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Math-life balance
Switzerland
Приєднався 12 січ 2021
My name is Mura Yakerson, I'm a mathematician working in algebraic geometry and homotopy theory, a CNRS researcher at Jussieu (Paris). On this channel I make non-professional interviews with professional mathematicians. I ask my colleagues about their personal experience in math, their struggles and lifehacks. I hope that this shared experience would be helpful for other people in the math community, especially for young mathematicians!
In the new series of videos, "K-theory Wonderland", I try to popularize abstract math by making possibly entertaining and accessible videos about K-theory, with the help of my wonderful colleagues!
Videos are uploaded on Fridays, at 6 pm CET. Enjoy the videos, and in case you have comments, critics or encouragement to share, please send me an email. Please spread the word!
In the new series of videos, "K-theory Wonderland", I try to popularize abstract math by making possibly entertaining and accessible videos about K-theory, with the help of my wonderful colleagues!
Videos are uploaded on Fridays, at 6 pm CET. Enjoy the videos, and in case you have comments, critics or encouragement to share, please send me an email. Please spread the word!
Відео
How to create chaos
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In this video I tell about the beautiful Barratt-Priddy-Quillen theorem, which shows how to get homotopy groups of spheres by applying the magic of group completion! en.wikipedia.org/wiki/Barratt–Priddy_theorem Related discussion: mathoverflow.net/questions/76541/what-do-the-stable-homotopy-groups-of-spheres-say-about-the-combinatorics-of-fin Lars Hesselholt's talk mentioned in the end: ua-cam....
My favourite K-theory fact
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In this video, I tell few general words about a theorem of Denis-Charles Cisinski about cdh-descent of homotopy invariant K-theory, proved in this paper: arxiv.org/abs/1003.1487 Denis-Charles webpage: cisinski.app.uni-regensburg.de/
When do things go smoothly?
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In this video, Hari Sudarsan (Orsay) is telling about Vorst's conjecture which predicts that K-theory can detect smoothness of algebraic varieties! Vorst's conjecture in characteristic zero: arxiv.org/abs/math/0605367 Vorst's conjecture in characteristic p: arxiv.org/pdf/1812.05342.pdf Minor edit from Hari: invertible elements of a ring always give classes in its K_1, see his previous video ua-...
First floor of the K-theory space
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In this video my student, Hari Sudarsan, talks about the computation of the first K-theory group of a ring. Enjoy! The computation of K_1 is a corollary of a more general fact, called "group completion theorem". You can read about it, for example, in my lecture notes (which follow lecture notes by Marc Hoyois): drive.google.com/file/d/1QotafUnsHB6uN5WS7ZjNQDzNxUQlTlBR/view hoyois.app.uni-regens...
Something from Nothing
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This piece of art, made by Jeremiah Heller, is a true fairytale taking place in K-theory Wonderland! More about this video: ua-cam.com/video/tqbhAITEDb0/v-deo.html Math prerequisites: zeroth algebraic K-theory ua-cam.com/video/FYY4pKkdDXQ/v-deo.html Math summary of the video: K-theory of a ring is defined as the group completion of the monoid of its finitely generated projective modules. If you...
It's suspense time!
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Creating suspense for the next "K-theory Wonderland" video!
The K-theory dream
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This is the third video out of three on the definition of algebraic K-theory! It is dedicated to the K-theory space of all algebraic varieties (more generally, all schemes). Made with: Peter Haine math.berkeley.edu/~phaine/ Thumbnail: made by Asama Lekbua Voiceover: Saad Slaoui web.ma.utexas.edu/users/slaoui/ Comments: 1) More precisely, Thomason-Trobaugh generalize algebraic K-theory to scheme...
The magic of group completion
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This is the second video out of three on the definition of algebraic K-theory! It is dedicated to the K-theory space of affine algebraic varieties (more generally, all rings). Made with: Peter Haine math.berkeley.edu/~phaine/ Thumbnail: made by Asama Lekbua Comments: K-theory of finite fields was computed by Quillen! en.wikipedia.org/wiki/K-groups_of_a_field References: 1) Lecture by Thomas Nik...
From negative numbers to K-theory
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This is the first video out of three on the definition of algebraic K-theory! It is dedicated to the zeroth K-theory of affine algebraic varieties (more generally, all rings). Made with: Peter Haine math.berkeley.edu/~phaine/ Thumbnail: made by Asama Lekbua Herwig Hauser Classic algebraic surfaces: www.imaginary.org/gallery/herwig-hauser-classic Comments: 1) Peter speaks about topological vecto...
What’s so cool about K-theory?
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Trying to explain my motivation behind the choice of algebraic K-theory as a topic for mathematical outreach
New video project is coming!
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Description of my new video project: "K-theory Wonderland"!
Live stream tomorrow 5 pm Paris time!
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Since I've been regularly getting questions about doing PhD in math, I thought we could finally make a live stream about it! Together with my colleague Sobhan Seyfaddini, a researcher in symplectic geometry, we will try to answer your questions about PhD experience. We will talk about psychological aspects (am I smart enough to do a PhD? am I too old? what if I fail?), as well as practical ques...
Interview with Katya Zoritch
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Katya Zoritch is a journalist and a writer, who grew up in a family of mathematicians. In this interview, Katya shares her insider-outsider experiences with math, compares literature and mathematical studies and gives a tribute to mathematicians, full of warmth and tenderness! Katya's webpage: katiazoritch.tilda.ws/ Katya's medium: medium.com/@katiazoritch The publishing house "No Kidding Press...
Interview with Jeremiah Heller and Vesna Stojanoska
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Interview with Jeremiah Heller and Vesna Stojanoska
The beauty of math in personal examples
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The beauty of math in personal examples
The oldest math institute in the world
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The oldest math institute in the world
"The Art and Craft of Problem Solving" by Paul Zeitz
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"The Art and Craft of Problem Solving" by Paul Zeitz
Live stream this Saturday at 5:30 CET!
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Live stream this Saturday at 5:30 CET!
William Thurston "On proof and progress in mathematics"
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William Thurston "On proof and progress in mathematics"
One of my favorite channels in the whole platform, thanks for your content.
thanks! :)
I just found this after struggling with Bott's lectures on K(x). I would love to see you achieving your stated aims, but like the postmodern plot I can't imagine how that could happen! I've subscribed, will start the binge-catchup.
Well, that's cute
Hey folks
Happy birthday, sorry for the long delay since it's literally only some few minutes ago that I stumbled upon your chanel by searching reviews on the The Art and Craft of Problem Solving book..and so by the way I want to ask if you're still reading/experimenting with it ?
cool, I loved that book! (read only some parts of it)
The best thing is to find someone who speaks your love language. I am happy that this channel exists! What a beautiful channel!! As a young ameture trying to follow the footsteps of Grothendieck, this channel is amazing to me.
Happy BirthDay! more interviews! try to score more prominent mathematicians like Scholze etc...
Happy birthday and congratulations for getting to be at the IAS. That is a nice experience to be a part of.
Happy birthday!
please continue the interview series! thanks for all your work!
yess please!
This video has real "early days of UA-cam vibe". Love it!
oh well :)
@@math-life-balance I totally meant it as a compliment! Too much UA-cam these days is a slave to please the algorithm and current fashions of what videos should be like.
Happy birthday!
Nice to see a video of my fav k theorist, I really want to visit IAS, even though I live 15 mins away, but never had the chance to visit, looking forward for more videos
do visit sometime if you can, it's great!
Welcome back 🍀
You asked for references to other outreach projects... Back in the late 1960s, my dad and his friend, who were both Math profs at Purdue University, self published a monthly pamphelet named the Indiana School Mathematics Journal. It went to school libraries all over the state of Indiana (U.S.). they had a contest each year for creative solutions to a problem or whatever. Anyway, one of the kids won the lrize once kr twice and eventually became a student and later a colleague. It was a great source of satisfaction for all concerned.
By the way, I love your show!
I didn't see the link in the description to the talk that you mentioned at the end
sorry! now you do (:
Does this have anything to do with K-Pop? K-theory
Only reason I have heard of K theory because D brane Ramond- Ramond charges can be interpreted in K theory terms but that is as far as I know.
Anyone know if Peter Haine and Eduard Heine are connected? What about Will Cavendish and Henry Cavendish?
Welcome to Oxford! Hope to see the new episodes from the evergreen English lawn!
Unintentional ASMR!
This discussion is applicable for people who wants to be a mathematician and people who are inherently talented means math comes to them effortlessly until or before taking up research mathematics. Math a young man's game since it requires inherent fluid intelligence than crystallized intelligence. It's a great discussion.
also on the most general universal definition of K theory
hey can you make one explaining the definition of higher K groups in terms of classifying space
How old is he?
Hunting and killing dragons (boojums). Black holes as finite systems. Finite stuff goes in and finite life span. Hawking radiation. Q.C.D. neutrino superfluidity in a black hole. A ghost boojum. Neutrino precipitation onto a boundary layer BEC before melting as one neutrino type. The one neutrino type with photon polarization flowing through. Creating a deformed alice ring. Alice and the boojum and ghost particles. Black holes are finite systems with solution sets. Big bang ghost boojum ( superfluidic neutrino production). Is another dragon and completely different animal from black holes. Though some similarities. Breaking symmetries, 1 to 3 foliation, fields, Ect... The universe as a finite system. From 12.5 light year diamiter flash over. To C*D when everything decays into photons and time losses meaning. The size of the universe then as a natural cutoff regime. Put a sister universe next to ours then rewind time to this time frame and you get a big distance. Also you calculate the next over probalistic universe that way. The universe and black holes as finite systems. Q.C.D. and tweedle sets and mapping. Schwartzchild for particle mapping and time slices. Kerr for G-flows and hyper surfaces and quantum boundaries. CERN for particle zoo mapping to energy densities regimes. Good luck in wonderland 😊
Welcome to wonderland! CERN ALICE detector, the white rabbit timing ToF. Root OS and trees. Alice strings and alice rings, and boojums. Snark graph theory and color theory Q.C.D., tweedle sets, quantum cats, and the particle zoo. Mad hatter an anagram for mathed art. 😮 The memetic history of wonderland is rich.
Nice! This is what I was looking for. I am a physicist trying to study k-theory for my thesis project, and literature on this topic is kind of hard for me, but this video encouraged me to keep going :D I will follow the next videos!
great, good luck!
Pidim pidim pidim :)
Its amazing beeing friends with people who proved nice theorems, hopefully one day we will see a theorem discoverd by you 😉
Thank you! and I hope that you present Bott periodicity! I am trying to understand that!
Nice video. I was expecting some nonlinear dynamics. The patterns in the homotopic groups of spheres is interesting. Good presentation.
Pretty nice video! I was not aware that the BPQ theorem could take such a friendly form 😃
I really do not understand why people always talk about nobles not being awarded in mathematics. Doing math is itself a pleasure..
Really cool videos! Please produce more!
You are so Sweet 😍
are all the projective modules supposed to be finitely generated? This is needed for Pi_0(proj(z)) to be N I think. Great videos!
Please keep doing this! Thank you
That moment you realize your teacher (Cortiñas) proved an amazing conjecture
Very clear and nicely motivated, I enjoyed the ideas a lot, thank you Hari and Mura! 🎉
I've been enjoying your series, and I saw the construction of an abelian group from semigroups in another talk by prof. Paul Baum after watching your series, and it all clicked! This group completion is like doing god's work, I would like to know if there are similar constructions for a magma to evolve through monoid and then semigroups. I have a few questions from the video, I know that it might not be answered since you have said that you may not be answering but here we go. How does a projective module would look geometrically? How does it look (trivially) for say the reals? Does this imply that the projective module is a semigroup? I know from wiki that it needs to have a basis in order for a module to become a proj. module. Is there a projective module counterpart for fields, what would this be ? I read that it's just called projective module since everything is nice and can be localized "everywhere", idk I guess by definition? Last question, the first homotopy group would be under what type of "classes"? I'm sorry if these questions don't make sense, I'm learning on my own after I fell in love with a ring theory course that I took last semester.
Some input: You can think of a projective module over a ring R as a vector bundle over a space associated to R, denoted by Spec(R) and called the Zariski spectrum of R-this is an affine scheme, a type of space in algebraic geometry. For a field F, Spec(F) consists of a single point, and a vector bundle over it consists of a single F-vector space V-i.e. all projective modules over F are free. For the ring C[t] of polynomials in one variable with complex coefficients, the space Spec(C[t]) looks like the complex plane, and it is a theorem that vector bundles on this space are always trivial, so that they look like a cartesian product V x Spec(C[t]), and all projective C[t]-modules are free. You can think of this as an analog of the fact that all vector bundles on a contractible topological space are trivial-though contractibility doesn’t quite make sense for affine scheme, a line certainly “feels” like it should be contractible. The existence of non-free projective modules over a ring R is an indication that the space Spec(R) is rich enough to support non-trivial vector bundles over it. As a simple example, if R is the direct sum of two smaller rings S and T, then Spec(R) will look like the disjoint union of Spec(S) and Spec(T), so you could have a vector bundle that has fibers of different dimensions over each component, corresponding to a projective R-module that is not free. Rings of an arithmetic nature also tend to admit non-free projective modules. Cheers!
I dont see any previous video he refers to?
oh, sorry, let me add a link
he refers to the video "the magic of group completion", where K-theory space was introduced
Just amazing.
This is great
Incredible!
Thank you. That was the first time in my life that I understood more than 2% of any K-theory material hahahaha
Great idea! And so nicely drawn und presented! Thank you! 👌
We need more videos bringing down advanced topics back to Earth like these. The RH series coming out now is also amazing.