Hi, this is Mitch Mitchell, and I'm gonna tell you a truth. You know over the course of the last Might as well say four or five weeks. I've just been kind of running myself Silly, I'm sure that some of you not many but some of you saw the video I did where I was talking about leaving Memphis family and maybe you saw the videos where I was in Orlando and I was in San Diego and Last week I did an interview on this page And it was the first one I'd done from home in a while, and I gotta tell you the truth. I wore myself out. I Probably hadn't been sick for 15 years 1999 I remember cuz I had strep throat as I got close to my heck forget that the weekend of my 40th birthday I got sick that had strep throat and Other than that for 15 years. I may have had like a little cold for a day. That was about it I had coughs. I had allergic reactions like when I first went to Memphis. Whatever was in the air I had some kind of allergies to that. I've had allergies to dust, but you know as far as a sickness Catching a cold and getting sick like that I hadn't had anything like that in a very long time and it was odd because I didn't know what to do I didn't have a fever. I just didn't feel well And so I said well, you know, do I take aspirin? Do I take ibuprofen? Tylenol, do I take nyquil? Do I take dayquil? Do I take cough medicine at all? Do I take something to try to help me breathe better? I really didn't know what to do. My wife said fluids and take the nyquil and the dayquil and take all that stuff She had her special concoction that I'm not gonna tell you what it is But I'll just tell you it burnt my throat more ways than one And it took some time to recover from this even last week When I first got home where I came home for good on October 31st So when I first got home, I still wasn't feeling well And that's where she had me making this concoction this stuff that I don't know where she Oh, I think she got it from Dr. Oz Dog gun Dr. Oz always getting in my life somehow But still she got it from that. This is her concoction. She swore by it I did that for some days last week and you know eventually I started feeling better I still have a tinge of a cough, but that used to happen all the time So I'm not you know fretting over a cough the rest of me feels great now Except for the fact that I really haven't gotten any rest One of my plans had been when I got home I was gonna pretty much take two weeks to try to rest try to get some sleep because I almost never slept Without pills.  No, yeah, Tylenol or acetaminophen PM That stuff made me sleep, but it also made me wake up groggy So I decided I wasn't gonna go that route to get some sleep I was just going to try to see if I could sleep and according to Fitbit and I've got the blue band right now because I lost the red band the last flight coming back home That's a story in itself. So I've had to order a new another red band, but I You know according to Fitbit the most I slept in one night since I've been home is four hours It's just not really going to get it done. I need more sleep. Now now you're probably wondering What is all this I'm talking about? Well, I'm talking about this because last I'm gonna say what this past summer. I don't remember exactly when but I'm gonna link to the video where I talked about it I had a weekend where I just had some stuff that just happened I basically I'm diabetic and I crashed my number went so low I couldn't really get out of bed and I was dizzy and shaky and that's what happens sometimes I had gotten really low because I'd exercised too much than the next day It went way off the scale the other direction because I ate the wrong things But I ate a lot of it trying to make sure I didn't crash and I went to other direction So since I've been using basically the my fitness pal app, which I've talked about before and I added the Fitbit I've been under control and that part has been pretty good in my life. But what led to all that?  I need to try to live by that which is take care of yourself first and As easy as that sounds and as beautiful as that sounds and as true as that sounds Most of us don't really do that We think we do even the narcissists think they take care of themselves first But they really don't because taking care of yourself basically says that you're going to do all the things that Make you comfortable things that make you happy things that make you feel good and It encompasses a lot more than just eating better and sleeping better For me for instance, it takes planning. I mean since I've been home I've not planned a single thing. I pretty much just been going off the cuff and I've had I had an event last Friday And it was just an off-the-cuff thing that I decided to go to kind of a networking thing That was across town and I didn't think correctly It's so I took the wrong road going through the highway where of course traffic was backed up I'm still going in a way that I initially thought I should do because I didn't plan it and That kind of thing has been happening I ended up having to take my mother to Niagara Falls that hadn't been in my plans and That basically killed about six or seven hours in a day that I wasn't expecting being on the road again And I've just got so many other things that are on my mind And you would think that my silly self would think to write things down so that I've got it Planned right because I know that writing the things down having it all out and then being able to label You know, what's the most important and try to do things in order? I know that works well for me and it works well for a lot of other people, but I haven't done it I ordered this book from Brendan Bouchard called the motivate motivation Manifesto and I've seen you know the couple of the videos first videos that he's put out And he's got like seven or eight videos so far and I haven't put anything in the place so really I haven't been taking care of myself first and I really need to get to that because I need to get to a clear state of mind I mean, how am I going to take care of my business? How am I gonna take care of me? How am I going to make money? How am I going to pay the national grid bill? If we have another year like last year with all those polar polar Vortexes and I wasn't even home last year in my bills every month for $500 a month And we're supposed to have one of those this coming weekend and then one next week What the devil? This is November. I mean, we did have snow already, but this is the Syracuse We're supposed to have snow in November But you know, there's this thing that basically says that sometimes we try to take care of other people or sometimes We're just kind of selfish, but even when we're selfish, we're not really taking care of ourselves We don't do the things that really make us feel better I can tell you the truth since I've been using my fitness pal and the Fitbit My I don't have those stomach issues that I was having before so I'm not sick to my stomach anymore I'm not eating a lot of the wrong things because this stuff is tracking for me And that's actually a wonderful feeling, but that's only part of it I've got to take care of some of these other things and I know that I'm not alone I know that there's a lot of you who aren't doing the same kind of things either You're not doing the things that make you feel good the things that make you happy You know, nothing says that we're always supposed to be happy But if we try to do these things to take care of ourselves We will be happier We will feel better and when you feel better and you feel happier You want to help other people that get to that feeling as well. So I just want to say, you know, let's all Try to take care of ourselves first You know, if you're on an airplane and my god, I got this airplane thing down They always tell you put on your own mask first if it drops down put on your own mask before you try to help someone else Man, there's nothing more true than that because you can't help anybody else if you don't help yourself first So that's my little bit of wisdom for the night or for the day depending on when or if you watch this You know, let me know your thoughts. Give me your opinions and you know, let's take this journey together So let me know and it's just your first time Watching this, you know, when I got plenty of stuff like this and some other things. I've got a lot of interviews Think about subscribing, you know, first time I'm mentioning this and I may mention this another time But when I hit 200 subscribers, I'm giving 50 bucks away. Yes, I am you got a long way to go though So hold your breath for a while unless all of a sudden I get really popular Yeah, that's gonna happen anytime soon. Anyway, I'm Mitch Mitchell y'all take care and thank you for watching You


To my colleagues in the audience and fellow floaters, to the audience in the virtual land, good afternoon and good day. I would like to acknowledge my two co-investigators, Dr. Eric Mathews and Dr. Jeff Alexander from AT Still University. This is an overview of our research project, in which I will discuss with you the background and significance of our work and also the purpose. If we look at the purpose, the purpose arises from a problem, differentiating expert floaters from novice floaters. And there are a lot of medical reasons why we need to standardize that type of importance, both in terms of sociology as well as in terms of the practice of medicine and healing. But I would like to ask the audience a few questions.  One? A few? How many of you meditated with your eyes closed? Wow. How many of you have experienced altered states of consciousness with your eyes open? A few again? What about closed? Yes. Well, the evidence is written in stone that we can experience these states of altered states by having our eyes opened. And this statue, this photograph of this statuette was taken by me decades ago when I studied yoga in Northwest India. This is from the Dilwala Temple, where there are 180 yogis sitting in geometric arrangements and all of them have their eyes open. And this temple is about more than 2,000 years old. What we set out to measure, we defined as the altered states spectrum, including the generalized altered states of consciousness, the relaxation response, and shamanistic states of consciousness. But to do this, we had to develop a model. And this model we called the psych cell model, which has, as its pillars, a model developed by Pereira called the soul cell model and also the orchestrated observation reduction theory, or CoR theory developed by Hammerhoff and Penrose, which has a lot of quantum mechanics. This is an overall view of our experimental approach. We actually did an anonymous survey of 100 participants, and then we analyzed the data statistically. Of course, in interpreting the data, we used our model. But this is our research hypothesis in terms of generalized altered states of consciousness, which we measured by the mystical experience for the tree scale, the relaxation response, which was measured by the experience from normal deviation scale, and also shamanistic states of consciousness, which was measured by the Grayson-Nerdet experience scale. Of course, there are these regions which we associate with mindfulness. There is some commonality or sharing of these regions with the altered states spectrum. These are part of our preliminary or descriptive results. Of course, there were more female participants than male participants. But what we did find was a type of a synergistic effect, especially in the expert floaters compared to the novice floaters. We were also able to develop two very important equations from statistical analyses. One for predicting whether an individual will be an expert or novice floater, and the other one, which is this one here, for differentiating an expert and a novice floater. This is the equation for predicting. Dr. Gilda Costa has spoken a lot about brain waves, but then how do we interpret these findings in terms of brain waves? We adapted a biophysical approach in which we went into quantum mechanics. We know that if we look at the effects of meditation, meditation which is part of the altered states spectrum, has all of these effects, including at a translational and transcription level, as was demonstrated by Basim and Benson about three or four years ago. But we also know that this is happening at a quantum level because electrons are involved in neurotransmission. We know that electrons can behave as particles and waves. We also know that with these altered states, there are associated ultra-low photonic emissions called biophotons. And according to Hammerhoff and Penrose, this is happening at the level of the microtubules. We also developed a non-equation. Please don't be scared by this. Because what it is showing you is that the generalized altered states of consciousness will produce photons associated with the brain waves. The relaxation response will also produce specific types of photons and also shamanistic states of consciousness. But this is one of the problems that we all have to solve in FLRS research. We want to know exactly what's happening inside of the individuals. And our approach to do that is to develop from, to have a biomechanical and a biomimetic approach in which we use robotic animals to first demonstrate that we can detect the changes by using ordinary light and then to develop devices that are sensitive enough from biomimicry of the organs of special senses of super predators. This is work that is already in progress. For example, the ampullae of Lorenzini and sharks, they have developed a device from that that can detect electroreceptive changes in hyperosmolar solutions. One other application of FLRS is connecting floaters by two biochips in which we can then observe what is happening in the biochips. My other approach that I plan to do, conduct at the Genelocampus of Howard Hughes Medical Institute is to utilize a technique called Line Sheet Isovue Microscopy in which you can actually see the thoughts of zebrafish. I would close by acknowledging those individuals who played a role in the research and I would also say tanks a million or tanks a million.


Hi, in this video we have discussed a number of practice questions which will be helpful for Prelims 2020. Let's proceed to the first question. Now the first question increase in internal production was made a priority for the first time in independent India during the prime minister ship off. Increase in internal production was made a priority by the first finance minister of independent India, Mr. Shanmugam Shetty. He was finance minister during the period 1947 to 1949. It was Pandit Javaharlal Nehru who was the prime minister during that time period and he was the first prime minister of independent India. So the answer for this question is option D Javaharlal Nehru. Now the next question, which of the following countries share border with Persian Gulf? They have given Saudi Arabia, Lebanon, Oman, Iraq. So the options appear as bit tricky. Now if you don't remember the map you would easily think that Lebanon is also a country that is open to Persian Gulf. Now it is wrong because Lebanon shares border with Mediterranean Sea and not with Persian Gulf. So if two is wrong you can easily eliminate options B and options option D. So now we are left with options A and C. From both these options we can see that Saudi Arabia and Oman share borders with Persian Gulf. Now with respect to Oman the area of Musandam Peninsula actually borders the Persian Gulf and Iraq also shares border with Persian Gulf. Therefore the correct answer for this question is option C, 1, 3 and 4 only. Third question global trends report an annual report on the world level trends on displacement is released by which of the following. This global trends report is released by United Nations High Commissioner for Refugees. So the answer for this question is option C. Now the next question is with respect to Economic Advisory Council to the Prime Minister. They have given two statements and are asking which of the statements are correct. The first statement economic advisory council to prime minister has been constituted to advise the prime minister on all critical economic and related matter which have been referred to it by the prime minister. The first statement is correct because that is the main function of economic advisory council. So statement one is correct. Now the second statement the chairman of the economic advisory council is the chief economic advisor to the government of India. Now this statement is wrong because the chairman of economic advisory council is different from chief economic advisor of government of India. The chief economic advisor heads the economic division of department of economic affairs which comes under ministry of finance. Therefore second statement is wrong but the economic advisory council is constituted with approval from prime minister that includes a separate chairman. So the correct answer for this question is option A, 1, 1, 3. This question is with reference to United Nations Human Rights Council. In the first statement they have given two statements and are asking which among the above statements are not correct. So the first statement it is responsible for strengthening the promotion and protection of human rights around the globe. We know that this statement is correct and that is one of the main purpose of existence of this human rights council of United Nations. Since this statement is correct and they are asking which of the statements are not correct the statement one should not be in answer. In the second statement India was elected as a member country from January 2019 for a term of three years. This statement is correct because the council is made up of 47 member states including India that is from January 2019 for a term of three years. The council's membership is actually based on equitable geographical distribution with respect to five areas. They are African states, Asia Pacific states, Latin American and Caribbean states, Western European and other states and Eastern European states. If you take African states and Asia Pacific states, totally 26 seats, 13 seats for African, 13 for Asia Pacific, 8 seats goes for Latin American and Caribbean states, 7 for Western European and other states, 6 for Eastern European states and India was elected as a member country from January 2019 for a term of three years in this human rights council. So the second statement is also correct and India was elected last year in the month of October 2018. So both the statements are correct so the correct answer for this question is not both one and two but neither one nor two. Option D is the correct answer. Now this question they have given three statements and are asking which of the statements are correct. Now the first statement is all member nations of BBIN are also member nations of SARC. Now BBIN stands for Bangladesh, Bhutan, India and Nepal. We know that these four countries are member nations of SARC also, South Asian Association for Regional Cooperation. So the first statement is correct. Now the second statement India is not a member of SCO, Shanghai Cooperation Organization but it is a member of BBIN that is Bangladesh, Bhutan, India, Nepal. Now India is a member of Shanghai Cooperation Organization in fact both India and Pakistan became members of this Shanghai Cooperation Organization in the year 2017. So the second statement first part is wrong therefore the entire statement is wrong. Now the third statement states that all member countries of SARC are also member nations of BIMSTEC. Now if you take BIMSTEC you could not find Afghanistan, Pakistan and Maldives but if you take SARC you can see Maldives, Afghanistan and Pakistan along with India Sri Lanka and our neighbour countries. We cannot say that all member nations of SARC are also member nations of BIMSTEC therefore the third statement is also wrong. So we have to eliminate two and three therefore we will finally available with option A one only. So the answer for this question is option A one only is correct. Now this question they have given two statements they are asking which of the above statements is or are correct. The first statement neonatal mortality rate means number of deaths of children for the first 28 days of life per 1000 live births. According to WHO this is the exact definition of neonatal mortality rate therefore the first statement is correct and this period is the most important time for a child's survival as it is the most vulnerable period for a child's survival because it requires highly efficient and proper health care for the child during that time. Now the second statement sustainable development goal target 3.2 aims to reduce neonatal mortality rate to at least as low as 12 per 1000 live births. We know that sustainable development goal three deals with health and well-being target 3.2 asks all countries to aim to reduce this neonatal mortality to at least as low as 12 per 1000 live births. So this statement is also correct. So the correct answer for this question is option C both one and two. Now this question is with respect to water verified paper audit trail they have given two statements and are asking which of the above statements are correct. First statement it is a printer attached with electronic voting machine. Now this statement is correct because VVPAT is an independent system that is attached with electronic voting machines that allow voters to verify their votes that is they can check whether the votes are cast as they have intended. It's a printer that is attached with EVM and is kept into the voting compartment. So the first statement is correct. Now the second statement whenever there is any discrepancy in the match between VVPAT slips and EVM counts the EVM count prevails. Now the statement is incorrect because according to rule 56 capital D4B of conduct of elections rules of 1961 the VVPAT slip count only prevail whenever there is any discrepancy in the match between VVPAT slips and the EVM counts. So therefore only first statement is correct and they're asking the correct statement. Therefore the correct answer for this question is option A1 only. Now this question is with reference to Baba Guru Nanak Dev Ji. They have given three statements and are asking which of the statements are correct. They have asked to select the correct answer from the quotes given below. So the first statement he is the founder of Sikhism. So the statement is correct and he is the first among the 10 Sikh Gurus. So the second statement is also correct. Kartarpur corridor is constructed by India and Pakistan as part of his 550th birth anniversary celebrations. Now this statement is also correct. So all the three statements are correct. So as we know already from Indian side this Kartarpur corridor will start from Deira Baba Nanak town in Gurudaspur district in Punjab till the international border between India and Pakistan. So this is from Indian side and from Pakistan this corridor will extend from the international border till it connects the Gurudwara Darbar Sahib in Kartarpur in Pakistan. So the correct answer for this question is option D 1 2 and 3. Now this question is with respect to Interstate River Water Dispute Act of 1956. They have given three statements and are asking which of the above statements are incorrect. So the first statement the central government shall constitute a water disputes tribunal for adjudication of water disputes that arises between the states. So this statement is correct. This is based on section 4 of the Act of 1956. See when any request is received from a state government with respect to any water dispute. And also when central government is of the opinion that a dispute cannot be settled by negotiations, the central government shall constitute a river water disputes tribunal. So the central government will notify in the official gazette that a water disputes tribunal has been constituted to adjudicate the particular water dispute. So this statement is a correct statement. Now we know the question is asking for incorrect statement. So when statement one is correct, it cannot be in the answer. So easily you can eliminate option A, option B and option C. So the correct answer for this question is option D 2 and 3 only. Now let's come to the second statement. It tells that the chairman of the tribunal is nominated by the President of India. But according to the Act based on section 4 subsection 2, the tribunal shall consist of a chairman and two other members who are nominated by the Chief Justice of India. So it is not the president who nominates the chairman of the tribunal. It is the Chief Justice of India. Therefore the second statement is wrong. Now the third statement, the decision of the tribunal is non-binding on the parties to the dispute. Now this is also wrong because according to section 6 of the Interstate River Water Dispute Act, the central government will publish the decision of the tribunal in the official cassette and this decision shall be final and binding on the states who are parties to the dispute. So here we find that the statements 2 and 3 are incorrect. So the correct answer will be option D 2 and 3 only. This question is with reference to the right to vote. They have given two statements and are asking which of the above statements are correct. The first statement, it tells that the right to vote has been explicitly mentioned in the Indian constitution. Now this statement is incorrect because nowhere in Indian constitution the right to vote has been explicitly mentioned. So even in fundamental rights we cannot find right to vote was directly mentioned in the Indian constitution. So the statement is wrong. The second statement, the right to vote as of now cannot be exercised by the persons confined in prisons with the exception of those who are subjected to preventive detention under any law for the time being enforced. Now this statement is correct. This is correct according to section 62 subsection 5 of the representation of the People Act of 1951. It says that no person shall vote at any election if he is confined in a prison but this provision does not apply to a person subjected to preventive detention. So therefore only the second statement is correct. Therefore the correct answer is option B 2 only. Now this question is with reference to Intergovernmental Panel on Climate Change. They have given three statements and are asking which of the above statements are correct. They are asking to select the correct answer from the given code. This IPCC is a United Nations body and the main purpose is it assesses the science related to climate change. So the first point is correct. Now the second statement, its objective is to provide governments with scientific information at all levels to develop policies at national and subnational level related to climate. So this statement is also correct. But the third statement, it conducts its own research. Now this is wrong. IPCC does not conduct its own research. The scientists who are working in IPCC, they assess various scientific and research papers that are published each year. So it is this part of assessment go into the various scientific papers and provide some kind of comprehensive summary with respect to climate change, the impact and also the future risks. So the third statement is wrong. So the correct answer for this question is option B 1 and 2 only. Now this question is with reference to Brahmos missile. Again they have given three statements and are asking which among the above statements are correct. The first statement, it is a hypersonic cruise missile. See this statement is incorrect because it is a supersonic cruise missile. So when we say cruise missile, it's an unmanned self propelled guided vehicle. See depending upon the speed of the missiles, missiles are classified into three types. One is subsonic cruise missile, then is supersonic, then hypersonic cruise missiles. If you take subsonic cruise missile, it flies at a speed that is less than the speed of sound. The speed of sound is 343 meter per second and this 343 meter per second is called as one Mac. Okay, so the speed of subsonic cruise missile will be less than one Mac or less than 343 meter per second. Now supersonic cruise missiles are those missiles that travel at a speed of around two to three Mac, that is approximately one kilometer in one second. If you take hypersonic cruise missiles, they travel at a speed of five Mac. So the Brahmos missile is a supersonic cruise missile. So the first statement is incorrect. Now the second statement, it operates on fire and forget principle. Now this is correct because missile guidance is not required after the launch of the missile because it can hit the target even though the launcher is not in the lineup site of the target. The last statement, it says that it is uniquely configured for installing in ships, submarines, aircrafts and on ground vehicles. Now this statement is correct and that is one of the special features of Brahmos missile. Overall, the missile can be configured for installing in ships, submarines, aircrafts and ground vehicles. So the correct answer for this question is option C, two and three only. Now this question is with reference to wild buffalo. They are asking which among the following statements are correct. Now the first statement, it is found only in the northeastern region of India. Wild buffaloes are found in northeastern region and also in central India, particularly in the state of Chattisgarh. And according to wildlife trust of India, the estimated population of wild buffalo in the northeastern region is around some 3000 to 4000 individuals. And they say that within the Indian landscape, the northeastern region constitutes the largest population of wild buffaloes. At national level, if you take the total number of wild buffaloes in India, they constitute 92% of world population of wild buffalo. So we can say more than 90% of wild buffaloes are found in India. So the first statement is incorrect. But if appropriate conservation measures are not taken to protect the available wild buffaloes in the central Indian region, maybe in future this statement may become correct. If the wild buffaloes become extinct in the region of central India. Now let's come to the second statement. They are saying it is protected by the Wildlife Protection Act of 1972. Now this statement is correct and wild buffaloes are protected under Schedule 1 of Wildlife Protection Act of 1972. So the second statement is correct. Now the third statement, it is listed as endangered by the International Union for Conservation of Nature's Red List. Now this statement is also correct. According to IUCN, total matured individuals are roughly around 2500 only. However overall we can say some 3000 to 4000 individuals are there in the world. And their population trend is decreasing. So they have been listed as endangered by IUCN Red List. So the correct statements are 2 and 3. So the correct answer should be option C 2 and 3 only. Now let's go to the next question. Consider the following statements with reference to diphtheria. They have given 3 statements and are asking which of the above statements are not correct. First statement says it is a contagious disease. When we say contagious, it is communicable disease. That is the disease can easily transmit from one person to another. So diphtheria is an infection of nose and throat that can spread easily through direct contact with the infected person through infected cough or sneeze droplets. So the statement 1 is correct. Now the second statement, it is caused by a virus. Now we know that it is caused by a microorganism for sure, but it is not a virus. It is bacteria. So it is caused by a bacterium called as corinibacterium diphtheria. So therefore the second statement is not correct. Now the third statement, until now there is no vaccine for the disease. Now this statement is wrong because diphtheria or pertussis is a vaccine preventable disease. So the third statement is wrong. So they are asking which of the above statements are not correct. Only first statement is correct. So the answer should be option D 2 and 3 only. This question is with reference to council of scientific and industrial research. So they have given 3 statements and are asking to select the correct statements based on the given codes. The first statement CSIR works under Ministry of Science and Technology. CSIR was established in 1942 and at present it is working under Ministry of Science and Technology. And the vice president of this organization is the Minister for Science and Technology. So the first statement is correct. The second statement says it is a body registered under Societies Registration Act of 1860. Now this statement is also correct. Now the third statement it is presided by the Prime Minister of India. Now this statement is also correct. The president of this organization is the Honorable Prime Minister of India. So the correct answer for this question is option D 1 2 and 3. Now this question is with respect to national essential diagnostics list. They have given 2 statements and are asking which of the above statements are correct. Now first statement it consists of general laboratory tests that are required for routine patient care and for diagnosis of a wide array of both communicable and non-communicable diseases. See this statement is correct. So it consists of essential lists of diagnostic tests that have to be carried out by the health providers. The second statement it has been developed and launched in India by the council of scientific and industrial research. Now this statement is incorrect because it was developed and recently released in India by the Indian Council of Medical Research. Earlier in December 2018 the Indian Council of Medical Research has released the draft of national essential diagnostic list for comments and feedbacks. But recently they have finalized it and have uploaded in their website. So the correct answer for this question is option A because only the first statement is correct. Now this question is with respect to persons belonging to Santal tribe. They have given 2 statements and are asking which of the above statements are correct. First statement they are the people belonging to the schedule tribes who live only in the state of Odisha. Now this statement is wrong because persons belonging to Santal tribe are also living in the states of Bihar, Jharkhand, Tripura and West Bengal and in all these states they have also been notified as schedule tribes in the list of schedule tribes. Other than Jharkhand they are called as Santals and in Jharkhand they are called as Santals. Now the second statement they are listed as particularly vulnerable tribal group. Now this statement is not correct because they are not classified under PVTG category in any of these states. So the correct answer for this question is option D because both the statements are wrong. Now this question is with respect to New Space India Limited. They have given 3 statements and are asking which of the above statements are correct. The first statement the New Space India Limited is the commercial arm of DRDO, Defense Research and Development Organization. Now this statement is incorrect. This is because the New Space India Limited is a commercial arm of ISRO under the Department of Space. So it was set up as a or a fully owned Central Public Sector Enterprise on 6th March of 2019. Now the purpose is to commercially exploit the R&D work of ISRO and it also carries out some commercial work for other constituent units of the Department of Space. It will perform the role of small satellite technology transfer to industries and it will also manufacture small satellite launch vehicle in collaboration with private sector and it will also produce PSLV launch vehicles through Indian industry. It will also produce and market space based products and services. It will also market spin-off technologies and products and services both in India and abroad. So these are the objectives of New Space India Limited. Now let's come to the second statement. The objective is to spearhead commercialization of space products including production of launch vehicles, transfer of technologies and marketing of space products. So these are the functions carried out by NSIL and the second statement is correct. Now the third statement Antrix Corporation Limited is the first commercial arm of ISRO. Now this statement is correct. It is also a fully owned Government of India Company under the Administrative Control of Department of Space. It was established in September 1992. So the third statement is also correct. So therefore we find statement 2 and statement 3 are correct and therefore the correct answer for this question is option C 2 and 3 only. Now this question is with respect to National Air Quality Index. They have given two statements and are asking which of the above statements are correct. Now the first statement there are six air quality index categories which are decided based on the ambient concentrations of air pollutants and their likely health impacts. See this statement is correct and the six categories are good satisfactory moderately polluted, poor, very poor and severe. Now the second statement both particulate matter 2.5 and particulate matter 10 are part of the air pollutants that are measured as a part of this index. Now this statement is also correct. See around eight air pollutants are checked. They are PM10, PM2.5, NO2, SO2, carbon monoxide, ozone, ammonia and lid. Therefore both the statements are correct. Therefore the correct answer is option C both 1 and 2. Now this question is with respect to Central Pollution Control Board. They have given again two statements asking which are the statements are correct. First it is a non-statutory body. Central Pollution Control Board is a statutory body that was constituted under Water Act of 1974. So this statement is wrong. Now the second statement one of its principal functions is to improve the quality of air to prevent, control and abate air pollution in India. This statement is correct. Now this is based on Air Act of 1981. So only the second statement is correct. Therefore the correct answer is option B 2 only. Now this question is with respect to Total Fertility Rate. There are two statements asking which of the statements are correct. First statement Total Fertility Rate means the total number of children born or likely to be born to women of childbearing age in her lifetime. Now this definition is correct. So the first statement becomes correct. Now the second statement as per NFHS4 data the TFR of India is higher in urban areas when compared to the rural areas in India. Now this statement is wrong because it is other way round. It is higher in rural areas when compared to urban areas in India. So only the first statement is correct. So the correct answer for this question is option A 1 only. This question they have given two statements and are asking which of the above statements are correct. Now the first statement both Tibetan Grey Wolf and Indian Grey Wolf are found in Peninsular India. Now this statement can be easily eliminated logically. See the statement is saying it is Tibetan Grey Wolf. Obviously it cannot be found in Peninsular India while Indian Grey Wolf can be found in some eight states such as Gujarat, Rajasthan, Haryana, Uttar Pradesh, Madhya Pradesh, Maharashtra, Andhra Pradesh and Karnataka. The Tibetan Grey Wolf can be found in Himalayan landscape particularly in the elevation between 3000 meter to 4000 meter. And that is one of the reasons why the Tibetan Grey Wolf is called as Himalayan Grey Wolf. So the first statement is incorrect. The second statement the Indian Grey Wolf is protected under Schedule 2 of Wildlife Protection Act of 1972. So this statement is incorrect. This is because it is protected under Schedule 1 of WPA 1972. Now two other animals one is Tibetan Grey Wolf and another is Leopard Cat. These two animals are also listed in Schedule 1 of WPA. Now the difference between Schedule 1 and Schedule 2, 3 and 4 is that with respect to section 11 of WPA 1972. For Schedule 1 animals they can be hunted only if they become dangerous to human life or only if they become disabled or deceased beyond recovery. And this permission has to be given by Chief Wildlife Order. But the animals specified in Schedule 2, Schedule 3, Schedule 4 can be hunted on two grounds for which Chief Wildlife Order can give permission. One if they become dangerous to human life. Two if they become dangerous to property. This property also includes standing crops on any land. Now given a case a Schedule 1 specified animal if it creates damages to property it cannot be killed whereas those animals that are protected under Schedule 2, 3 or 4 if they cause damage to property they can be hunted under the permissions of Chief Wildlife Order. So both the statements are incorrect. Therefore the correct answer for this question is neither one nor two. Now this question is with respect to G7 grouping. First statement the grouping includes 7 leading industrial countries. Now this statement is correct. If the statement is given as 7 leading developing countries then the statement would have been wrong. Now the 7 leading industrial countries that are part of this G7 grouping are US, UK, Japan, Italy, Germany, France and Canada. So this statement is correct. Now the second statement in 1998 Russia was formally admitted to the group making it the G8. Now this statement is also correct. But after the Russian annexation of Crimea the G7 nations decided in 2014 to meet hereafter without Russia. Anyhow the second statement is also correct. Now the third statement India is not a member of this grouping. See India is not a member of this grouping. We India will be admitted once it becomes a leading industrial country. But at present India is not a member country. So all the three given statements are correct. Therefore the correct answer for this question is option D, 1, 2 and 3. Now this question is with respect to balance of payments. They are asking which of the following comes under capital account of India's balance of payments. We know that balance of payments is divided into two accounts. One current account, two capital account. Imports and exports come under current account. Therefore one and two will not be part of this capital account. And we know that both foreign portfolio investment, foreign direct investment are capital investments and they come under capital account under the foreign investments. Other than this we can find external assistance, external commercial borrowings, short term credits and NRI deposits. These are also part of capital account of balance of payments. So the correct answer for this question is option B. Now this question is with respect to the World Energy Cities Partnership. They have given three statements and are asking which of the above statements are correct. Now the first statement it is established in 1995 and it is a non-profit organization whose member cities are globally recognized as international energy capitals. The member cities are recognized as international energy capitals and our neighboring country China has three such cities which are member cities in this partnership. But no Indian city have become a member city in this partnership. So this makes the second statement incorrect because it says one or more Indian cities is or are members in this partnership. Now the moment you decide the second statement is incorrect you can arrive at the correct answer. This you can do by eliminating the options which say the statement 2 is correct. You can eliminate option A, you can eliminate option B and you can eliminate option D so that the probability of attempting the correct option will become 100%. So the correct answer for this question is option C 1 and 3. Now coming to the third statement the secret area of this partnership is in Houston in Texas state of United States. Now this statement is correct. Houston is called as the energy capital of America. Third statement is correct only the first and third statements are correct so the answer is option C. Now this question is with reference to Paris Agreement we have been given two statements and they are asking which of the above statements are correct. The Paris Agreement's central aim is to strengthen the global response to the threat of climate change by keeping a global temperature rise this century fell below 2 degrees Celsius above pre-industrial levels and to pursue efforts to limit the temperature increase even further to 1.5 degrees Celsius. Now this statement is correct this is the main ambition of this Paris Climate Accord or Paris Climate Agreement. Now coming to the second statement this landmark agreement was reached in 2015 on the 21st session of conference of parties to the UN Framework Convention on Climate Change. Now this statement is correct the 21st session of COP was held in Paris and that is why it is named as Paris Climate Accord or Paris Climate Agreement. See the conference of the parties of UNFCCC is the supreme decision making body of the convention. Here when we say convention it means United Nations Framework Convention on Climate Change and also know that the conference of the parties they meet every year. Every year the presidency with respect to the COP also rotates among five recognized UN regions. Not only presidency also the venue of this conference of the parties. The five regions are African region, Asian region, Latin America and the Caribbean, Central and Eastern Europe, Western Europe and others. This sessions of COP are also called as International Climate Change Conference. Last year it was conducted in Katowice in Poland in the month of December. Both options are correct therefore the correct answer is option C both 1 and 2. Now this question is with reference to sites convention they have given three statements and are asking which of those statements are correct. First statement the convention on international trade in endangered species of wild fauna and flora is an international agreement to regulate the international trade of plants and animals including their products and derivatives to ensure their survival in the wild. Now this statement is correct. Now the second statement India is not a party to this agreement. India has been a party to this convention since 1976 after the agreement came into force in 1975. So the second statement is incorrect here. India is a party to this agreement or this convention. Third statement. Once the second statement is wrong we can eliminate option B and option D and this increases our probability of attempting the correct answer to 50 percent. Now the third statement appendix 1 includes species threatened with extinction and the trade in specimens of these species is permitted only in exceptional circumstances. The first and third statements are correct. Therefore option C is the correct answer. Which of the following animals are classified as vulnerable under the international union for conservation of nature? Red list of threatened species. Star tortoise, smooth coated otter, small clawed otter and toke gecko. The first three animals are now protected under appendix 1 of sites convention as the 18th conference of the parties to sites convention recently approved India's proposal for better protection of these three animals. Star tortoise, smooth coated otter and small clawed otter. All these three animals are also listed as vulnerable in IUCN red list. Toke gecko has been listed as least concerned. So therefore fourth point should not be there in options. So we can eliminate option C and D. So the correct answer for this question is option B 1, 2 and 3 only. Now this question is with reference to commonwealth parliamentary association. They have given two statements asking which of the above statements are not correct. Now the first statement it is a voice of the parliamentary democracy across the world. See commonwealth parliamentary association is the voice of parliamentary democracy across the commonwealth countries. So the first statement is incorrect not across the world. Now the second statement the objective of the commonwealth parliamentary association is to promote rule of law and individual rights and freedoms and also to pursue the ideals of parliamentary democracy. Now this statement is correct. So the incorrect statement is first statement therefore option A becomes correct answer. Now this question is with reference to werewolf syndrome. Few kids in Spain getting affected by this syndrome because of medicine mix up or because of wrong treatment of gastric reflex. This syndrome is also called as hyper trichosis which refers to excessive hair growth. So therefore the correct answer for this question is option D a medical condition that causes excessive hair growth in the human body. So the correct answer is option D. These are some of the practice questions for the day. If you like the video click the like button, comment, share and subscribe to Shankaray's Academy YouTube channel for more updates and content on civil service exam preparation.


Black Hands you'll take me to his Stay at your time The use of energy in the world is increasing and that is causing lot more fossil fuels such as coal and gas to be used to produce energy Of course this implies the pollution implies greenhouse gas emission that strongly affect and negatively affect.. ..the climate change ac, for example, we can use cleaner technologies or other more renewable technologies like wind and photovoltaics, and perhaps in the future others such as tidal and wave power. Policy makers can in fact better plan the use of energy, the production of energy by fostering the use of renewable energy sources and energy efficiency. ac mae'r cyffredin iawn i'r grannu gwahanol, ond mae'n ddiwedd i'ch mynd i'ch cyfan o'r ddod yn dda'r ffordd. I ddod i ddod i'ch gael o'r ffordd i'ch cyffredin iawn? Mae'r polisi E wedi gwneud. Y polisi E wedi'i unrhyw gyffredin iawn i Ff7. Mae'r pryddwyddiad yng Nghymru i'r 2.6 miliwn i'r hollu 3.2 miliwn. ac rydyn ni'n ffordd yw 9 parnydd, a dyna yw yw yw 11 oed. E-Polisi yn y blynyddu yw'r tynnu cyffredinol cyd-fawr yn ymgyrch, o'r ddim yn ymdegau arall. Ymdegwch yn ystafell o'r ddweud o'r ffordd yw'r cyffredinol yw'r cyffredinol. My goal is to establish a set of web-based sources using e-participation tools and from these web-based sources to try to crawl for the posts of the public and try to infer what is their opinion concerning different alternatives related to energy policies. So, one further aspect we are looking at at the policy project is how the different energy policy actually affect the population of the Emilia Romagna region. And what we then did is actually looking whether particular groups such as different age groups or different educational groups react differently. So, we get a better understanding of how people actually perceive photovoltaic but also how policies can be best designed to help them to do photovoltaic. And this is where optimization technology comes in because here we want to make decisions that are optimal with respect to the distributions of the funds to the bids. So, in particular, we want to fund the bids that are good so that produce a relatively large amount of power given the amount of money spent on it. And on the other hand, we don't want to fund the bids that ask for a lot of money and install a relatively small amount of power. One of the components of the policy project is a global optimizer that basically takes into account some target function that the policymaker wants to optimize to maximize or minimize. For example, he wants to maximize energy. And then he can post additional constraints on the energy sources and constraints on the budget, for example. And then he computes one plan. And the plan basically can be compared with other plans, so alternative scenarios in the future. It has an impact on the environment here in the interface. And it can be compared concerning cost, energy, and also all the environmental indicators. The general goal that we have to provide an interface that can be used not only for policymakers to observe these trends on the opinions, but also to use this information to feed in the models that search for the optimal plans and taking also into account this general opinion of the public. A policy has the main aim of providing policymakers with a decision support system that enables them to compare alternative scenarios and to assess their impact on the environment, the society, and the economy. So basically a policy is based on decision support techniques and optimization techniques to enable policymakers to assess all the phases of the policymaking life cycle. E-policy actually has great potential to be transferred to other areas as well. Other areas of energy policy and indeed other areas of policy in general.


Thank you very much and thank you to the organizers for the invitation to speak. So I'll just say that so Luke mentioned, look you're already laughing I haven't said anything yet. So at the beginning Luke mentioned you know several categories in which people benefited from OFA and I would say I like fall into several of those categories. I'll might kind of tell some stories at the end. So today I want to talk about some questions around Hilbert's 13th problem and their connection to the moduli of the Bieling varieties and this is joint work with Benson Favre and Jesse Wolfson. This is Benson here. This is Benson. You know I make the remark that when I have the graduates students coming in they seem to know more and more and the reason is they start earlier and earlier. This is not Jesse. This is Jesse's son Leo. Okay, so what kind of question do I want to consider? So if you take a variety of an algebraic closed closed field of characters to zero and let's just consider a connected finite etal cover of this variety and we're interested in some sense in the geometric complexity of y over x and what I mean by this and I want to ask myself kind of what is the smallest the smallest dimension such that this cover comes from a pullback of of something of that small dimension so we'll define the essential dimension of the cover through the smallest integer such that there's a dense open u and x and a map u to some u prime such that first of all u prime has dimension e and y comes from the pullback of a covering u prime over e prime some finite etal covering and let me just say here the fact that in this definition you're allowed to take some dense open is absolutely crucial so that's something to keep in mind a lot of these questions become much easier if you just insist that u is equal to x but we don't want to do this here and maybe the reason I mean the reason will maybe become clear a little bit later on then there's a second kind of definition where we also allow composites of such coverings so what do I mean so the second definition resolvent degree uh where I have the same thing I have a covering and then I want to consider the smallest integer such that there's a dense open and a tower of coverings over the dense open such that each of them has essential dimension less than or equal to r so each one of these comes from something of smaller may well possibly smaller dimension r can be r might be the dimension of x and also the at the top I dominate the covering that I started with okay and of course everything is connected everything is well I assume that y over x is connected right otherwise I think from the beginning because of the other question about the empty sense certainly them terminates 12 you don't want some you should better assume that the finite oh you mean there's they should be non-empty if they're finite at all but they could be empty I think a finite is like finite is being subjective but yes, let's uh that's for uh connected and for completeness we have said the connected here means also non-empty yes not like you hope okay already the talk became empty within in a few minutes okay so okay so here we have the definition again of resolve and degree so there are two notions again right one is like for the individual covering whether it comes from something of small dimension and then you have like towers okay and then there's a notion of uh for a group just for a finite group you can define essential dimension and resolve and degree of the group as the soup overall coverings y over x such that the gala closure has group g I'm in characteristic zero my k was characteristic zero okay so later on i'll use some arguments right at the end in mixed characteristic but for now most of the talk k will be in characteristic but the question is in characteristic zero um Okay, so we're up to here um Okay, so we have this definition So in fact it turns out this notion of essential dimension resolve and degree if you have a covering it's the same for the covering or for its normal closure So it's kind of invariant to that so this is for a group g But notice that when you reduce the field definition you don't say that the g What okay when you take the g it doesn't mean that the the g-toss so If you take a g-toss over a variety it doesn't mean the generic lead comes from a g-toss so Yes, you have to prove that though It's true You mean the question are you asking just if you have a covering but now it has some extra structure like it's a g-toss So because suppose you have a g-toss To settle in the gala closure As group g Okay, so your definition is that you can reduce the field definition to a south field or to a south field degree here Okay, but just as a finite talcaval Not as a g-tosser Yes, but but it's the Yes, exactly. Yes. Yes. Yes. Yes. It's the same. Yes. Okay Did everyone Yeah, so first question, I mean which we're going to sweep under the rug is here. I'm just when you have a covering I The question is about reducing it to smaller dimension but as a covering But maybe it has some extra structure. Maybe it's a local system or a g-tosser and maybe you want to reduce The dimension with that structure. In fact, it turns out that it's equivalent to that, but that's a little lemma Which took me a little bit longer to prove Okay All right So these definitions are due to a Resolven degree are due to Broward, Shamar, Anold and For an essential dimension are due to Bula Reichstein But in fact, they formalize a circle of questions going back to Hamilton, Hilbert and others Actually, as as you'll see like this subject is a very strange subject because you know, usually you have like one definition And the second definition using the first one comes after that in time Or maybe you have like a conjecture and then the theorem gets proved after the conjecture in this subject Everything is kind of in the opposite order. You'll see so for example here Sorry, I've got here the definition of resolvent degree was formalized by Shamar, Anold and Broward And the definition of essential dimension was given later by Bula and Reichstein I mean they gave it in a kind of more general context Okay So let's look at an example This was the classical one of the classical examples that was of interest to Hilbert So let's look at the space of monic separable polynomials of a degree n So it's given by affine space in n minus one coordinates just given by the coefficients minus the discriminant locus And this has a covering where I look at the solution of the polynomial, right? So you have f as a polynomial and then z as a solution to the polynomial. So this gives a covering And well the essential dimension of this covering is the Of course this is a this covering its normal closure has gala group sn And it's kind of the generic sn covering So its essential dimension is the essential dimension of the group same for resolvent degree And notice here this is going to be kind of one of the rules of the game The resolvent degree of sn in fact turns out to be the same as the resolvent degree of an Because this is just an index two subgroup And as we'll see in a second When I have a cover of degree two, I can always kind of reduce it to Something one dimensional. So I mean that's kind of easy, but I'll mention in a second So what is known about the resolvent degree? So for n equals one It's due to the Babylonians that this is equal to one This is the paper Okay, so Sorry Can I enlarge it? Yeah, this is I mean this is a um I of course, I can't literally if I try to do it now. It'll be a disaster, but uh I'm not sure that the ideas that you use for that In the formulation of the notion like you have to speak about algebraically close Yeah But I already mentioned earlier of that in the subject everything is lacking reverse order So it's true that the Babylonians didn't know what a finite detail cover was Nevertheless, they had proved this theorem As you can see because the paper is right here Right, so the point is that um When uh n equals oh, uh, sorry did I mean n equals one? I mean n equals two Sorry n equals one is not so interesting. Sorry, that's a typo n equals two n equals two Yes No, no, no monic Monic. Yes. No, no monic, but you can delete you can you can get rid of one We're not doing that. Yes, but we're not doing that. Yeah, it should be n because Oh, sorry. Sorry. Sorry. Okay. I knew there would be some typos here. Yeah. Okay. Anyway Um, that's fine. Okay. So this should be an n. Anyway, so this should be n equals two That's terrible. Okay. So uh, but let so the point is you have a quadratic formula, right? So if you have a covering of degree two Uh, then you know that this is basically given by extracting a square root Okay, and which means and then this function f Gives you a map to gm And so then this comes just from this application by by degree two That's the result of the Babylonians Okay And then for n equals three and four you have a similar thing um By kind of there was this classical problem of solutions of polynomials of some degree Where there could be solved in radicals. So you have to target a cardano and Ferrari Solved this in degree three and four notice there you in the formula you have to kind of compose Functions right because you have to take a sequence of radicals Um Okay And then for n equals five there's a result of bring from 1786 that it's still equal to one So the point there is after you extract Some roots for example a square root of the discriminant. I think there are also some other things You can bring the polynomial into fifth degree polynomial into this form So you you kind of only have one parameter Uh, and then well Hilbert was interested in this kind of question He conjectured that for n greater or equal to six the Resolvent degree was greater or equal to two and in particular for small values He had computed and he made some conjectures for small values So if n equals six is two n equals seven is three This is the one that has to do with if you look in Literally the 13th problem of Hilbert and the icm address. It has to do with n equals seven Um And then uh, it's four if n equals eight and nine and one thing is he had already shown an upper bound in these small cases he'd checked that uh That the resolvent degree was at most this value in each of these cases In particular in the case of nine the fact that nine is the same as eight As a slightly tricky argument You mean there is an argument showing that the answer for eight is equal to the answer for nine Well, yes, but With the eight with the answer. No, no, no, I don't know if Yeah, that I don't know if that's true. Maybe um I mean he he just got an upper bound so And the and the royal bound is broken No, this is a conjecture conjecture Okay, it's part of the conjecture. So the statement is still this is still sorry. The whole thing is a conjecture. Yeah Isn't I mean you can see that from the types at latex typesetting see it's like all conjecture Okay And here's a remarkable fact. There are actually no examples of covers which you where you it's proved It's proved that the the resolvent degree is bigger than one So for essential dimension, that's not the case there are you can do something for essential dimension There are non trivial upper bounds for a resolvent degree So this is going to be one of those theorems where everything happens backwards. Okay, so there's a theorem which you do Hamilton That if you look at the resolvent degree of this cover for the solutions of the polynomials Then well, of course, this is at most n Okay In fact, you can do better than that But what they what he showed is that if you take any positive integer r Then there's some h of r such that Oops such that n for n bigger than h of r you have this Okay, sorry about the typos Unfortunate you can't kind of go up there with a torque and correct it. Okay So basically if you so if you fix r and n is big then you kind of can improve the bound Okay, but in Hamilton this this h of r grows incredibly quickly And then this result of Hamilton was forgotten. It was conjected by Segre in 1947 And it was reproved by Brouwer in 1975 And this is Hamilton and Brouwer But again in the days of Hamilton, I believe that things were The notions were the more primitive That's right, and I'm going to explain what the primitive notions are so I kind of deliberately I mean I introduced it this way maybe for my benefit because I always get confused with the The primitive notions I'm going to try to Sorry, what was that? Well, I I will in a second, but before I confuse you I will you know, I'm going to tell you how I think about it. So Well, also how I'll say Brouwer thought about it. Okay So here's the historical interlude. This is the question. How did they think about it? Okay So they thought about this invariant in terms of whether if you have say a solution of a general polynomial of a degree n It could be expressed in terms Of a composite of functions of r variables where r is less than n Okay, so let's try to translate this into that notion Okay, so if you have a cover, let's first try to think about the the notion of a central dimension in that kind of setup So if you have a cut a finite cover and let's assume we've already kind of replaced x by this open Okay, so let's consider first a section Of this cover now this cover we thought of as connected So of course, there's no literal section But you can think of this section as either kind of being a multi-valued function or maybe it's defined locally okay And let's suppose now that this y to x comes from some y prime mapping to x prime with the dimension of x prime less than the dimension of x Okay, then you can choose. I mean, so y is the fiber product of y prime and x of x prime So you can actually choose a section here and then this guy comes from here And then f is a function It's really determined by f prime So if you think about what's going on here, it means that f is a function and this number of variables if you think of Some local coordinates here So if you also think about this question, let's say in terms of real or complex analysis, just take functions In the classical example, yes, whether it is a composite just of analytic That's right. Yes, and this is something which doesn't require to have this algebraic That's right. Yes. I'll get to that too There I mean, there are many variants of this question Um, depending on the kind of functions used Okay, uh, so there's a function in this number of variables That's how you think of f Okay, so there's our diagram and now let's think about the situation of a composite So if you have a tower like this and each one of these has essential dimension equal to r say Then you choose sections like this And then if you think about what's going on then this composite Section is a composite of these functions these sections and each one of them has our variables so So this is a this kind of section is given by a function in our variables. Okay And so what Hilbert actually asked about in in the thirteenth problem Is he discusses? I mean Hilbert. I should say Hilbert has um He wrote about this question in other places So the this thing about I think algebraic solutions is what he was interested in But what he wrote in the thirteenth problem? He asked whether This was equal to three and then particularly asked whether you could just show this in In kind of a naive way namely whether if you have we have a function in Sorry, so you have this general equation of degree seven Okay, and you have the you have a solution And whether it could be written as a composite of function in Functions the less than equal to two variables even locally even at the level of continuous functions. So locally means I mean We're over p seven which is let's think of it as a complex variety But you can you just look at a little region Which is a little cube and you ask us so there you have a solution And you ask yourself. Can you even write it there in that way? But uh, it's also zero zero one is more like In rm. No, right. So I mean well, it's complex manifold. So it's a real manifold m is Yeah, m has a particular value that's right. That's true No, but if the functions are to be analytic or real Well In his thing, I mean that he discusses actually different kinds of functions Well, continuous ones are one of them one one class function. He works as in a real domain or Or in the complex domain. It's not so I mean, I think at one point he's asking this question where he's just asking about continuous functions But that would work with the real polynomials or complex polynomials Well, that I don't quite understand. I mean you have like you have this setup, right? So If I restrict to a cube in here, I can ask whether I have the solution function I can write as a composite of continuous functions or not for example, yeah, but when you use real variables, you have twice as many variables so it's not um And how to formulate the question with the world variables when you work when you change complex variables, yeah So no, so right. So I think you have to think of it as as as 14 real variables. I guess, right You won't You want to know it's not possible to write as a constant function It's most two variables with in terms of complex variables not in terms of real variables Or maybe it's it just can do their continuous functions that he's asking about So I don't Yeah No, no, he's really asked about I mean he asked it also for analytic functions, but let me just Okay Yes, he asked he asked to show that it can't can't be written that way Okay Yeah, so maybe here. It's here. It's ambiguous if I if I don't specify the kind of functions But he's let's say he's asking about continuous functions here Okay um So this is what an old and colmar grove Proved could be done. So they prove that if you have any continuous function on a cube It's a composite of continuous functions of one variable In fact, this is more precise The statement yeah And now you might be a little confused because if you're thinking about it classically like this In terms of these coverings then of course if you restrict the covering to a cube, it will be a trivial covering So what is left to do? Well, the point is that if you're thinking about solutions of your polynomial You have really not just a covering but also an embedding into the app online. So it's really this structure That kind of you have to reduce So all so if you risk so if you restrict to a cube then kind of This covering structure disappears and you just have this function left and of course in the other formulation You don't you don't care about this. So it turns out in the algebraic setting Which I formulate the problem this kind of choice of primitive root doesn't doesn't change the problem either So in some sense, this is kind of orthogonal to To the other question The question is if you can reduce the covering to covering of things of dimension at most If you want to think about the multi-valued solution functions, then Essentially, we'll have to follow this but then we'll have to apply some algebraic morphism. It means polynomials And so we have to use polynomial and this polynomial is Like you have addition right functions of two Yes, that's right lose the one. No, no, that's right So so so there's a question here, which is when you're when you're uh, sorry when you're um Adding and multiplying that's strictly speaking a function of two variables. Okay, but if but for us we kind of that's allowed for free Okay, so it's true. In fact, it's if you want to get into the history you might wonder Why did he'll consider seven here given that he didn't even know the answer for six And one reason could be that he wanted just a clean formulation like this And since you always have to have at least two variables This was kind of the first case where you have a non-trivial bound if you're allowed to if you allow the stupid two variables where you have additional multiplication right Okay Happy all right Okay, so that's the end of the historical interlude So here are some examples from geometry From classical examples So let h3 3 be the modular space of cubic surfaces and b3 Modular the action of pgl4 So this is a four-dimensional space and then we're going to consider the kind of so if you have a a cubic surface And p3 It's a kind of classical fact that if you look at lions and p3 which lie on the surface There are 27 of them. So this is meant to be a picture And uh, so you can consider the such such lions, right? So this is a 27 sheeted cover Okay, so every point here you have the 27 lines And it's group is the vial group of v6 So, I mean it has to be a subgroup of s27 and it's the vial group of v6 And so when I say it has the group w of v6 what I mean is the the the normal closure has the scalar group And the conjecture is that the resolvent degree of this covering is three And there's a theorem of Burkhart and Klein Which says that it's at most it's less than or equal to three. I think so. It's the guy who worked on this kind of geometry I guess anyway, so you can so there's a reduction of the dimension by one here This is four-dimensional Okay And uh Then there's another kind of famous classical example where you have smooth cortex in p2 Modular reaction of pgl3. This has dimension six and then you can consider For each such quartic you can consider the lines in p2 which are tangent to the quartic at two points So called bi-tangent Okay, and this is a 20h there are 28 such lines So there's a 28 sheeted cover and the group of the normal closure is the vial group of v7 living inside s28 And it's conjectured that the resolvent degree here is six And so one thing that I want to explain is how to reduce all these Try to reduce these questions to another kind of covering where maybe one feels one has more techniques which is the modular space of principally polarized abelian varieties So let's consider ag the modular space of principally polarized abelian varieties And if I for any prime p I can look at the The p the p torsion of the universal family So then this group this covering has group sp2 gfp and So here's a proposition on which reduces the resolvent degree of these coverings from classical geometry to this setup Uh, in fact there are two so you see you have to concentrate here because it's g is the genus And then p is The prime so here I have 2 3 and here I have 3 2 Okay, so this is reducing the resolvent degree in this case to the resolvent degree of The kind of the three covering of the of the universal family of abelian surfaces and here I have The two covering for abelian three folds for the biotangent problem Okay, so let me let me kind of sketch the proof of this The point is that the two groups in this case are related. So let's just do the first one Here the covering that the vial group of v6 This has a degree to a subgroup which is nearly isomorphic to sp4 f3. It's ps When you define the resolvent degree, yeah for recovering again you You had some connectedness assumption, but of course the p torsion is not connected Because of the zero section, right? So Essentially you you have to take soup of all connected components or just here maybe yes everything is connected except for the zero right Yeah, right the thing you care about us is kind of the the Yeah, I mean the thing which is giving you kind of the monodermy the Right, I guess. I mean, yeah, that's right. It's the thing minus the zero section if you like but It's not the moderate space is the cost moderate space. Yes. Yeah, that's right. So I'm here. I'm ignoring Yes, so you should add some level structure away from p that doesn't matter You have minus one automorphism. So you don't have an universal family No, no, don't worry about that. You should you just add I mean I wrote ag Okay, but you just add some level structure That's not going to change anything Essentially independent. Yes. Yes, of which level structure five, right? Yes. Yes Okay, and we know that the monodermy then will be the full sp Right, okay So let's yes. We're doing the first one So remember here the monitor group was w v6 the bio group v6 This has an index to subgroup which is nearly sp of f3. So the covering group here Right, so this is this is for genus two So this would be sp4 of f3 Okay But we already saw that the resolvents degree is kind of insensitive to quadratic extensions So that that means the groups on these two sides are related And in fact what you show that both these families are versatile So you can imagine for any group g there's a notion of a kind of a versatile FAM a versatile g cover It's one which is kind of general enough that any other one comes from pullback From it. So for example families of polynomials, that's a versatile sn cover And for the other one there's a similar versality argument and the group theory looks like this again There's an index to subgroup which is actually sp6 of f2 okay, so at least for me this is this is kind of motivating because um I think for ag What you would expect is there's no reason for this resolvents degree in general To be any smaller than the dimension of ag And that's what we conjecture. There's one exception when g is two and p is two And that's because in that case the group sp2 g the In that case the group sp2 g fp namely sp4 f2 Is not simple. It has an index to subgroup And that allows you to reserve to reduce that that means you can pass to that quadratic cover for free And that allows you to reduce the resolvents degree by one. So in that case when g is two uh So if g is two this number here is three But in fact the you see you can show that the resolvents degree of that covers at most two In that exceptional case But I think otherwise there's no reason to believe That this is any smaller than the dimension of ag Oh, sorry, that's the remark to add an extra level structure. Yeah, so this conjecture is Yes for any But I have the feeling that's like not the main point. Okay, no, but but because It's true that it's not obvious that this is if I add a level structure Which is prime to p. It's not obvious that this is independent of p. Sure. Yeah, right, right That's right. Okay Any other questions? Okay, so one thing is that this agrees with the conjectures in this case for the two classical problems So remember in this case we said it should be three Okay, and then we're related this one to um To one degree related to To get three Sorry A two that's right a two three. Oh, yeah, right. That's right. Sorry. That's right No, I was confused because she was two and so I was still thinking about this example But then p is three, right? Yeah, good. So So in that case right so the dimension of a two will be three and we're conjecturing a three here And then in the other case it's a three two Which means the mention will be three times four on two. So it should be six As before Yep, I guess but We're not even can yeah, okay, I should uh, well, let's see if you mean if g is one G is one I get one So that seems to be correct Yeah, it can't be any smaller than that Uh, okay, uh, so at the moment we proved this at the level of essential dimension So that if I take this covering, this is just the dimension of a g so again I take this covering so I can't contract it to anything smaller So that's what you would guess and I'll sketch a proof of that at the end In fact, there's a generalization of this Uh, so to explain this let me take the p the The seagull parabolic in sp2 gfp. So in the standard representation It just corresponds to upper triangular matrices which are in the symplectic group And let you be its unipotent radical so the The the structure of view it's an abelian unipotent group and it's just its rank is equal to the dimension of a g And then if I have any group in here I can take its intersection with you And I'm going to note by eg the fp rank of This intersection. Okay, so it's something Okay, and then what I can do Is I can start with the gala closure of this guy Okay, and I take the I take the the the um The quotient corresponding to the group g so I'm sorry So, uh, so then this this covering has group g here from from this ag tilde to ag And the statement is that central dimension is at least eg Okay, so when g is the whole group Then ag is of course Then ag a big g is of course equal to a little g And this is just the other proposition. It says just says that the the central dimension is equal to the rank of view Which is the just the dimension of ag Okay, so let's apply this To the problem we were interested in from before with alternating groups Uh So for this I need the following uh proposition So it turns out there's a family of in characteristic two There's a family of representations of an Which I won't describe but The property it has is that if I intersect it with this With this u Then this in fact the maximal elementary bill in two subgroups of an meaning the one of maximal rank And there's a formula a simple formula for it is two times the integer part of n over four And so in particular we get uh Yeah, we get an estimate for this an cover here for the central dimension um This is just to remark that these coverings here Uh turn out to be versal when n is five and six, but probably not in general So vers again versal means that the kind of the most generic kind of coverings And so one thing is that kind of in the literature There are there were methods for computing the essential dimension of versal coverings in this case But in general these are probably not versal. So it's kind of a new new result to be able to compute the essential dimension So in the literature I guess people Have already worked on this for eight like the essential dimension of a So the essential demand of am Yes, they know it. I don't know if they know what there's some law of bounds Okay, so yeah, and this is compatible So it's better be But that is exactly the previous result or you are improved You mean you mean there's the bound is is the bound that they got Just this bound somehow That i'm not sure. I mean, I know how to compute the I know I know how to compute a law of bound for the essential dimension of an it's obtained by computing what computing what's called the something else which is the called the essential p dimension which is Less than or equal to the essential dimension and that can be like using a result from a career that can be reduced purely by group theory But we haven't actually done that calculation. So you have to kind of look at the um I think you have to look at like the smallest something like the smallest complex representation of the p-sealer subgroup of of an You look at the dimension of that guy Yes, right Maybe even um, sorry Yeah, maybe you need to look at the dimension of the smallest faithful one or something like that Anyway, so for these covers you have this estimate And so let's look at these the first let's look at the first The values of the first the first few values of this ean. Well, it's a very simple function. So you can write it down here okay, and Let's compare this with hilbert's conjectured value for the result resultant degree of the sky Okay, well, we know for four and five. It's actually should be one. So let's forget about that Okay And then for the other values you see that this is nearly the bound that uh, he conjectured for Resolvent degree namely for a solvent degree. He conjectured two three four and four. So only in seven It's kind of off by one um Okay, and so the the conjecture is actually for n greater or equal six you have This is also a bound for the resolvent degree Of the of the of that cover and so particularly a bound for the resolvent law bound for the resolvent degree of a and itself so So we have some kind of progress towards this but it's still open Right, so this would imply the conjecture for six eight nine And the conjectures on cubics and by tangents that I explained before Okay, so let me to end let me sketch a proof of how you show this bound on the essential dimension Um, ah, this should be a capital g Okay, the reason I put a small g was psychological because I want to restrict immediately to this case Okay, so the general case is kind of similar but Okay, so we want to show that the essential dimension of this covering is just equal to the rank of this maximal unipotent, which is the dimension of a g and Well the idea is if this covering comes from something of smaller dimension Let's let's say a g mapping to v So first of all This has some integral nice integral model and then I can make an integral model of of v Over okay where now I switched okay was algebraically closed before But now I'm going to switch settings and assume k over qp is finite So there's some kind of specialization argument that allows you to do that Um, okay, so this is now an integral thing and then um What you actually want to do is pass to the piatic completion and then Over then this ag twiddle that I had before this was kind of this fp local system So now but now we're working integrally right So before I had this agp twiddle without the circle It was this fp local system his mondrem. He was the symplectic group sp2g fp Right, but now I put a circle there that means that Even characters to if I want to extend characters to p it doesn't extend as an atar local system But extends as a finite flat group scheme Okay, and what you what you show Is that actually you can choose this v hat zero so that this descends to v hat zero at least on some formal open In the ordinary locus of this guy right In any case when you're doing essential dimension you in any case have to restrict to an you have to allow yourself to A strict to an open so this is no not really In some sense this is cost free in terms of what you're trying to prove Okay, so you descend not just the local system, but in fact the whole finite flat group scheme And now you think about the defamation theory of these finite flat group schemes so if you take any If any close point in the ordinary locus Then in characteristic p so this isn't let's close point then you can think about in any tangent direction If you go in any tangent direction this gives you a defamation of this The the fiber of this finite flat group scheme at x Okay, let's just say over the dual numbers And then it follows well either from set a theory a growth in the messing theory or this set a theory works better for the for the generalization to an arbitrary g That in any in any tangent direction you get a non trivial defamation and that in some sense Well, there's no redundancy kind of if you go this gives you this gives you a every direction gives you a different Defamation And then the point is we get a contradiction because if you if this comes by pullback from some Something of smaller dimension you can't get enough defamations Okay Over the sky or that guy But how do you know that the integral model exists over p which one of of If it comes from something of smaller dimension, that's me Yeah, but then how do you get an integral model including p Of this one. Yes, you just I mean remember. We're always allowed here to restrict to an open So This I mean we can assume this is affine and I can just take the intersection of the rings Okay, and then you have to do a little bit more like here when you show it descends you can always replace You replace something by its normalization in here as well And then you can descend the finite flag group scheme Okay, this seems to be non trivial You know that the Essentials of this make it generically, you know that the covering comes from We uh-huh, but then the final group structure is yeah No, you have to I don't claim this is completely obvious, but maybe We can I can explain it to you later, but Okay, which part are you worried about the descent to v? Okay, okay, because there You have a final group scheme on a general five. Yeah, I'll say you yeah. Yeah. Yeah it's not The models of final extension the final flag group scheme is not Uh But you mean that you can descend reason the same day Basically you do it by I mean if you restrict things enough then this map has already flat and then um I mean in fact we do this just in a formal neighborhood But because all you that's all you need. I mean we're working on the ordinary locus here So this is an extension of an atoll part by a multiplicative part, right? And so each of those parts descend And certainly in the order in in a formal neighborhood because they're just kind of trivial and then you have to compute the extension classes And then you you get that like any extension class So basically if you have an extension class That extends to a finite flag group scheme here it already extends to a finite flag group scheme here Okay, so that's the end of the talk the end of the official part of the talk um and uh so I so I mentioned that uh that I benefited from kind of offer suggestions in In a few ways one story I wanted to tell was I think it was now 15 or more years ago. I was giving a talk in in or say and um After I afterwards I mean I should be a tea. I asked maybe over a question It was a kind of group theoretical question about Representations of fundamental groups of curves and if you have such a thing where every simple closed curve had finite image This implied that the representation find an image. Anyway, the talk was about something completely different afterwards. Um afterwards uh Ophrin Luca, Lizzie and I went up for dinner and then after kind of several glasses of uh wine Opha came up with a counter example and here is a picture of the Of the of the bottle of wine of the actual bottle of wine and uh So, you know when when my co-authors and I was kind of struggling with some of these questions I would some to say this is exactly the kind of thing you should ask opha perhaps over a nice bottle of wine Okay, thank you So there's one compliment Luke told me When you asked the question at tea, yeah, sir Heard the question You want to tell the whole story? I'll do it rapidly so Luke sent sarin email after the dinner telling him Opha settled it So I had asked say the question at tea is the yeah, so then said called Luke very early in the morning earlier than Luke normally gets gets up I said Gabbard to come and Luke said this is unlikely Why don't you think about this a little more? Say I called back a little later Gabbard our razor You have a story? All questions about the talk are also are also allowed Talk about Shumora Arnold You wrote the names there, right? So they have an article I forgot where it is it's in the In the in the 1960s where they just asked this question I think it's in some kind of proceedings Where they you know questions and all direct geometry being discussed Yeah, what about it? I mean Yes, you can yeah So there it's even somehow more complicated, right because You have like the mapping class group So implicitly you need some local kind of flattening model of because you are you are working with Well, maybe it's not so difficult, but you want to to pass on the characteristics of the situation to support this game Okay, at least in the neighborhood of your Generic point of social fiber. So you have kind of the disorient evaluation. I mean you needed a good model for the map in terms of Something which is smooth between smooth things over the BBR. This is this is okay This is part of the argument Yeah, I mean the the thing is in the argument. It's not quite as I think this is still okay like this, but But this is you see you really only need it in a formal neighborhood of a point. Yes, but Right. Yeah, sure. I don't want to just put the paper up Sorry, that's right So some other questions Yes We stopped at E7


In 1926, there were enough galaxies known for Edwin Hubble to create a morphological classification scheme. This is his diagram. His students called it the Hubble Tuning Fork. Hubble's scheme divides galaxies into three broad classes based on their visual appearance. Elliptical galaxies have smooth, featureless light distributions and appear as ellipses in images like Centaurus A. They are denoted by the letter E followed by the integer N, representing a degree of ellipticity. Spiral galaxies consist of a flattened disk with stars forming a spiral structure and a central concentration of stars known as the bulge like the whirlpool galaxy. They are given the symbol S or SB if it has a bar core followed by a letter A through C. As we move from A to C, the spiral arm structure becomes more open, the amount of dust in young stars decreases, and the central bulge of the galaxy decreases in size relative to the disk size. Lenticular galaxies also consist of a bright central bulge surrounded by an extended disk-like structure, but unlike spiral galaxies, the disks of lenticular galaxies have no visible spiral structure and are not actively forming stars in any significant quantity. NGC 2787 is an example of these. They are designated S0. These broad classes can be extended to enable finer distinctions of appearance and to encompass other types of galaxies such as irregular galaxies, which have no obvious regular structure, either disk-like or ellipsoidal. Large Magellanic Cloud is an example of this. Since Hubble, others have added characteristics such as bars, rings, and spiral arm characteristics.