is obvious because in that case we just, this is just a constant, the constant either 0 or not. Now if n is equal to 1, then we are over an algebraically closed field, so we can write f of x equal to x minus b1 to the n1, x minus say bl to the nl where the bi are some elements in k and the ni are positive and you just factors into linear polynomials because k is algebraically closed. So thus the zero set of f just consists of these points b1 to bl and so we take any point b in k without b1 to bl then f of b is different from 0. And why can we do this? S k is algebraically closed it's infinite, k is infinite because an algebraically closed field will always be infinite and so certainly if we take away these finally many points there will be still some. So now comes the actual dry one, what? Now comes the case n is greater than 1, here I assumed n is equal to 1 because the proof was in dimension 1, now we look at the general case n is bigger than 1. Now n, so it is somehow induction on n but we also we need the case n equal 1 in the induction, so that's why it's a bit strange.  And we assume that f is not 0 so that means that not all the f i are 0. So there is an i there's a j such that fj is not 0. I mean as a polynomial it's not 0. So by induction on n we find that there is some tuple of you know b1 to bn minus 1 such that I put it into this fj it will be known 0 such that fj of b1 to bn minus 1 is different from 0. So then we can make a new polynomial we just take g of a variable x is just defined to be f of b1 to bn minus 1 comma x. So this is not the zero polynomial because you know after all there is one coefficient which is non-zero. So this is in kx without zero it's a non-zero polynomial and so it has a zero it has a it has a there's a point where it's not zero so so thus there exists b in k such that g of b is different from 0 that is f of b1 to bn minus 1 comma b is different from 0 b. Okay so it was in the end not so difficult but anyway so we have found always a point where it's non-zero. So now we come to the actual we start with the actual proof so we will just go about and start with number one. So we want to prove that this is finite subjective morphism so we have our polynomial f so we take the top degree homogeneous part of f so the it's a big f so we notice some decomposition into homogeneous components we take the one of highest degree so this will be some non-zero polynomial so this is so this is in particular f of t is in particular homogeneous so if we put the last variable xn to b1 it will not be the zero polynomial you know if you just look at it if you put take homogeneous polynomial put one variable equal to one you have precisely as many terms as before no terms cancel so if the polynomial was not zero before it's not zero afterwards you know you can get back the previous polynomial by just homogenizing so this is not zero so in particular we can use this stupid remark so thus there exists say b1 to bn minus 1 in you know a n minus 1 such that if I take fd of b1 to bn minus 1 comma 1 this is different from zero okay so this is what this stupid remark was useful for now we can change the coordinates on our an we just shift everything you know all the coordinates the first coordinate we replace x1 by x1 minus b1 x2 by x2 minus b2 and so on so by shifting the coordinates we can assume that b1 to be n minus 1 is actually zero no so by a change of coordinates assume that fd zero zero one is different from zero now when we so the f that we use to for this hyper surface is well defined only up to multiplying by non-zero constant you know the zero set does not change if we multiply by non-zero constant so this is some non-zero number we can as well assume that this number is one so by multiplying f by a constant can assume fd is equal to one but what does it mean it just means that so if you have a polynomial a homogenous polynomial in in these variables x1 for xd so these are all the monomers have degree d so there's only one monomial of degree d which will give you one if you put only the the nth variable equal to one all the other ones equal to zero all the ones that once give you zero so this statement just means equivalently that the coefficient of xn to the d in either fd or in f is one okay so this is what we and you know this should make you think of what we had about these these finite maps there was something that in algebra is finite over another one so if you if you add an element which satisfies a monic polynomial to some algebra then the extension is finite so here we it looks like we might get there let's see how it works so so let now we take this projection p from say zf so p as a projection we just take projection to the first given by the first n minus one coordinates so we just you know take the first n minus one coordinates of every point and we let say w n in the coordinate ring of zf to be the class of the last variable so so then I claim that so maybe I claim that a of zf will be the pullback of k x1 to xn minus one a joint omega n I mean the extension the k algebra extension like this because after all you know the the a of zf is just a quotient of k x1 to xn by the ideal of this thing so it's generated by the classes of x1 to xn so the the pullback just pulls back the class of x i the x i you know on the n minus one to the class of x i in here so this is okay and the the last one the xn is pulled back to this one so it's really the we find that the coordinate ring of zf is just this no because this says nothing else than it is the ring generated by the classes in eight set zf of the xi but now we see that this omega n satisfies a monic equation so so we know that the coefficient of xn to the d and f is one so f is equal to x n to the d plus sum i equals one to d minus one ai xn to the i where the ai are some polynomials in k x1 to the xn minus one no that's just what it says that they really let the coefficient is this but what does it mean if we now you know the in zf we just take maybe i want to still keep the statement so so we have that a of zf is equal to k x1 to xn divided by ideal generated by f so we have in thus in a of zf we have a relation that f is zero the class of f is zero and a of zf so that zero is equal to omega n no wn to the d plus sum i equals one to d minus one well the pullback of the ai times omega n to the i so we have a monic equation so this implies so we have precise the statement that this thing is obtained from this by adding an element which satisfies the monic equation and we had a lemma which said that under these assumptions under these if one has this then this one is finite over this that is pi from zf to a n minus one is finite okay so we have found that indeed we have a finite map like this so now we come now surprisingly the ah we are not finished because we are supposed to show that it's a finite surjective morphism okay so we have to see why this map is surjective but that's kind of easy so show that pi is surjective so we take a point we want to be n minus one in n minus one we have to show that the fiber of it is non-empty so you know to see it's not empty so we put it's kind of similar to what we had before we put say g to be the polynomial where we so we take f and we replace the first coordinates by these so g of x so some polynomial and we know so we know that the coefficient of x to the xn to the d of f is is one so that implies that this polynomial is not zero because it's not affected by okay so the coefficient of x to the x to the d of this polynomial is one so and is well is not zero and actually it's non-constant because the coefficient as a set of x to the d is non-zero so therefore g has a zero say b in k well and then obviously if this has a zero then this is a zero of this thing so we have a thus we have that the inverse image of this point this was b so we call it a so the inverse image of no we have a point we have to show you know it's surjective so we have to show for every point the inverse image is non-zero but it was certainly not written very prettily so so this inverse image prior to the minus one of b is just a set of all b1 to the n minus 1 comma c such that f of b1 to the n minus 1 c is equal to zero which is nothing else then you know this b times the zero set of g which is non-empty okay so the map is indeed surjective so a finite surjective map here and now the surprising thing is that we have done most of the work now we kind of do some basically reduce the the main statement to this is it clear you well I said you know actually it has a zero it has it might have many zeros no no so I know it has a zero so z of g is non-empty and then this will be non-empty but in particular it contains if you want if it contains the point b times a okay now we come to the second part so so if say x is just equal to an then you know it has a the identity is finite then it's clear so assume it's not equal to an so assume that so assume x is in an is a closed up variety and okay so and we want to prove that we want to prove it by induction on a x should be non-empty obviously because otherwise the statement would also be for be false but okay so let's see so we want to somehow use use this case so you know x is not equal to an so it will be there will be some f in the ideal of x so so let f be an element in the ideal of x without zero so it may be equal to assume irreducible so if all right you know as f is as x is not equal to an it follows that the ideal of x does not consist just of zero so there is an f there and we can then also assume it's irreducible because ix is a prime ideal so whenever we write f as a product of two factors one of the two factors must be in the ideal of x okay so we can apply the first part so there exists a finite subjective morphism say now here it's also called pi whatever maybe what i call pi from the zero set of f to an minus one and we know that x is contained in the zero set of f is closed we know that the embedding of a closed subset into something into of a closed sub variety into a variety is a finite map so the map the the embedding of x into the f is finite so thus if i take say pi tilde which is equal to pi composed with i from x to n minus one this is a finite morphism so we have a finite morphism from x to n minus one but obviously there's no reason to assume it's subjective i mean the point is we can we want to be able to find once possibly smaller k such that the map becomes subjective because you know by definition of finite so to be finite we need that what is it if we look at the map x to y this will be finite if a x is a finite f upper star of a y module or something is finite over this okay and now if the map is injective then it turns out that the pullback is surjective that's actually a homework exercise and so therefore you know if they are equal certainly one is finite over the other and then the composition of finite morphisms is finite so this is finite so where am i so this is not necessarily finite but we can look at the image where we now we can use the induction hypothesis y lies in a n minus one by induction on n we know that there's a finite morphism from y to some ak okay how would i would call it finite morphism finite subjective morphism so phi from y to ak for some k now this thing is a finite morphism as a map from x to a n minus one but actually maps to y so then we know that if we viewed as a map to its image it's also finite morphism so that was one of the things we proved so we have that pi tilde from x to y is finite and so if i put now maybe this should have if i not now put the thing that we are talking about to be um phi composed with pi tilde this is a map from x to ak this is certainly finite as a composition of finite maps and it's also subjective as a composition of subjective maps because this map you know this map was just uh you know if we have restricted here on this side to the image so by definition it's finite and the other is subjective and we also have um we have a finite subjective morphism here so n subjective and so that proves it okay so this is this Neuter normalization theorem so we want to prove so we will see uh in a moment how one can apply this for instance to prove that the dimension of a n is equal to n if we find the time before that i want to show one more kind of topological property of finite morphisms that is you have the statement that if you have a finite morphism and you have a sub to have two sub varieties two irreducible closed subsets in the source which are one strictly you know one contained in the other but strictly contained they are not equal then the same holds in the image it's not it cannot happen that if you have two sub varieties one contained in the other which are not equal that they become equal by mapping with the finite map and this will in particular imply that the fibers of a finite morphism are finite which is you know a good reason to call it finite okay so let's see that so lemma let say phi from x to y be a finite subjective morphism so let so z strictly contained in w we close sub varieties of x then I have that the image of z is strictly contained in the image of w so you don't have the two things become equal if they were not equal to before so somehow things cannot be contracted so first we can so we can restrict the map phi to w no so therefore we can assume that x is equal to w and we can in the target we can restrict the map to the image of w it still is a finite map if it was one before so we can assume that y is equal to f of w okay so this simply this simplifies a little bit so in other words we the statement would be that so in other words so if so if z is strictly contained in x then f of z is strictly contained in y so where z in x is a close sub variety so I always use variety so this only makes sense if things are irreducible okay so we have this tiny simplification so now we want we have to check this so we have that z is strictly contained in x so there will be so this was actually I changed it from phi to f but now I may be so we take there's no f you know here it was called phi and here it can move fast itself as an f but it's still a phi so let g be an element in the x which is not zero such that g restricted to z is zero that means that g is in the ideal of z in in ax and you know we know that if z is not equal to ax it's a close sub variety there will be some function which vanishes on it no that's one of the things we always know so we take such a thing we really want to finally use the finiteness whatever to show that then there will be something similar in the image so now we again we have to use the finiteness and we again use this by having this thing with a monic polynomial so this g will satisfy monic polynomial over ay so g satisfies a monic equation say g to the n plus sum i equals zero to n minus one say phi star of ai times g to the i is equal to zero no where the ai are elements in a of y no that's what the finiteness tells us so what do we so now if we have such a monic equation we can assume that the degree is as small as possible so there might be more than one monic equation which is satisfied we take the one with the smallest possible degree so if this is the case in particular it cannot be true that the whole thing is divisible by g so the coefficient of g to the zero must be non-zero because otherwise we could just divide the thing by g so we have phi star of a zero is non-zero so it follows that phi star of a zero it's different from zero no otherwise divide by g and we get a monic equation of smaller degree because g is after all non-zero we can certainly divide by it okay so but now we can bring this thing to the other side so it means that phi star of a zero if we bring it now to the other side so this is non-zero this we just if we take it out we can divide by g and so if i'm not mistaken this is just equal to minus g times g to the n minus one plus sum i equals one to n minus one phi star of a i g to the i minus one so we have just you know brought you know this phi star of c zero to the other side and then we obviously can divide by g and so we get this but you know we see that this thing is divisible by g so if this thing is divisible by g it means that it vanishes on that because g vanishes on that but if you know phi star is just obtained by taking a zero composed with phi if a zero composed with phi vanishes on that it means that a zero vanishes on phi of that but so what would have we found we have found a non-zero element in so this is a non-zero element a zero is a non-zero element in ay which vanishes on phi of of z so it means that phi of z is not equal to y and that proves it so we somehow so we find just that the constant coefficient of this thing must vanish on the image so the thing is not equal to okay and now as a corollary we get the thing that I mentioned so if say again phi from x to y is a finite subjective morphism then all the fibers of phi are finite are finite okay this is quite simple it follows basically directly from the statement here so you know that the fibers are finite is equivalent to the statement that every irreducible component of a fiber is a point you know because you know you know in algebraic set has finitely many irreducible components and if each of them is a point then it's finitely many points okay so it's enough to show so every irreducible component of say phi to the minus one of y where y is a point in y is a point well that's very similar it's very simple so I call this component maybe large z so we take a point small z in large z then obviously the image of the small z is y which is the same as the image of the large z if you want you can also put brackets around to make it into a set so by the statement if they're equal if the images are equal the things you started with are equal that's all okay so this was the whole story okay so that was as much as I wanted to do for now about finite morphisms and now we want to apply it to study dimension so I maybe should recall so I should recall the definition of dimension so so if x is a variety then so if I have a chain that empty set different from x0 contained in x1 and so on until xn the chain of irreducible closed subsets in x so we just call this a chain in x and n we would call the length of the chain in safety speaking they're n plus one elements but we call the length n okay so then so actually I call this not call I will write just x0 x1 and so on until xn the chain in x and n will be its length and then the dimension of x is it's not precisely correct in the notes so it's called the dimension of x so this will be either the maximum the maximal n that's such a such that we have a chain in x if such a maximum exists and infinity otherwise so if one you know in in analysis want to say it's a supremum of the length of the chain now it's a bit strange and that's why I also wrote it slightly incorrectly in the notes that we know that we have it if we have a descending chain of closed subsets it will be finite so in that sense one would think there would be always such a maximum but in theory in Iparora this is not obvious because it could be that every chain is finite but there might be chains of bigger and bigger length for one given set we will see that this is actually not true so we will we will prove that all quasi-projective varieties have a finite dimension but until we prove that we cannot use it in our arguments so we for a while have to pretend we don't know that because we after all don't know it yet yes what in no no no infinite I don't know why I I don't know why I wrote empty set yeah no certainly not zero I mean another question is what kind of dimension you want to this I didn't dwell on what kind of dimension one wants to give the empty set yeah I think the most reasonable thing to say that for the empty set it should be minus one okay that that fits best with with the formulas so and I mean to deal with this infinite for a while we say that obviously infinity is smaller equal to infinity and if n is in z then n is smaller and in particular smaller equal to infinity okay no if we want to write down and so note that so remark so if x well no I mean we don't write I will use it so now let's look at the following lemma so we want to somehow show some basic things about dimension the first one is we would like to so to show that if we have a close sub variety in a variety then its dimension is smaller okay this is however will a priority not be entirely true because we might have some trouble with infinity but apart from that it is so let y so first let y in x be a close sub variety then the dimension of y is smaller equal to that of x and if the inclusion is strict and the dimension of y is not infinite then the dimension of y is strictly smaller than that of x okay later we will prove that all varieties have finer dimensions so that so if we have a strict include this just says that if you have a strict inclusion then dimension of the smaller one is smaller no but for the moment we are not yet there the second statement is let f from x to y be a surjective closed morphism of varieties then the dimension of x is bigger equal to the dimension of y okay so so let if y0 so to say y k is a chain in y then we can then it's also a chain in x and thus the dimension of x is bigger equal to that of y because the fact to prove that the dimension of x is bigger equal to that of y we need that for every chain in y we find one in x which is at least as long and we can just take the same no because it says and this this holds independent of whether some of them is infinite or not so on the other hand so if now but if now y is strictly contained in x we can even get another chain then y0 y1 and so on yk strictly contained in x is a chain in x so that means for every chain in y we can find a chain in x which is longer so if the dimension of y would be infinite this wouldn't really prove anything but if the dimension is finite then you know we take the chain which is you know such that the k is the dimension and we find the dimension of x is larger this is one yeah and second is a bit more it takes slightly more effort but it's not big deal so again so we want to show that the dimension of y if x is bigger equal to that of y so that is we want to find for every chain in y a chain in x which is at least as long that's enough so let say yn be a chain in y so what we want to do is show that there exists a chain in x so x0 strictly contained in x1 and so on in x such that well just if I take f of xn is equal to yn so I mean the fact that f of xn is equal to yn will imply that this is always strict you know because they are different and then we have found a chain of at least the same length as the corresponding chain in y so the dimension of x is bigger equal to that of y okay and so we do it so we use induction on n so anyway if n is equal to to 0 well we can just take inverse image of x0 or something then it's anyway it's easy um anyway we'll see that but now let's we assume otherwise um what yeah yeah so n equals 0 is clear so otherwise so we do induction on n so let z1 so whatever cr be the irreducible components of the inverse image of yn minus 1 so the point is that I mean in theory we could just think we take as the xi the inverse image of the yi but that wouldn't be allowed because we need these things are always irreducible so we have to take irreducible components but you know you know that the union of the xi of the f of xi is equal to yn minus 1 and they are closed and yn minus 1 is irreducible so it follows that one of them must already be equal to to this so thus one of the f of xi is equal so we can just take this thing so then so maybe I so for for some i it's equal to that then for this i we have a chain so so this so that means f of xi so if I take the map now if I take f from xi to uh yn minus 1 this is now a subjective closed morphism and so we do indeed um anyway now we can apply the induction hypothesis and see that there is you know we we are in the situation we just start now with yn minus 1 make induction over n now we have a length of chains so thus by induction there are so we get a chain x0 it's contained in x1 and so on and as xn minus 1 we take this zi is a chain in x with f of xi is equal to yi well okay and then so here I write f xn but I what I meant obviously yeah so I'm sorry but this is not written correctly no I want that f of xi is equal to yi for all i because then it means we really have a chain here okay so now we have this under n minus 1 and then for the last one we just have then you know we have that if we take x0 the last one xn is always x so the last one is is a chain with so f of xi is equal to yi for all i so I mean here we just have taken the previous chain we have left out the last one and now we put the last one back and over definition we have that the map from x to y is a finite subjective morphism okay and now this will allow us to prove not a finite subjective a subjective closed morphism now finally we can use this to prove that finite subjective morphisms preserve the dimension so we see that if we have a closed subjective morphism the dimension of the source is bigger equal to that of the target and finite morphisms are closed and finite subjective morphisms are closed and subjective and so we have to show that also the other inclusion holds so let so this is I call theorem that f from x to y be a finite subjective morphism morphism of varieties then the dimension of x is equal to the dimension of y so we know already that the dimension of x is bigger equal to the dimension of y because f is subjective and closed so we have to show the other inequality the dimension of y is bigger equal to that of x so that is for every chain in x we must find the chain in y which has the same length so let x0 xn be a chain in x so so let for all i let yi to be just the image of xi and the claim is y0 contained y1 to yn is a chain in y which then proves the dimension of y is bigger equal to that of x so the main point is that you have to show that these inequalities are strict no that none of them become equal but this is true that yi is always strictly contained in yi plus 1 because because this is true for the xi and we had proven that finite morphisms preserve strict inclusion of closed sub varieties so indeed the inclusions here are all strict and the yi are irreducible as images of something irreducible so this is indeed a chain in y of length n and so this um proves this yeah now my task which i don't have very much time the next task is indeed to prove that the dimension of an is equal to n so let's see how i can go about this so this is now you want to apply what we know so far to to prove that which then will also prove that at least all the fine varieties have finite dimension so theorem the first statement is the dimension of a n is equal to n somehow obviously that's a very basic thing if this were not true then we would have chosen the wrong definition because obviously it makes no sense to have a notion of dimension which doesn't give the obvious dimension to the obvious thing okay so we will again also compare with hypersurfaces so let f in k x1 to xn be an irreducible polynomial then the dimension of the zero set of f well we want it to be 1 less is n minus 1 so zero f okay so if we take the zero set of one equation it says dimension one less and the third one which is rather simple conversely any sub variety x in a n of dimension n minus one is a hypersurface so if i have a sub variety of the n which has dimension n minus one it's a zero of one polynomial well because okay you see well i will just start so first i do something which i call implication of one to two but we will actually also need it in the proof of part one which is that we which is which will be the statement that we want to prove that the dimension of a hypersurface is the same as the dimension of a n minus one okay which one are equivalent no these are not these are things that we prove three statements there's nothing to do with the equivalent no we prove that dimension of a n is n we prove that yeah yeah but at the point is just i shouldn't maybe call it like that you know we want to prove all these statements and you know we we will prove something that once we have proven one we'll prove two okay but it's a bit more tricky because in the proof of one we will use this statement okay so what i really mean is just so we first so so first proof that the dimension of a zero set of f of such a polynomial is equal to the dimension of a n minus one okay so once we have proven one this will prove two but you know first we have to prove one so why is that so this is quite simple so let f be a non-zero polynomial then there exists a finite subjective morphism from the zero set of f to a n minus one this was the Newton normalization theorem so thus it follows that the dimension of that f is equal to the dimension of a n minus one maybe i don't call it one implies two this is what we use but it means that now we don't have to prove two anymore once you once we prove one two is automatic no non-constant otherwise not you know if it's constant it will be empty and then you know hypersurface you always need that that it's not constant so so we can now we want to prove one which is the main step and we cannot maybe quite do it now but i can prove at least the trivial direction so let say i take z i to be the zero set of say you know f x i have the variables are called x i so x i plus one until x n in a n so for instance x z zero z zero will be just the zero set of all the variables so it will be the point zero and z n will be this there will be nothing here this will be a n so so then z i is isomorphic to a to the i and thus so in particular it's irreducible and thus we have that z zero strictly contained in z one strictly contained in z two and so on is a chain in a n of length n so it follows that the dimension of a n is bigger equal to n well maybe now we'll try even the converse direction is not very long it's only slightly surprising so we want to prove the opposite inequality no so i mean if i put here from x n so it's maybe you don't like the notation but it's you know it's like you would do if you write a sum in in a program or something you know it's going up from this to this so if this one is bigger than this there's nothing so so x x n minus one would be z of x n and z and so i mean anyway z n is supposed to be just zero set of nothing yeah and then z n minus one is z of x n z n minus two z of x n minus one x n and so on i mean this is if ever you have written a a program in which there are sums you will notice that you are allowed to do it that way if the lower index is bigger than the upper index then the sum is empty and the same here okay so we prove the opposite inequality so by induction on n it's always induction so for n equal to zero it is trivial because a zero is a point and it certainly has dimension zero we can only find the choice a chain of length zero so now let x zero strictly contained in x one and so on say x k minus one which we call x strictly contained in a n be a chain in n power we don't know what this number k is that we want to find out you want to find out that this number would have to be smaller equal to n minus one anyway now so we know that then obviously x in strictly contained in n minus one is a closed subset closed sub variety so the ideal of x will be non-empty so i can find the polynomial f which is non-zero which lies in the ideal of x so let f in the ideal of x be irreducible so first i can find a non-zero element and then i can maybe write it if it's not irreducible right and it's written as a product of two factors then one of the two factors must lie in this prime ideal so i can find an irreducible element as i used it before so then x is contained in the zero set of f now we somehow have to use the part i mean the part two know if thus you know the dimension of x is smaller equal than that of the zero set of f so um it follows that k minus one is smaller equal to the dimension of the zero set of f which is equal to the dimension of a n minus one you know but we um which is a small let me try again um you know we had found that the dimension of the zero set of f is equal to the dimension of a n minus one no that was what we had said that is what's written here okay so i'm just using this and this is equal to n minus one by induction okay so this makes induction quite powerful because we may we assume that the dimension of a n minus one is n minus one by induction okay so now um so this is f such so thus so we have that so k plus one k minus one is equal to n minus one thus the dimension so for any chain in x you know the length of the chain the length of the chain is actually equal to k the length of the chain is at most k so the dimension of the n is smaller equal to k no because we have written any an arbitrary chain and its length is k no k minus one plus one which is equal which is smaller equal to to n and this is what we wanted to prove it's not a contradiction okay okay so um so i will the third part i will prove next time this also will give me occasion to review the statement and then it will be tomorrow yeah so you can you don't have to look forward it for too much time