Please welcome the first violinist conductor of the Harvard Law School's increasingly digital symphony You can be sure he will enlighten us and also that this might be some serious fun the Harry N s professor of law John Paul free Dean Minow, thank you for this honor in every possible way I've Spent a great deal of time trying to think about the history of this place and the school as I've been preparing for today And one of the things that I've come to see more clearly than before is how important what you and Elena Kagan before you are up To with the curricular reform at the Harvard Law School in particular and how excited I am to be part of it And I hope that today we can have a continued conversation in the spirit of your leadership Thank you all for coming. This is incredibly humbling I'm sort of shy about the spectacle, but grateful all the same that you've come What a wonderful group of colleagues and family and friends. I have And it's fun to spend an hour with you now I want to make two. Thank yous first and then on to the substance The first thank you all of those things were indeed embarrassing. They were not at all all about me The co-production I think is the right word And as I look out on this group and recognize where we are here in Langdell Hall I wanted to say a particularly special tribute off the bat to my colleagues in the library community I've always known this is a special special place since I was an undergraduate not that far up the street I was one of those students that would come up to the law school to study. Yes librarians I was one of the ones who did that as you may know, we have to keep undergraduates out of this library It is so wonderful at exam time much to the chagrin of the Dean of the college I hope that one is not here for that purpose But I've always thought of it as a special place Since that time though having my office in this library has made me realize It's not just a place under collection, but what an amazing group of people work here It's an amazing honor to have the chance to work not just at the Harvard Law School about the Harvard Law School Library, this is an anxious time for everyone working in libraries particularly at Harvard as we review our practices I wanted to start out by asking those who do not work in libraries to join me in a round of applause for the library community for all of you And then one other thank you, and I promise I will go on to some substance and this is really for teachers librarians and teachers I think very similarly I've thanked the library community. I want to thank also the Berkman community What I'm going to talk about tonight is really a joiner of these two worlds of library and information and information and technology It's extremely touching to me to see Jonathan Zittrin my first cyber law teacher and Charlie Nesson I suspect you're high banker who I don't see but is here he's back there and all of my friends from the Berkman Center You make this an amazing place to work and to learn and I'm very grateful for that But for every student every lucky student, and I see many of you here There's often one teacher one person in the course of learning about something who? Makes the impossible seem possible for a student There is one person who has done that for me You will not wish to be singled out right now, but I'm going to do it anyway But Terry Fisher you have been an incredible mentor and teacher to me I know you work on what it means to lead a good life and a good society And you have done that in unparalleled ways So I'm deeply grateful for all that you've done and to all students I wish you one fond hope which is the you will find someone as wonderful as Terry in your time while you're here at the Harvard Law School All right on to substance I want to make an argument as a lawyer in favor of a new form of Legal information actually more specifically a structure for legal information, but I want to ground it in a historical trajectory So I'm going to make the case that there have been four previous phases There are historians in the room who will probably tell me I'm oversimplifying the story Dan Cochalette and Charlie Donahue, but if you'll let me just go fast over legal information To get to the present and to the future. I'll then make a proposal in favor of a new system of legal information I will then lay out its merits and demerits, and then I will suggest some implications That may not be positive or negative, but which I think lie ahead. So that's the road map So for those who are not Lawyers or law scholars. I'm going to let you in on a secret that is evident to everybody who is which is The title of this lecture path of legal information is a play on words the very simple play on words There's a great law review article called the path of the law by Oliver Wendell Holmes So you may know a student here and then professor Was on the state Supreme Court here in Massachusetts and then on the US Supreme Court And Holmes gave us many things including this great This great article the path of the law. He also gave us a few things that are here in this room Dean no, it's hidden by Charlie Donahue over there. You may know this little lunchbox. I love that lunchbox It's a metal one if you can't see it over there whenever first years come in here deans like to point out that lunchbox of Oliver Wendell Holmes and Sometimes use the following image that mr. Justice Holmes would walk from his home in DC up to the Supreme Court with that box It's a lovely little image But it turns out in fact if you read a recent biography Written of mr. Justice Holmes. Here's the real story every week day morning at 11 30 when the court was in session Holmes Descended his front steps walked a few paces down I street on Lafayette Square and so forth and then later in the day a gentleman named Craig followed later with Holmes's lunchbox in a metal box It's a slightly different story that each Member of the Supreme Court had someone to bring their hot lunch and Holmes favored it anyway That's not the real gift from Holmes the real gift is this talk this amazing Article on the path of the law where I wanted to start It's usually remembered by law students for the image of the bad man the Clients the bad man who sees the law in an instrumental sense how he can do something and avoid the law Coming down on him, but I want to cite it for a different premise He actually described in many ways the legal information system in this 1897 article Holmes wrote of a body of reports of treatises and of statutes in this country and in England extending back for 600 years And now increasing annually by the hundreds and Holmes then goes on to describe what the job of the lawyer is which is the interpretation of those For the bad man and then he writes This is the key part for the most important and pretty nearly the whole meaning of every new effort of legal thought is to make these Prophecies more precise the prophecies on behalf of your client and to generalize them into a thoroughly connected system So I want to argue for is a new thoroughly connected system of legal information in a digital plus era Not entirely digital but predominantly so and which builds on the historical growth of legal information over time So like any good story it starts in the 12th century This is the thanks to Charlie Donahue who preclude me in that King Henry II was the key to this early period This was the time at which in his court legal matters were redacted written down and Recorded for posterity within the court of a single King Fast-forward then a few hundred years This is even further than a few hundred years to have Mr. S. Mr. Henry NS The man who's being honored today with this chair Mr. S. Was a great collector of the second period it starts in the late 15th century And printing of course is the main innovation where things like Littleton's tenures are printed in the 16th century and pass around first as a manuscript then as a printed work All of a sudden the legal information could be accessed by a large number more people You have during the same period of mr. S's Collection the works of coke you can see this enigmatic quote up here. That's sir Edward coke He wrote a famous book which was coke on Littleton But you get the point which is all of a sudden the law is described by scholars in a systemic way and printed and shared Now just a note on the point of access to knowledge It would take some people a year's worth of money to buy one of these books So it wasn't exactly broadly distributed But important that it was accessed and we now have many of these things actually in a wonderful collection during the cocktail time Thanks to Mary person and Dave Warrington. The s collection has been put out on display, which is very exciting Fast-forward to the third phase in the end of the 18th century. This is Sir William Blackstone Blackstone was a clever guy. It turns out he was a professor at Oxford and in series of lectures the venerian lectures He set out yet another system of law and the English tradition But he also recognized the importance of cheap publishing He was someone who captured the zeitgeist in a new way and for the first time in the Anglo-American tradition All of a sudden lots of people could access the law in these printed forms and in a systemic way He described the entire body in some respects of the common law. He also managed to get it internationally Read so one interesting thing Sir Edmund Burke in before the Parliament in 1790 Makes the argument that this guy Blackstone sold more copies potentially in the United States than he had in Britain That in his in this new country more people had bought the law Okay fourth phase and then we'll get to today fourth phase This is Christopher Columbus Langdell the man for whom this building is named and Langdell did something that Endures in some respects to this day. He was roughly speaking contemporary of homes Along with John B. West he brought in the case system in two respects the case system of teaching which Persists here in the first year from predominantly but also in the schools of education and business and so forth John B. West at the same time Decided that he would publish these same cases the reports the raw material of the law and this brought us a modern system Much happens in the 20th century our Dean Ames and others add add statutes and regulations so forth to the picture But this fourth phase is the extent to which all of a sudden we have The kind of environment that Holmes had as he was writing his work when his room is surrounded by these cases And that's what brings us roughly to the present day So I want to argue in favor of a fifth inflection point and a fifth system going forward a new system of legal information And here's the key difference, which is that it's emerging now. We can kind of see it happening But we see it happening in a desultory fashion my argument is that we should have a new legal information system Which is grounded in a set of open data the basic point being that when a clerk writes a law Opinion or you have a scholar writing it's in a digital format in the first instance The fact that we print it out is actually in a way just an artifact It's an effective way to read it and we can certainly continue to do that But my argument is that we should in fact be presenting these data in a systemic way in an open stable Interoperable manner on which we can then build new things So here I would invoke the scholarship of Jonathan Zitron on generativity the notion that this is an open set of information On which we can generate new meaning about the law. That's the core premise So why does this make sense here are a few reasons? One is cost If you think about the role of libraries today one thing that we do of course is to buy a ton of material here at the Harvard Law School We spend four million dollars roughly on legal materials We're blessed with a dean who sees fit that we should devote a lot of our budget to the library We in fact are trying in a way as we have for years to have the world's greatest Private law library collection in the world which we do but it's getting increasingly hard to do that It's also unclear what exactly to do. So here's one way to see it about 20 years ago before I had this Honor to do this job The Harvard Law School library in theory at least bought everything in the law in every language in the vernacular Around the world that was the premise We didn't even have a collection development policy because we could buy it all and we could bring it here So this zip code literally in fact not just this is a zip code But this building right we could put it here and someone like Holmes could surround himself with this information We all could that's no longer literally possible hasn't been possible for a while But we're now sort of admitting it and one reason is in fact That the people who publish it and this is not meant to be a commercial rant If our Westlaw and Lexus reps are here as is not a knock on you But that people who publish the law make a great deal of money on it compared to other Forms of publishing it's also important to note that Thompson West and others who repackage in Westlaw and Lexus are taking public domain materials These are not subject at least at a federal level to Copyright they make a lot of money on it just as one example in the worst budget year in history We were asked by one of our vendors to pay 44 percent more for the same stuff that we had bought the exact year before We said no and of course push back in support, but you see the problem. We no longer can collect it all here second problem that I think it responds to Maybe familiar with the Google books project. It's a wonderful thing on some levels the notion that we could have access to the world's corpus of books or From anywhere in theory from every library in the world But it turns out that there are some slightly scary bits about this and the primary one that it stands for is the Proposition that there might be proprietary control over the corpus of knowledge that we have created It has good parts and bad parts But the notion of having this amazing potential digital library of Alexandria controlled by a Profit-motivated entity not one with the public interest at its core is a key problem What else might it let us do we here at the Harvard Law School? Thanks to Peter Subur and other leaders have made a commitment to open access for our own scholarship We as researchers we as teachers and scholars don't make any money from these law review articles We have committed that for a journal article. We will put it in the public domain in essence We will allow the school to publish these works And it seems to me that this is also a way of Systematizing that set of information if we simply take our articles and put them into the internet They won't make all that much sense. This is part of a system of putting these works together in important ways This image thanks to Meg Cribble who helped find it is of something called the book barn I like the idea of a book barn, but the reality of a book barn probably isn't so great if you think about the notion of just taking all the legal information in the world and putting it into Cyberspace and sort of saying good luck the likelihood that people will find what they need is very low So it seems to me that a core piece of this is not just to let the digitization of legal materials Happen in that general sense, but in fact to design it to do it deliberately and then to go build that system in a way That actually makes sense What are some of the drivers of this? I want to focus on three drivers of this system One is our students we are after all an institution devoted to the training of Lawyers more broadly and it turns out that our students aren't learning only in physical ways using regular physical books Or scoster and I've written a book called born digital in which we studied the youth media practices And one thing that we found of course is that our young people are living Children eight and five living lives that are highly connected They're often doing more than one thing at a time learning in different ways It has great parts and it has parts that we need to mitigate But I think we as teachers need to recognize this change in the hybrid environment in which our students are living and working It's of course not only our children who are living in these ways. They're probably people blackberrying right now I can't see you, but if you are I'm sure you're doing it unless the signal is no good in here This of course is our president the first Blackberry toting president in the history of mankind Quite a wonderful thing. So it's not just kids who are accessing the world in these ways and that world of legal information Could do with keeping up a little bit So one note there's a lot to be said about the research into these new media practices But one note is the extent to which young people Interact with media There's a presumption that the media that they can access our digital in nature So just to take one example, you have a five-year-old daughter named Emma line who is high-spirited and fun She was not invited tonight because she would be a little too high spirited right here We were recently on a vacation having forgotten our regular digital camera So we'd gotten one of those disposable ones an M line was taking photographs of people's feet and back sides and so forth the sort of Photographs that children take that aren't very good and she flipped it over and said daddy. Where are the pictures? She wanted to delete them right she had never seen one of these cameras The premise for her was it was digital that you could upload it and share it with your grandparents She never had that experience of taking a roll of film out of a camera and bringing it to CVS and giving them $19 and waiting three days for the prince to come back or not So the presumption is that images are digital think also of media files of music It's no surprise that iTunes is the number one music retailer in the United States or that tower records has liquidated its stores Of course the premise of a song is that it's in the digital format YouTube is the number two search engine in the world owned by Google So there's maybe something there But you get the notion of video presumed to be in this format and last of course is Prince this really Complicated last bastion in some ways of digital media. So we know that young people tend not to read newspapers In fact for journals and so forth We know that they are rarely in fact pulling those journals that we buy off the shelf But turns out there's one anomaly in this whole story, which is an interesting one I know if you noticed as you walked through the reading room and saw the way that students were studying you presumably saw people Mostly with laptops and then also a casebook beside them When you go out you will notice this the notion is when we ask kids about long-form arguments They tell us that they prefer books in the classic sense the codex the traditional book And we ask them why they use the same thing adults say which is the three bees the bed the bath and the beach They prefer this form factor of the book. So there's an anomaly though. They presume this to be a digital era There's still a preference for other forms of organization And to me what that says is we have to do better in imagining the learning objects Imagining the form factor of the digital book and I think actually that the iPad may do that I have now seen my eight-year-old son reading his first book this week for a homework assignment on his iPad or my iPad for that matter And perhaps that it's a form factor thing, but the presumption is that the media or digital So should the lobby so in addition to thinking about changes in youth practice think also about changes in the Computing system one of the large trends is cloud computing. I'm not going to get particularly technical here But the basic premise is a lot of the computing power has changed from being in this format to being in the cloud If you use Gmail or Google Docs, you are using the cloud as a place to store your material The application as well as the power this of course gives the notion that in computing It might make sense for us to be storing this core set of material in the online digital format And third are changes in publishing. I mentioned the iPad I think this may be the moment people have been saying this for a while But that books may well go toward the digital this summer as you may know the sales of Kindle Books surpass the sales of hardcover books by a loss on Amazon this summer again I think the iPad may be a form factor that is helpful in this regard But actually I think the trend in publishing that is perhaps more important to this picture is this machine here Anybody's been to the Harvard bookstore? This is the called the espresso book machine It's from a company called on-demand books and we brought our kids there when they unveiled it because I thought it was perhaps historic I still think it might be it's quite wonderful if you haven't seen it You should go the basic idea is you go to the bookstore you type into a browser the Book that you want. I did F. Scott's Fitzgerald's the beautiful and damned you get a whole bunch of editions of it You choose which one you give them eight dollars on your credit card and three or four minutes later outcomes of paperback, right? So why is this important in the whole story? It's important because I think that the paradigm might shift from a predominantly print based Environment where the digital is the afterthought you write the article you print out the journal article And then you put the digital file online to one where it's the inverse that the digital file We can solve problems like authentication becomes the key one And in fact the print out is in order to get a different way to interact with it rather than it being the archival Format I think this is a key shift, and I think it's one that we have to make deliberately rather than have it happen Okay, so what does this mean and how might we take advantage of it? This is a picture of six people who might be in the room. This is the digital lab team I think one important trend is the trend toward interdisciplinary teams thinking Martha just described in terms of co-production one of the people here has been working with Charlie Donahue to set up a server a Faculty member who has his own server in order to co-produce materials based on this legal information I think this premise of putting computer scientists and designers and lawyers and librarians Into a team in the service of building this new system is crucial And they might do lots of wonderful things they already are doing lots of wonderful things But to me this is where the wonder and the creativity lie on the generative part of the top of this design So think about all the repositories in which if Peter Suber is successful all schools will be putting their scholarship They are like the book barn if they're just kind of everywhere on the net We need to build the connections between them that seems to me the job of these interdisciplinary teams And one way of course in which someone might get access to all these articles Is through Google Google Scholar again look to the research about how young people are Accessing these materials is almost always through Google Google Scholar Wikipedia the predominant set After they ask their teacher they go to these resources not in the first instance to a reference librarian And I think this is a possibly okay thing But I'm actually a little bit worried about it if you think about what this might mean for libraries If you combine Google and Amazon it could put us in the position of being roughly speaking warehouses for physical materials That's the bad story. Why is this so well if you talk to a graduate student about their research process They say we've got something we want to learn about We might ask a peer to see if they have the right book But let's assume that they don't they go to Google to try to find it or Google Scholar Which does actually a very good job at helping them find some things They might then go to Amazon to say is this book there and look at the recommendations They use these recommendations as well We use those recommendations and then when they tell us they go to the Hollis catalog here at Harvard They often do so to see if the book is here could they get it for free and then physically come and get it If not, they might get it through these other means I think that's not a great outcome for libraries add that to the print-on-demand Version of the future of libraries of the point is someone to do research Goes into a system finds the thing that they want and library might be a place where they can just get it printed out for them I think that misses the point of all of the intelligence that we could bring to bear on behalf of scholarship So one argument I think is crucial is to say the effort should not be so much about Collecting all the same materials library after library but to focus on the search engine to focus on the interface To this massive material So we're not all competing on the size of our collections as libraries But rather competing on the systems and the interfaces and the search engines that we can build on top of it Another thing that they can and are doing actually right here in this building that I'm so excited about one of the Problems that people note about a digital system of information is that you use you lose the serendipity Browsing in the stacks right who doesn't love that idea of walking into the stacks You smell the must you have the experience right of these books are read before you and oh my goodness You were looking for this book, but look at these fabulous books that are here and here Of course you want them we can't recreate the must I guess we could but that's sort of the point I've learned also in the library of business there worse things than must some really crazy things that Dorothy Africa knows exactly what I'm talking about There's put it this way There's a freezer room somewhere here that you put things in to make them usable again my idea though and the idea of this Digital lab team that we have here is the week actually can do much better at that serendipity business in the digital space So think about Harvard alone. We have 73 libraries right not only of 73 different libraries We also have a depository 26 miles away. So think about it this way We are basically full on campus you bring a new book onto campus We spend four million dollars a year doing just that here at the law school at least some book is going to go out to the depository Right, so there isn't a stack. There's not a stack at the Harvard Law School library There is not a stack at Harvard University that shows this much less think about these other systems There is no one stack for the serendipity to happen at but we could create it in a digital format They're hard at work creating the stack view and in this case You can also let people use different ways of sorting the information create stacks that make sense to you This one shows the circulation heat map in this case someone has searched for gravity's rainbow And they can see which objects have been checked out how many times they could say how many times has a professor Checked out this book this year. This is a simple minded version, but they might say aha This is the version that I want to read or you might say graduate students or students and so forth You also might think about this as a way to put lots of other information in front of users that they can use to sort or recommend things for other people and I think we could do much better in the serendipity business In the digital format Would note also that we can do much better in the teaching and learning materials zone There's a project that Jonathan Zitron and Charlie Nesson Lawrence Lessig and I are working on to hack the casebook so think about this core idea that the US government works that are the cases that we teach are in the public domain if in fact, we had a system whereby the job of the teacher was to array those cases and Then to put different bits of information. They might in fact be multimedia. They might be video They might be audio. They might be anything and to present to a student a somewhat cheaper version of a casebook We pay a lot of money for those public domain works In fact one that you could present either in a virtual format or print on demand You could have for $30 say the printed version of it I think in this format we could do a much better job of presenting legal materials now There may be some faculty colleagues in the audience who are authors of very popular textbooks I see a few who may not like this idea quite as much as I do but I think it's an interesting and positive heuristic and if we had this basis of Open legal materials both primary and secondary. This would be a real possibility And last I would note the promise of doing this in a global environment I think one of the great Exciting bits about the legal information ecosystem that we could build is that the whole story I told from that King Henry the second period to today was really about the Anglo-American tradition in law I think the possibilities of this system for comparative law across regimes if we all agreed roughly speaking to the same system For how to put primary materials or secondary materials online I think the pathways that could open up for comparative legal work would be extraordinary Okay, so this is not all perfect. I realize I've given you a pretty good Excited version of why we should do this. Here are some merits and demerits of the system I think the primary demerit is a series of costs That may or may not be enduring costs. So the first obvious cost is a money cost of doing this One party that doesn't particularly like my ideas is the courts the administrative aspect of the courts Why at least in the first instance it would cost a bunch of money to do this We don't give enough money in our society to our courts to make their information available We should give more money to the courts and make make this transition possible. I do not think this is an enduring problem I think it is cheaper to publish primary legal materials in the way that I'm suggesting Just uploading them with a certain scheme to it in such a way as to make it publicly accessible Then it is to do the kluji process that we do today We think about generally all the costs you can get out of a system when you don't have to print something and Pass it around physically. I think there are obviously some costs that could go out of the system Second very high cost is the cost associated with privacy I think of this as the redaction problem But I think the notion of putting all of these legal materials that right now can be accessed in county courthouses and so forth But putting them into a single system might make it possible to expose things about people that they wouldn't want to have known We would have to get very good at figuring out how to redact information I don't just mean social security numbers. That's trivial But really thinking more broadly about what we would and wouldn't want in the system So I would make the argument perhaps we wouldn't put family law materials in it for the first instance You wouldn't put things that involve divorces and children and so forth into the system You might think also that we don't want to put every Deposition into this having been deposed recently thanks to a case that I was involved in It's not a fun experience and you say lots of stuff when pressed by good lawyers That you really hope isn't recorded for posterity and then accessible through a Google search So we just assumed for instance that deposition materials speaking from personal experience were not included in the system So we have to think carefully what makes sense to be in this. What is necessary for the purpose of Advancing access to knowledge and what isn't a third problem is authentication of the documents Some librarians probably some in this room don't like my idea because we haven't yet figured out how to authenticate well enough The documents in digital format so if you have a printed out one There's some sense that that is somehow printed and stamped with somebody's seal of approval and is more reliable than the digital version I happen not to believe that inherently. I think that with digital technologies We actually could do a better job of authenticating these materials But it is clearly a cost and one we would have to work out the government and private sector would have to work Together in a standards like process in order to make this authentication problem go away I think again, this is a near-term cost. So so some of the costs are near-term. I think the privacy one is potentially enduring Here's another enduring potential de-merit So again, if we think about the research practices that we all use but certainly our students as well Let's imagine that you are seeking some information. What do you do? You tend to put in a keyword search right into a search box like Google and then if the search engine is good You get what you want you cut and paste it into your brief, right? Now being too good at that might actually come with a major problem associated with it I think it's entirely possible that lawyers get to the point or students learn in such a way That they get the information, but then actually don't see the rest of the context that it's too easy It's too good. It's too powerful And that we don't ask our students to step back and understand the context in the way that they might There are challenges there will be challenges for teaching in this way But I would submit those are challenges that we have right now That anybody sitting here who teaches legal research and writing has already seen this challenge over and over again And that we actually in the system should accept that and build Around it. Okay back to my idea. Why do I think it's so great? Here are the merits lined up in addition to the ones I said before Here's some exciting things. This is the geekiest of the things I think that creating interoperable legal information that could be brought together with other forms of information Will lead to new knowledge. This is an example. Thanks again to meg of How the code of federal regulations can be downloaded in xml format as can the federal register and brought together This is happening right now. I think we need to structure and make more sense of it Think about the system that we're building, but I think the interoperability of this information can be enormously enormously powerful Another thing can help with is the problem of scale and legal information One of the reasons the costs are so high is that much more is being published. This is a great Indication of how long it takes to produce 500 volumes of the federal reporter As you can see it took 50 years in this instance takes a lot less long now We can't afford we don't have the space we don't we should do a better job of doing this in a digital format And I think the system could do that Back to our students again one of the things that is so exciting about what's happening In the context of a digital era is the extent to which people create not just content for the web blog entries or Facebook postings or videos, but also create code You think about the Really disruptive technologies that have emerged in the last several years think about facebook or youtube or nabster These were created by college students right or the great search engines yahu and google created by graduate students We have in our midst the computer scientists stewart-sheber is training them right now Who do this in an extraordinary disruptive way? And I think there's a great set of projects that combine the computer Scientists with the lawyers and librarians to make sense of this for our field in ways that will be extraordinarily helpful I would note also the work of company or organizations like cast one that d minnow has been involved with Who make available information to people who otherwise can't Access it for people who are disabled who can't read a regular printed out text Technology can make these kinds of information vastly more accessible And again, this is a project worth doing and if we had a reliable system. I think would emerge Another very positive thing. I think we will see new connections that we haven't been able to see before I see jeffrey schnapp back there a leader in the digital humanity space This is a visualization of one of the earlier periods in publishing the republic of letters. This was Bob dartin and others know the story much better than I do But this shows the pathways in which those letters travel We could envision new things that we've never before been able to see in these digital environments. Why is this important in law? Well, I think go back to one of the trends that I mentioned before the thing that happened When langdell and west started to publish their cases one of the things that happened was We started to see the anomalies in the law So langdell starts us off with teaching based on cases and once west starts publishing all of those cases People could see as homes and others did that there were gaps that there were human beings who had created these different cases In different jurisdictions and that the law was not actually this perfect seamless connected system I think this system would continue that trend in important ways one of the effects of course of the system That west brought into play was the use of statutes regulations and so forth to as a teaching tool Dean minnow it may interest you that my reading group the other day I described that leg reg legislation regulation was in fact a new course of the harvard law school a few years ago To the astonishment of the students who said how could you not have been teaching legislation and regulation forever? This doesn't make any sense and yet this is one of your curricular reforms My sense is this kind of visualization these kinds of connections will continue that general trend Okay Five possible implications. I'm not sure if they're in the category of merits or demerits, which is why I put them here at the end I think one thing that we would see would be changes in the perception of the law itself By both practitioners and people outside of the law So for those who are outside of the law you might see the law in different ways because you would see the extent to which There are unevenness to it I think that if you were to put artificial intelligence and computer programmers and so forth To the task of looking across a mass of primary material. I think we would see biases I think this is a hypothesis But you might see biases related say to gender or to race in terms of outcomes in ways that we haven't seen before I think this could be helpful in terms of the Accuracy and understanding of how legal systems work But it might undercut the way that people see the majesty of the law We as lawyers are pretty good at creating these wonderful spaces that make the whole thing seem pretty terrific and together My sense is this could undercut and actually have an undercutting effect on hierarchies and so forth Second with respect to practice. I think this is another one of those uncertain Situations, I think that for judges for those who administer justice people like my brother who have to interpret Regulations and so forth and whose work is then exposed in a different way I think this could make them uneasy I think it would make them uneasy in the first instance much as charlie nesson's efforts to webcast his Proceedings have made courses courts resistant. They haven't wanted to be exposed in particularly this way. I think it will Perhaps change over time the extent to which they will get used to it I think we need to prove that in exposing the work of judges and administrators of justice that in fact It could be better and more accurate over time and not meant to embarrass But I think this is a real cost the potential of chilling the way in which people practice the law One very unusual idea I think that a possible side effect of this system would be that judges and those who administer Justice might have a little bit of the medicine that their kids are getting right now with respect to privacy So I heard one supreme court justice describe once his experience of life which was Being in a heated building in the morning having his breakfast going down to the Basement getting in a car in a heated garage driving in that heated car to the supreme court getting out of a Garage in the basement supreme court going up to the court so forth back and forth I think there's an extent to which it's possible that some people who have lived in a relatively Well protected environment might realize that our kids are living in Lives that are often recorded from the point at which they are born to the point at which they Will persist of course, but to the end of their life, right? We haven't yet lived lives 90 years plus that are completely recorded in a digital era My sense is this might lead those who make laws and those who interpret them To have a kinder view towards substantive privacy protections And this might be something that would be a weird side effect of this regime to see the world in a slightly different way In the way that sometimes their kids do Last in terms of scholarship I think for those of us in the scholarly World this would obviously have an effect on what we do This is another quote from Holmes where he says for the rational study of law The black letter man may be the man of the present But the man of the future is the man of statistics and the master of economics He was plainly right in lots of ways There are wonderful people still doing black letter law in some respects But there's no doubt but that law and economics is an important and ascendant field since the time that he said that Statistics the field of empirical legal studies is exploding in great ways It's my friend Jim here We also have brought into the library two people Perina and Travis who are Our statisticians to help with this work of the law I think there will be incredible new opportunities for understanding the law and its trends through the lens of other disciplines brought to bear on the system And the other effect with respect to scholarship might also be an extension Of the rise and fall of the tradition of writing treatises the notion that for a long time in that arc it was People who are learned describing the law in these relatively holistic ways and treatises We've seen a decline of that through the late 20th century My sense is that having individual people describe the law in its meaning rather than presenting the raw materials and teaching the skills to interpret them would continue in that respect Two other possible implications Professor Wilkins who gave most recent chair talk here Is friendly with a wonderful guy named Richard Susskind who's written a very provocative book called the end of lawyers Do I think this system is the end of lawyers? Of course not neither does Richard Susskind for that matter He has a question mark you can see here Important he himself is a lawyer quite a good one apparently Sells a lot of copies of this book I do think that many of the trends that are in play discussed by the program on legal profession and others in this new environment Will be accelerated. I think the digital environment is an amplifier of other trends the trend for instance of globalization of outsourcing All of the things that David Wilkins focuses us on and Richard Susskind I think will persist and will be amplified by this trend And I think that's crucial to watch to think about the way in which the practice of law may change Okay last of the potential implications does this mean the end of libraries Well, no there too of course, but I think it's actually the other way around I actually think this makes Libraries and librarians more important not less important over time Okay, so why is that possibly so if in fact you have all this great and material available at the end of a google search When I took this job I would go to backyard barbecues or cocktail parties people would say ha ha isn't this funny you digital boy Are going to undo this great library right now that we have google we don't need libraries You will just go in and dismantle it Right. I didn't think that was all that funny at the time I think it's now even less funny and here's why I think libraries are more important For three reasons. So first is as place You know how many of you had the experience of walking in through the first floor walking up to the reading room and coming here But just a few things that you had to pass as you walked in the front door You were confronted on the left immediately by joseph story. This was the bust the physical presence of a man who saved the harvard law school from near extinction Then how many students did we have and when story took over were we down to one? We were down to one, right? Just destroy this young looking guy over here came in as the professor Wasn't even quite the royal professor of locks. I'm not sure that we called it that at the time Well, that was that money, right? And he saved the harvard law school. You have a sense of our place and our history Walk up those stairs and come down this Pathway you have to pass students this place is packed this place is packed more than it has ever been before As I noted before those are students who are here. I think for the fast wi-fi I think they're here for their present friends who are next next to them and studying in social places But there's something about the space and the contemplation that is possible here But I think in some ways is a safe harbor from the connected world of the starbucks over there and so forth There's something about the physical space and why we come here beings have been very I don't know interested in taking space away from libraries. This dean has not done so yet And I think she has good reason not to she walked further down that Pathway on the left as you're going out it'll be on your right You see the portrait of mr. Justice tony. This is a wizened man somebody who has clearly got the weight of history on His shoulders and in his face He's the guy who wrote the dread scott decision and you look at that picture Even a few years later people knew this was a disaster for american history and you can see it in his face in that picture And then you come into this room and it's filled of course with these great treasures on the Wimsie of the Holmes lunchbox, but we're also forced to confront the history of the school the Portrait over there the family portrait Is the beginning in a way of the school? That's isaac royal the guy standing up there This is a portrait by robert feek one of the early colonial portraits of a family and Janet hallie's jenna hallie here She gave an amazing amazing chair talk in 2006 about the royal chair which she has the difficulty of this Is that the royal family made its money from slaveholding in antigua? And we have this here as something we have to embrace and struggle with our own history Where we came from and where we're going and I think libraries help evoke that in an important way So I think as space as place not just as museum, but as a rich living intellectual heart To where we work and where we learn libraries will persist I think second with respect to collections. That's where the biggest change will come in We won't collect in the same way. I don't think forever I don't think we and all the boston area law libraries will continue to buy all the same reports And compete in the aba statistics on the size of our collection I think those days are numbered But I think mr. S did a good thing by giving us his collection There are people like Dave warrington and others who look after it in extraordinary ways Not just presenting it and preserving it in the literal sense But making sense of it for scholars in a living way for students who come through this place I think it's crucial that we have these physical objects In the form of books and collections another example why we have to do what we do Not every regime in the world is stable not every regime in the world is collecting its legal materials for Eternity in the way that we are here. So we have in our collection just two examples The pre-soviet materials that are constantly in use even in microform downstairs and these horrible machines to get at it But they're constantly so much so that when I was tempted to move them off campus We had people up at my door complaining you can't take away the pre-soviet materials Why well the russians the russians who were Creating the soviet union didn't really want their law around and the fact that we have it Makes it a lot easier for people to get at it and it's very hard to find now in russia another example of this is the pre The ottoman collection before aditur comes in we have late 19th century turkish materials the people come here and say Thank goodness you have them because we can't get them in turkey There's something about the way in which this place has thought about legal information All around the world for the ages that I think has incredible importance And I don't think that has to do with digital or physical that has to do with a commitment To recording and keeping the law And then last of course I started here But the people the community of people who make possible the access to knowledge that is Here in this place is extraordinary for any faculty member who has ever experienced the magic of rida the notion that at any point you can pick up the phone or send an email and say I need this and it comes relatively quickly making your scholarship much richer and faster and more effective The key to that is not that louise ragno is a totally wonderful lady which she is if she's here Right at the edge of that who gets it to you But when homes talked of a thoroughly connected system Turns out he was talking about the harvard law school library team There is a huge team from the people who have to select it in the first place to make sure it's here The people who buy it the people who then catalog it and put it on the shelves and make it accessible That at the core of this community Is a team effort and something that I don't think will go away just because it's digital I think that what librarians do at core is to render sensible a highly complex system In part by creating an intellectual edifice on which to hang these doctrines But also to make it alive and to make it accessible at key moments Okay Very last idea and then we can go to the wine back there, which I know charlie at least was eyeing earlier Um, so here's the game plan I think which is that when we built this building when we built langdell Um, we went out and hired some architects this little rendering here of langdell hall shows Shepley bullfinch was involved Langdell of course is a building that has not just this library But also has classrooms on either end This was a learning environment that we designed and presumably The designers were the teachers the people thinking about and librarians who Thought about the space and how it should work in the context of the university My sense is that we haven't yet done this for a digital page We haven't yet thought about the fact that our students do a lot of their learning in virtual environments that our students Just as frequently come in through our virtual front door as our physical front door I don't think we have yet put together in the same room or the same virtual community for that matter Information architects as well as the physical architects as well as the teachers and others I think what we need is a design surex to build this new Thoroughly connected system of legal information for a hybrid age for a digital plus era My sense is if we get it right That we better for the jailhouse lawyer working on his appeal who now sends us letters asking for access to this library Or for the prose say litigant working on her family law matter We better for the disabled person the person who can't get access to the information because They can't read it in that format I think it will be better although in the first instance uncomfortable for the administrators of justice and judges and so forth I think it will be better although uncomfortable in the first instance for the teachers and learners of law I think we can do much more with this open system I'm totally confident it'll be better from an economic perspective that it will create jobs in that generative jonathan zitrin or collaborative cooperative yokai bankler sense I'm and i'm totally sure that we better for democracy in terms of access to justice and access to information So my argument is that we should go design and build this thoroughly connected system of legal information for a digital plus era Thank you so much The dean says that we see a couple questions So anybody tell me where i'm wrong professor zitrin The lunch boxes were for you. I knew that you wanted the hot lunch, right? Yeah, your articles nonetheless, of course, they're totally included the generative internet check Harvard law review, right good Or smarter law professors like you who write bots that do that for them, but Go and ask the syringe jonathan has a very high rank Yeah, yeah, bigger the class the better It's great. It's a great question. I could imagine it in 1998 internet and society you posing this and Wrapping our minds around it. Um, so I want to defend the idea of the long form argument created over 25 years I don't know charlie donnie. How long did your last book take you? 25 years Really good book Exactly The greatest greatest friend of this library is charlie donnie. No doubt and with good reason This is someone who has helped to create this collection that has made extraordinary Results out of it in the form of this scholarship So I do think that the long form argument that is the book developed over the course of a lifetime Of course, that's crucial. That is the thinking about the law and I wouldn't in any way denigrate that I think that the analysis of the law that is in the form of many law review articles that is A form of doctrinal work, but which renders more sensible Broadly these disparate doctrines. That's crucial one thing. I was going to say to Terry fisher one thing I don't thank you for is your own chair lecture It was on the disaggregation of intellectual property and it was not that it wasn't illuminating It was that it was so good as to be paralyzing to me in the last few weeks Thinking of this as what a chair lecture is meant to be that kind of work essential I think I do think that the what it will do in part though is put pressure or perhaps create opportunity To do things that should count as legal scholarship In the form of using computing to try to understand it in different ways, which I don't think has yet been done I think of it as the extension of the text analysis Extension of the ai things that you've done and that stewart doesn't otherwise I think that can stand for legal scholarship and in fact can open new avenues And I think that that should be what the next blackstone and others in fact are doing so I guess I think of it as new avenues and new possibilities I think it may render less useful some form of obviously black letter law that I think has been in decline But I would absolutely stand for the classic book writing long form argument And I actually hope we don't go down the road of tweeting more for instance as law professors I probably tweet too much or writing blog entries too quickly as much as I do want to engage in that connected form of public discourse Professor Wilkins I have a great question So I don't possibly have an answer to it But I have a few little ways toward an answer possibly and it's also not a new question as you well know So in that second period the one that goes 15 16 17th century where printing is coming In one of the histories I was reading thanks to Dave Warrington and others who sent them my way So Littleton writes his 10 years. They're in manuscript and they get printed Then coke the guy of this out of old fields must bring the new corn quote He writes his book and it's this coke on Littleton, right? And one of the debates is whether or not the interpretation that coke does the gloss on Littleton itself is law Right and this is something that back then people were thinking about is that Scholarly work something that is in fact the law. I know in other legal systems I think in Europe predominantly there is a sense that sometimes the work and international human rights and so forth, right? The work of scholars is itself The law to some extent it can be cited as Presidential and so forth. So I think we already have this weird complation I'm not positive though that this does anything more again than amplify that particular pressure or that trend I think also that when we think about what to collect here, we already have the problem of saying What is interdisciplinary work that ought to be here versus in white, right? So human rights is a perfectly good example should we be collecting it or others My sense is that a thoroughly connected system would say we don't actually care. It's both, right? It's both human rights material and its law and we can categorize it both here I would say to the beginning of David Weinberger's book everything is miscellaneous the idea that multiple categorizations Can make us not engage with that quite as much as an organizational system But I think we still have this core problem, which is law is itself information Right, and there's also information about the law and this gets us tied up all the time when we think about whether or not That is problematic or it's just something to embrace and that's the part where I get held up If law is itself information, what is information about the law? Dean Minow, you get the last one Yep So I would continue to close the space to protect our law students During exam period when they are anxious and they need the seats even this week We got complaints from students saying that even though we're open 24 hours that they want more floors open Beyond the second floor in the later hours because the seats are full in the early hours It's fairly astonishing our previous acting dean Howell Jackson wanted us in fact I think to restrict the hours so students would go home and sleep Which the different philosophies here have different deans and thinking about it Um, but in a serious sense what I think should be open Is the platform that involves the primary and the secondary law in a virtual sense That to me is the bedrock on which everything else happens on top of that though I see open and closed systems co-existing So one question is would west law and lexus still exist? Of course they would and would we pay for them? Of course we would would law firms pay? Of course they do a wonderful job at organizing the law and making it accessible at key moments in order to you know bring your case But what I would imagine happening would be a much greater diversity of perspectives that would create those systems beyond the john b west one So you go through all of those pictures of the guys. They're all white guys who kind of look like me, right? Maybe a few years later. I imagine that there's strength in the diversity of having many more people look at the same core of information Lawyers and non lawyers people from here and elsewhere who would interpret it in ways through lenses Computerized lenses or just human eyes and see things in new ways So the part that would be constantly open would be this bedrock I think of information and we would then have open and closed spaces as we do today and physically open and closed spaces as we do today


And let me thank Ahmad and Fabrice for this nice invitation and the organization of the conference, and particularly Ahmad for his hospitality during my current stay here at the RHS. Thank you. So I'm going to be discussing today some problems concerning the deformation and variation of algebraic cycles focusing on the equal characteristic P situation. So to begin, let me describe the rough type of problem that we'll be interested in and some existing and new conjectures. So for the most part, we'll consider some smooth projective family of smooth varieties over a field. We'll have some closed point of the base, closed just for simplicity. And to be precise, let's take some codimension I cycle on the fiber over this point. And I'm not going to be to set any torsion questions today, so I'll always be working with cycles tensor q. Then the type of classical problem that one wants to study is the following question. When does this cycle extend to the whole family x? In some sense, there are various more precise formulations you can give. So in characteristic 0, the problem is at least conjecturally reasonably well understood, because we have the variational hodge conjecture of Groten-Dieg, 66, if I remember correctly. So this says that assuming the characteristic of k is 0 and with notation exactly as here, then the following are equivalent. So firstly, the condition that really interests us, the cycle does extend. So the cycle extends from the special fiber to all of x to be precise, mod homological equivalence. So that is the same, or precisely, I can find some z tilde to the codimension I cycle on the whole family x with the same DRAM class after restriction to the original fiber. And this extension, mod homological equivalence, is really the best one can ever hope for. So that's what we'll study throughout. Although it's slightly misrepresent for Groten-Dieg wrote, the expectation is that a sufficient condition is the obviously necessary. So you have the quity, what is the DRAM homology? You can take 1 over q over k. So which one is this? That doesn't matter. And if I've taken a closed point, it doesn't matter. No, but k is the field of characteristic 0. So it's the field of the rational. Oh, k, k, k. Yeah, DRAM homology over k. Over k. Yeah, of course, of course. I exclude it from the notation because DRAM homology is not going to appear very much. Yeah, absolutely over k. Yeah. So the expectation is that the obvious necessary condition is sufficient. That is to say, it's enough that the DRAM cycle class, living in the DRAM homology of the special fiber, lifts to the DRAM homology of the whole family x, DRAM homology over k. Or do you assume that the point is a resin field k? Well, I take it to be, in fact, very soon, k is going to be algebraically closed. But in the cases, as long as it's a closed point that doesn't matter. And if I compute DRAM homology using the DRAM complex, it doesn't matter whether I compute it over k or over finite extension of k. No, but I have a similar condition, too, that the class for k could sink, but it's not there. In any case, I only care about the case k algebraically closed. So all we can impose the condition that the class is flat. That is to say, it lifts to a global section on the base of this DRAM local system. So what we know about this conjecture, in the sense that there are two primary results, what I'll call theorem a. So this is part of Delinia's DRAM de la Parti fix. So it's the condition 2 and 3 are equivalent. So I can't reach up there any longer. But it says that the obvious map from the group in 2 to the group in 3 is surjective. And from that surjectivity, one sees that the two conditions are equivalent. And then we have the result of left shats, which in the absolute case goes all the way back to 1924, stating, of course, he didn't have the variational hodge conjecture. He was considering the absolute case, but it follows from left shats result that the variational hodge conjecture is true for divisors. That is to say, in code I mentioned 1. And apart from that, OK, we have some special cases where we know the hodge conjecture, and therefore we can deduce variational statements. But essentially, apart from that, we don't know much else. But as I said, it's not characteristic 0 that interests us today. So from now on, OK is going to be a perfect field of positive characteristic. So in this setup, we can still consider the problem. And Groten-Diek, in the same footnote where this variational hodge conjecture appears, also proposed, I say proposed, there's about five words on the topic, proposed a variational take conjecture, which is completely analogous. But very little seems to be known about. It seems not to have even been very widely studied. And so instead, I'd like to, in fact, follow the same philosophy that Le Fou mentioned at the very end of his talk yesterday, that to study defamation of problems in characteristic p, we should work periodically. And so the main aim today, instead of trying to formulate such variational questions using allatic co-amology, we're going to form an analog in crystalline co-amology. And let me remark immediately that I'll make comments later about rigid co-amology. So let me fix some standard notation for working with crystalline co-amology. W is W of k, the ring of width vectors of our perfect field k. Big k is its field of fractions. For any reasonable scheme over k, we'll be more clear later about what reasonable means. I can consider the crystalline co-amology. And I will continue to ignore torsion questions. So I'll always work with crystalline co-amology with p inverted. And I'll, hoping this doesn't upset you, Professor Kerr, I'm going to continue to omit the k. Everything's taken over k. We have the absolute Frobenius, which acts on the crystalline co-amology groups. And so I can consider the eigenspaces, which I'll denote with standard superscript notation. And finally, I recall that analogous to the Dirac cycle class maps that we see in the variational Hodge conjecture of p to the i. So it's the eigenspace of the Frobenius with eigenvalue p to the i. So we have in this crystalline set up crystalline cycle class maps, which associate, to any code I mentioned, i cycle on our variety, its corresponding value in the 2i crystalline co-amology. And in fact, we know that it lands in the middle eigenspace of the Frobenius. In the cases in which I apply the crystalline class map, it is indeed going to be proper. If it's not proper, then you're right that there's been some subtlety regarding the crystalline cycle maps. But you can certainly define it now using some technique in k-theory. I mean, if you use, let's say, Geisel-Lavine's computation of k-theory and characteristic p, one can easily define the crystalline cycle class maps for any finite type k-ski. Well, I got quite worried about this at one point. When I started looking back over the classical literature, this restriction of the cycle class map to the proper case. And although we don't need it, it's maybe helpful to recall at this point just to put ourselves in the right frame of mind, at least part of it's very large. If x is not proper, then it's very large. It's very big, yes. This is why I'll make some comments about rigid co-amology later. So as I say, just to put ourselves in the right frame of mind, let me recall part of the crystalline formulation of the Tate conjecture, which is normally formulated erratically. If x is smooth, projective over a finite field, then the surjectivity part of the conjecture will state that after tentering the cycle class map up by qp, we get a surjection onto the eigenspace. So I think it can now go here. So now we have enough to formulate an analog and crystalline co-amology of the variational hot conjecture. So k continues to be perfect of characteristic p and f, s, and z are as in the formulation of the general problem at the beginning. And to save me writing it so many times, I'm going to let c be the crystalline class of my cycle z. Then the conjecture states that the following four conditions are all equivalent. And I'm going to give them names so that I can talk about them. So firstly, the condition of interest is that the cycle z extends to the whole family mod-homological equivalent. So that says the cycle extends mod-homological equivalent. And one suspects that a sufficient condition is the obvious necessary one, which are called the crystalline condition, namely that the crystalline cycle class in the crystalline co-amology of the special fiber lifts to the crystalline co-amology of the whole family. Now since we know what eigenspace that should lie in, we could impose the slightly stronger condition instead that the cycle class lifts to the expected eigenspace. And finally, since we would like to have a nice analog of the situation of the variational hot conjecture, we also consider a flatness condition stating that the crystalline cycle class of our cycle is flat. That is to say, it lifts. In fact, if the lift exists, it's unique to a global section over the base of Augus's convergent F-isocrystal. Now I'm not going to use the flatness condition really at all today. So if you are not an expert on F-isocrystals, you can more or less ignore this final part. But now again, the same problem about non-closed, I mean, the residue field of the point, because the crystalline co-amology we use is over the field factor of the bit vector of k. But when you have a closed point, you have to consider the bit vector of the extension. Then you have vector space on a different field. So when you say the class lifts, I mean, so it is also not clear that what you are doing is well that your kind of conjecture is enough to consider it for algebraically closed field, because it's something missing in, I don't know. How about I take it k to be algebraically closed? No, but the question is, do you prove that your k to be algebraically closed field implies the general case, or did you see it? Well, if you construct a cycle at the level of the algebraic closure, it necessarily comes from some finite level. And a standard transfer argument then will push it down to whatever finite level you want. So it was enough to construct the cycle on the whole family x after base changing to the algebraic closure. No, but the point is, suppose you have a small s to find out the quadratic extension. So over the algebraic closure, you get two points. So suppose you can lift each one of them, but you don't mean that the lifting are the same. So you can check the lift. It does, because it's flat. It's determined by its value at any one of the points. No, but one of your conditions is that the homology class extends just to h to i or something like that. Then the non-flat condition too. And with this condition, it is not clear that if this condition is verified, then suppose you know the conjecture of the algebraic closure, then it is not clear that the cycle you construct is the sense to, it's clear that it is over the quadratic extension, but it's not the same. But then I can simply transfer it down to the original extension. If I can sort of cycle over some quadratic extension, see I can sort of line bundle over the quadratic extension, I can then just take its norm down. Because it doesn't satisfy the condition that you want on the quadratic extension. It satisfies only at one of the conjugate points, but possibly not at the other. It does, because I assume the existence, I assume the flatness. I assume the existence of a flat class, which hits it at the special point. No, in the conjecture that you said the following are equivalent, yes? You wrote there the same question as before. So the content of the conjecture, this is the crystalline analog. For simplicity, we can look at the original one. So the question is whether it is reasonable to put this conjecture when there is this change of field, the closed point is not rational. And so I'm saying that it doesn't trivially follow from knowing the conjecture over the practically closed field that condition 2 is. No, I agree. I agree. In order to reduce the algebraic closed case, you need to work with condition 3. No, but to prove that the same problem will be improving the 23R equivalent. Because the way you would do it is you use, again, you use delinso axiope to work on the algebraic closure. And there you know that you can lift one of them to a flat. Again, you will have the same problem in descending from the quadratic extension. It will not be a. Can you assume to date? Yeah, we can assume it's algebraically closed then. And we can discuss afterwards. But once you've got the equivalence of the flatness condition with the others, I believe this problem can be avoided. It could be a problem in your ethnicity. So let me then take it to be algebraically closed if that will settle the issues for today. I can't even see what the assumption is now. He's happy to have questions, I think. So I make some immediate remarks. So firstly, we can certainly see that the deformability condition, the crystalline condition, and the flatness condition are exact analogs of what we see in the variational Hodge conjecture. Secondly, regarding some obvious implications, deformability implies the crystalline phi condition, which in turn implies the crystalline condition, which in turn implies the flatness condition. And finally, so this rigid cohomology comment I've been alluding to, we could consider some obvious analogs of the conditions in which we replace crystalline cohomology everywhere by rigid cohomology and the convergent isochrystall by an overconvergent isochrystall. But it turns out that these conditions are completely redundant in that you get an equivalent conjecture. So if you can prove the conjecture for crystalline cohomology, you automatically get it for rigid cohomology by virtue of the fact that the crystalline cycle class map factors through rigid cohomology. And conversely, if you can prove it for rigid cohomology, then because rigid cohomology maps the crystalline cohomology, you get the conjecture for crystalline cohomology. But it turns out that working directly with rigid cohomology is a lot less convenient than working directly with crystalline cohomology. So we follow the crystalline route. Although from some philosophical point of view, the conjecture might be more natural with rigid cohomology. Let me state the main results then. Maybe I'll try to stick to algebraically closed field k to avoid any further problems. So the first theorem, which is an analog of theorem A up there, states that the conditions Chris phi and flat are, in fact, equivalent. I'm assuming k is algebraically closed. And the second theorem, which provides an analog of left sets result for line bundles, states that this crystalline variational take conjecture is true for divisors. So in the flat condition, the group A0, Chris, is a finite dimension? It is finite dimensional, yes. It embeds into the crystalline cohomology the special fiber. And my claim is that because it's an embedding, these problems that you mentioned don't matter. OK. And so in the proof, you just work with crystalline with out rigid. That's correct. That's correct. I mean, an alternative approach. So by Kedlaya's fully faithfulness result, the global sections of the convergent isochrystal agree with the convergent sections of its over-convergent extension if the over-convergent extension exists, which is essentially a conjecture of Bertelot. And so then you can then play the whole game in rigid cohomology instead. So as an application, we can consider the following situation where x is smooth and projective over a finite field, which unfortunately is not algebraically closed. y is a smooth hyperplane section. And we can consider the question, let me take this to be dimension at least 3. We can consider the question of extending line bundles on the hyperplane section to the ambient variety. And the type of corollary that comes from a simple pencil argument, so I've replaced divisors by line bundles now, if I take this line bundle on the hyperplane section, then it extends to a line bundle on the ambient variety x. If and only if its first crystalline churn character extends to the crystalline cohomology of the ambient variety. And what one can do with that is show that if you want to prove the take conjecture for divisors, where I now even mean the allatic etal formulation of the take conjecture over some finite field, then it's enough to consider the case of surfaces. So roughly, how does this go? You want to prove it, let's say, for your three fold once you know it for surfaces. You pick some hyperplane section carefully. Specifically, that means that you want to ensure that the hyperplane section doesn't have too many more, doesn't have a much larger Frobenius eigenspace than the ambient variety. And then you simply apply the previous corollary to start constructing line bundles on the ambient variety. And I should mention explicitly that I recently learned this corollary does exist in some unpublished short manuscript of De Jong from a few years ago. So it does seem to be known to a handful of experts. So let me turn out away from the applications again and back to the results. So the key to establishing theorem two is going to be a local formulation of it, in which I definitely want K to be algebraically closed though it's not true. So I'll take X to be smooth and proper over the spectrum of some power series ring. Y to be the special fiber and L to be some line bundle on the special fiber. Then the result states that L extends to a line bundle on the whole family X if and only if its first crystalline churn class has the analogous extension property. Except as opposed to previously, I'm now going to be careful as to which eigenspace I work in. So I am going to insist that the lift of the churn class does line the expected eigenspace. That can be eliminated, but it turns out to be much more natural to work with the eigenspace condition. So again, it says that if you've got some line bundle on the special fiber, then the obvious necessary crystalline obstruction is in fact sufficient for extending the line bundle. For example, if you take X to be a smooth, proper family of K3 surfaces or abelian varieties over KT, or maybe I emphasize again that definitely K is now able to breakly closed, excuse me, smooth, proper, super singular family. To be precise, I just require H2 to be isoclinic of slope 1. Then it follows from theorem 3 that the co-kernel of the specialization map from the Navon-Severi group of the geometric generic fiber to the Navon-Severi group of the special fiber is killed by a power of p, which for smooth, proper families of K3 surfaces is an old result of my garden. But I feel that this somehow gives the conceptual explanation behind it. You have surjectivity of Picard groups because you have surjectivity in crystalline coloramology. I've got to use this fishing device now. So for the final 20 minutes, I'll discuss some ideas behind the proofs, maybe main ideas. I hope. I'd like to think there's more than one. So I guess all the main theorems are up. So theorem 1, which is the equivalence of these conditions, at least over an abelian closed field, is proved by modifying Delinier's original argument in characteristic 0. Delinier's original axiomatic argument is no restriction on the characteristic at all. And so that immediately gives some of the implications. And the hard part is incorporating the Frobenius to get a handle on the crystalline phi condition that imposes some restriction on the eigenspace. That's what doesn't appear anywhere in Delinier's original situation, to generation of Ray spectral sequences. Objective OK. Yeah. So then once you've got theorem 1, it's enough to prove theorem 3 to get theorem 2. So theorem 3 is the local formulation of theorem 1, theorem 2, excuse me. And if you can prove the result in the local formulation, then by some relatively standard type of art and approximation argument, you can prove the result in the global setting. So everything reduces to theorem 3. And so from now on, we put ourselves in that type of local situation. A will be power series in some number of variables over k, which again, from now on, is definitely algebraically closed for these results. X over spec A is smooth and proper. Y is the special fiber of this family. Y sub R is the infinitesimal thickening of the special fiber Y. Then theorem 3 is going to be deduced from a considerably stronger result, theorem 4, as follows. So we suppose we're going to deal with all co-dimensions at once. So I'll take some element in k0 of y. Everything's more torsion, so I can identify this with the sum of the child groups of y. Though it's probably better to think of z as being the class of some vector bundle on the special fiber y. And the theorem gives conditions under which the class of this vector bundle admits infinitesimal extensions of all orders. And we'll see that these infinitesimal extensions to all order exist if and only if the crystalline churn class of our class z, which sits in the crystalline co-demology of the special fiber, lifts churn, sorry, sorry, sorry. Keep doing this. Thank you. If and only if it's crystalline churn character lifts to the expected piece of the crystalline co-demology of x. So several comments I should make about the theorem. Firstly, it does imply theorem 3 since the Picard group is a direct sum earned of k0 on which the only non-vanishing part of the churn character is the first churn class. And this is key. Theorem 4 tells us about infinitesimal extensions of vector bundles. But if you have a line bundle which admits infinitesimal extensions of all orders, it's the same as a line bundle on the whole Schemax. So if you want to extend the line bundle up to x, it's enough to extend it infinitesimally to all orders. And that's how theorem 4 gives you theorem 3. Secondly, I'd like to stress that theorem 4 should be viewed as an infinitesimal version of this crystalline form of the variational Tate conjecture I'm discussing, which is valid in all co-dimensions as opposed to most of the results today which have only been for divisors or line bundles. And finally, it's an analog of the result of Bloch, Anno, and Kertz, for those of you who know this, in that 2012 inventionist paper in mixed characteristic. So they consider the situation of having some smooth proper x over zp. And they start with a k0 class on the special fiber. And they prove that it admits infinitesimal extensions to all orders if and only if it's crystalline Schoen character. And now the test is to see how the crystalline Schoen character looks in terms of the Hodge filtration on the special fiber. And they prove that if the necessary condition is satisfied, then indeed you have infinitesimal extensions to all orders. And this is a perfectly analogous statement but in equal characteristic p. And so in the end, everything reduces to theorem 4. And so I'd like to finish by giving a brief sketch of the proof of that theorem. So although the theorem is inherently only a statement about k0, the proof is based on recent results in higher algebraic k theory and topological cyclic homology. So I can't give them, I certainly can't give a definition of topological cyclic homology. That takes a two hour talk. But you should think of it, it's not completely wrong to think of topological cyclic homology as some form of derived crystalline cohomology or maybe derived log-Hodge-Witt cohomology would be better. But let me say derived crystalline cohomology. That already gives you some idea of what it's doing. So then the proof goes as follows. We need to understand the difference between vector bundles on y and vector bundles on the r-thin fantastical thickening of y. And the general machinery of topological cyclic homology gives you a comparison map called the tracemap. Let me omit the zeroes, because as I mentioned, it's really a statement in higher algebraic k theory. Gives you a comparison between the difference in k theory to the difference in topological cyclic homology, which as I've said, it's on derived form of crystalline cohomology. So we can almost believe that the result is going to work now. It tells us that the obstruction for k0 is some derived obstruction in crystalline cohomology. Because we have a result of McCarthy from 97 telling us that this tracemap is an isomorphism in essentially full generality. You take any nilpotent thickening, even of non-commutative rings, and the theory produces an isomorphism for you. So that's the very general statement that starts us off. Can you call that step one? I'll try to break. And the k theory question involves, is the positive or also negative or the negative is zero? Also negative. The negative of y is zero, but the negative yr might not be. OK. And the difference is in the sense of spectra? Yeah, yeah. So I mean the homotopy fibers are weekly equivalent. Is this the after-tensoring with q? This is on the nose. On the nose for nilpotent thickening in any characteristic? Let's say characteristic p. Or at least where p is in the nilpotent ideal. Otherwise, I would need to p-complete both sides. The statement will be true in full generality after p-completing both Tc and k theory. Taking the p-completion of the spectrum. No, but you don't have a p in general. So I don't need to do it here. I don't need to. I mean if you're in characteristic zero, it's a different. Then it's true ration. No, then it's just not true. Then you should replace the right-hand side by classical cyclicomology. In characteristic zero, it is classical. Cyclicomology. And then you can play the same game actually to prove deframational Hodge statements in characteristic zero. The comparison with cyclicomology is older. That goes back to Goodwillian in the early 90s. Maybe in late 80s. So a consequence of this more or less tautologically is that our vector bundle, class Z, admits infinitesimal extensions to all orders if and only if the same can be said of its value in topological cyclicomology. So it makes it compute some topological cyclicomology. And the key second result, which is a result of Geisler and Heselholt from 99, tells you what topological cyclicomology of a smooth variety looks like. Emphasis on smooth. So because Y is smooth, they calculate the topological cyclicomology as pieces of logarithmic Hodge-Wittcormology. So already at this stage, we see that the class of the vector bundle admits infinitesimal extensions of all orders if and only if some property is satisfied by something awfully crystalline-looking. Thank you. And so the main difficulty is then to describe the topological cyclicomology of all these nilpotent thickenings, which are manifestly non-smooth. So we compare it just by functoriality to the topological cyclicomology. I should answer this also by q. Of x itself. And the third key step, which is recent joint work of myself and Bjorn Dundas, is the formal functions theorem for topological cyclicomology, telling us that this is, in fact, an isomorphism. So in contrast to k0, where a limit of k0 classes on the thickenings does not give you a k0 class on x. In fact, in topological cyclicomology, you have a limit of Tc classes on all the thickenings of the special fiber, and it algebraizes to a Tc class of x itself. And set p is in catecp. All mixed characteristic, as long as you p complete. It's a very general statement that if you work over any, say any Zp algebra, which mod p has a finite p basis, then the result goes through. Any Zp? So the result works if you have a smooth proper scheme over the spectrum of a complete ring, complete netherian ring, a complete netherian Zp algebra, complete for some i-addict topology, any ideal i, with the property that the ring mod p is finitely generated over its p-th powers. Yeah, yeah, that's finite p basis. No, no. And nor are there any smoothness conditions necessary. So very general, very general formal functions there. And i is contains p. Wait, i doesn't contain. No, n name is complete for the zero i-addict topology, so. Well, then I get a trivial statement that Tcx equals Tcx. It's relative to i, so I take the thickenings of the special fiber over i relative to powers of i. It's the exact analog of Groten-Tix formal functions for coherent cohomology. Sequeling of, do you use also special fiber for p? No. No, so once you'd probably assume. Yes, we'd better assume p is in i. And here also, when you take limit of Tc0, yr, isn't it more natural to do homotopy? Yeah, so I'm being sloppy about limbs and homolims.  But the natural statement is indeed that Tcx identifies with the homotopy limit of the Tcyr's.  Though that doesn't play any role in the proof. You can ignore the limb one term anyway, so it's not necessary to kill it. So what's so great about this is that we've now reduced the problem to understand topological cyclic homology of x, which might not be a smooth variety, but it's still regular. And that's enough to apply the Geyser-Hessel result again. So we apply step two again, which describes Tc of regular things to identify this with the log-hodge-wit co-homology of the whole family x. It's bad, but it turns out to work. Thank you, I keep forgetting the Q. I mean, so many of the snaps hold without putting Q, but. Of course, the usual references for there are V, it is not in this generality. So fortunately, either one looks at Professor Ilouzi's paper and checks that many of the results hold in greater generality using some now on the Popescu trick. Or you look at a paper by Atsushi Shihou, who has already checked many of these results. Yeah, yeah. No, I highly recommend that. He has a paper in which he exactly considers hodge-wit co-homology of arbitrary regular F.P. schemes and checks what are the minimum necessary conditions so that everything works. So it's not so bad after all. So finally then, step four, we want to identify this logarithmic hodge-wit co-homology with the expected eigenspaces in crystalline co-homology, which is, in this case, a completely classical comparison, since y is a smooth popper variety. But it turns out that the analogous comparison map for x itself is not quite an isomorphism, but you can still show that it's surjective using a very similar arguments to the smooth popper case. And so the final conclusion is that your vector bundle class on the special fiber admits infinitesimal extensions to all orders if and only if its value in the crystalline co-homology of y lifts to the crystalline co-homology of x with the restriction, which you can eliminate by, if you're projective, you can eliminate one of these left-shed arguments. But somehow, for the statement of the theorem, it's most natural to impose the eigenspaces restriction. Yeah. So that completes the proof of the sketch and of the talk. Thank you very much. Is there any questions? Yes. I have a question here on one. All right. Remember, the new key spot here and the proof is the weight of the number. So when you have your egg, which is on parter, then it's going to come back to take an egg bar. And the image of the HN of the egg bar into the HN of the egg in the bottom part is the weight inflation. So do you use some other option? Delinio uses this to extend the degeneration of the Lorentz spectral sequence from the projective case to the proper case. And I deliberately imposed the assumption that my family was projective to avoid that. But actually, I think that's a very interesting question. And I think it, I've given it some thought, and it seems to reveal some unknown aspect, either of crystalline or rigid coromology. We can consider precisely the situation of having some closed embedding of smooth, proper varieties. And we can suppose that I have some open, which contains the image of y. And then what Delinio does is he compares the image of the coromology of u in y with the image of the coromology of x in y. And he shows that the same. And it would be great to have an analog in crystalline or rigid coromology, but it doesn't seem to exist at present. And definitely, if I'm eliminating these projective assumptions or for extending the results, I think that's a necessary step. So I've talked to some experts in piatic coromology about this, but I get some general feeling that the theory of piatic coromology is still not at an optimal state. So here's the second question. You said that Tc is how it's close to that dirac crystalline coromology. Yes. You have the unheat coromology, so could you make the statement that you have to be precise? So I'd make the statement firstly that, as you see, it coincides on smooth things with logarithmic Gram-wit. It's very hard to say anything precise. But I think Bargab would agree with me. It's very interesting that this was coming. Yeah, I mean, I know he's thinking about this. I know he's thinking about the relationship of his theory with groups that you also see on the topological cyclochomology side. Well, let's discuss afterwards. Let's discuss afterwards. Yeah, yeah. I'm going to continue after the line. Thank you.


My name is Stacy Null and I'm the SEI Africa Center Director. My research focuses on water and poverty with a specific focus on how water is used in rural neighborhoods. A big issue in sub-Saharan Africa right now is foreign direct investment and especially large-scale agricultural investments. SEI Africa wants to get involved in this and to help national policymakers make decisions on how the environmental and social impacts of these investments can be managed. My areas of expertise focus on the intersection of small-holder farmers between land agricultural land management technologies and sustainable development as well as vulnerability assessment on disaster risk reduction. My name is Jacqueline Senyago. I work with the SEI Africa Center and my research focuses energy, particularly bioenergy. And I've also been working on other areas such as climate change, adaptation, sanitation. If you deal with the reality, with the real issues that affect people, then it's making an impact on what you're doing. That's why I like what I'm doing.


A bill to require motorists to use hands-free devices when talking on the phone while driving has passed its first committee stop in the Minnesota Legislature. A House Transportation Committee approved the bill on an anonymous voice vote after hearing emotional testimony from several people who lost loved ones in crashes caused by drivers who were distracted by cell phones. A Senate committee has a hearing on a similar bill Wednesday. Legislative leaders have said they expect hands-free legislation will be enacted this year and with bipartisan support. The bill has at least one more committee stop before it reaches the House floor. A Senate committee has a hearing scheduled on a similar bill Wednesday.