Math-life balance
Math-life balance
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Birthday greetings from IAS!
Birthday greetings from IAS!
Переглядів: 1 687

Відео

How to create chaos
Переглядів 2,1 тис.10 місяців тому
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
Переглядів 1,9 тис.10 місяців тому
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?
Переглядів 2,3 тис.11 місяців тому
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
Переглядів 2,9 тис.Рік тому
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
Переглядів 3,5 тис.Рік тому
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!
Переглядів 1,5 тис.Рік тому
Creating suspense for the next "K-theory Wonderland" video!
The K-theory dream
Переглядів 2,5 тис.Рік тому
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
Переглядів 2,3 тис.Рік тому
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
Переглядів 6 тис.Рік тому
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?
Переглядів 7 тис.Рік тому
Trying to explain my motivation behind the choice of algebraic K-theory as a topic for mathematical outreach
New video project is coming!
Переглядів 3,1 тис.Рік тому
Description of my new video project: "K-theory Wonderland"!
Live stream tomorrow 5 pm Paris time!
Переглядів 1,5 тис.Рік тому
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
Переглядів 4 тис.2 роки тому
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
Переглядів 4,2 тис.2 роки тому
Interview with Jeremiah Heller and Vesna Stojanoska
When the balance gets broken
Переглядів 5 тис.2 роки тому
When the balance gets broken
The beauty of math in personal examples
Переглядів 4,8 тис.2 роки тому
The beauty of math in personal examples
The oldest math institute in the world
Переглядів 3 тис.2 роки тому
The oldest math institute in the world
Interview with Dhruv Ranganathan
Переглядів 7 тис.2 роки тому
Interview with Dhruv Ranganathan
Interview with Kevin Buzzard
Переглядів 9 тис.2 роки тому
Interview with Kevin Buzzard
"The Art and Craft of Problem Solving" by Paul Zeitz
Переглядів 3,5 тис.2 роки тому
"The Art and Craft of Problem Solving" by Paul Zeitz
Live stream this Saturday at 5:30 CET!
Переглядів 1,1 тис.2 роки тому
Live stream this Saturday at 5:30 CET!
Interview with Maria Chudnovsky
Переглядів 9 тис.3 роки тому
Interview with Maria Chudnovsky
Asking my mum about math & life
Переглядів 2,9 тис.3 роки тому
Asking my mum about math & life
Interview with Tomer Schlank
Переглядів 4,6 тис.3 роки тому
Interview with Tomer Schlank
Interview with Saul Glasman
Переглядів 7 тис.3 роки тому
Interview with Saul Glasman
Live stream this Friday
Переглядів 1,5 тис.3 роки тому
Live stream this Friday
Interview with Giulia Saccà
Переглядів 7 тис.3 роки тому
Interview with Giulia Saccà
William Thurston "On proof and progress in mathematics"
Переглядів 5 тис.3 роки тому
William Thurston "On proof and progress in mathematics"
Interview with Irakli Patchkoria
Переглядів 4,9 тис.3 роки тому
Interview with Irakli Patchkoria

КОМЕНТАРІ

  • @user-td4ii9px4s
    @user-td4ii9px4s 15 днів тому

    One of my favorite channels in the whole platform, thanks for your content.

  • @tinkeringtim7999
    @tinkeringtim7999 2 місяці тому

    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.

  • @weserfeld4417
    @weserfeld4417 4 місяці тому

    Well, that's cute

  • @user-ev2rj1bi4r
    @user-ev2rj1bi4r 4 місяці тому

    Hey folks

  • @badraityassine
    @badraityassine 4 місяці тому

    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 ?

    • @math-life-balance
      @math-life-balance 4 місяці тому

      cool, I loved that book! (read only some parts of it)

  • @ym0101
    @ym0101 4 місяці тому

    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.

  • @adarkol1575
    @adarkol1575 4 місяці тому

    Happy BirthDay! more interviews! try to score more prominent mathematicians like Scholze etc...

  • @TranquilSeaOfMath
    @TranquilSeaOfMath 5 місяців тому

    Happy birthday and congratulations for getting to be at the IAS. That is a nice experience to be a part of.

  • @manueldelrio7147
    @manueldelrio7147 5 місяців тому

    Happy birthday!

  • @persistenthomology
    @persistenthomology 5 місяців тому

    please continue the interview series! thanks for all your work!

  • @DavidRoberts
    @DavidRoberts 5 місяців тому

    This video has real "early days of UA-cam vibe". Love it!

    • @math-life-balance
      @math-life-balance 5 місяців тому

      oh well :)

    • @DavidRoberts
      @DavidRoberts 4 місяці тому

      @@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.

  • @michaelnovak9412
    @michaelnovak9412 5 місяців тому

    Happy birthday!

  • @alexandershapiro28
    @alexandershapiro28 5 місяців тому

    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

  • @mustaphabachaou7254
    @mustaphabachaou7254 5 місяців тому

    Welcome back 🍀

  • @rustyshimstock8653
    @rustyshimstock8653 5 місяців тому

    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.

  • @AkamiChannel
    @AkamiChannel 7 місяців тому

    I didn't see the link in the description to the talk that you mentioned at the end

  • @dukeyin1111
    @dukeyin1111 7 місяців тому

    Does this have anything to do with K-Pop? K-theory

  • @knight3481
    @knight3481 7 місяців тому

    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.

  • @pupfer
    @pupfer 8 місяців тому

    Anyone know if Peter Haine and Eduard Heine are connected? What about Will Cavendish and Henry Cavendish?

  • @borisshteynas8793
    @borisshteynas8793 8 місяців тому

    Welcome to Oxford! Hope to see the new episodes from the evergreen English lawn!

  • @grothendieckriemann5893
    @grothendieckriemann5893 9 місяців тому

    Unintentional ASMR!

  • @vayuagni
    @vayuagni 9 місяців тому

    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.

  • @040_faraz9
    @040_faraz9 9 місяців тому

    also on the most general universal definition of K theory

  • @040_faraz9
    @040_faraz9 9 місяців тому

    hey can you make one explaining the definition of higher K groups in terms of classifying space

  • @davethesid8960
    @davethesid8960 9 місяців тому

    How old is he?

  • @LaboriousCretin
    @LaboriousCretin 9 місяців тому

    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 😊

  • @LaboriousCretin
    @LaboriousCretin 9 місяців тому

    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.

  • @miroslava6199
    @miroslava6199 10 місяців тому

    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!

  • @adarkol1575
    @adarkol1575 10 місяців тому

    Pidim pidim pidim :)

  • @marcosmartinezwagner8505
    @marcosmartinezwagner8505 10 місяців тому

    Its amazing beeing friends with people who proved nice theorems, hopefully one day we will see a theorem discoverd by you 😉

  • @math4wisdom
    @math4wisdom 10 місяців тому

    Thank you! and I hope that you present Bott periodicity! I am trying to understand that!

  • @TranquilSeaOfMath
    @TranquilSeaOfMath 10 місяців тому

    Nice video. I was expecting some nonlinear dynamics. The patterns in the homotopic groups of spheres is interesting. Good presentation.

  • @victorantoniotorrescastill2534
    @victorantoniotorrescastill2534 10 місяців тому

    Pretty nice video! I was not aware that the BPQ theorem could take such a friendly form 😃

  • @arijitpyne3435
    @arijitpyne3435 10 місяців тому

    I really do not understand why people always talk about nobles not being awarded in mathematics. Doing math is itself a pleasure..

  • @user-mw3kp9he8d
    @user-mw3kp9he8d 11 місяців тому

    Really cool videos! Please produce more!

  • @user-ev2rj1bi4r
    @user-ev2rj1bi4r 11 місяців тому

    You are so Sweet 😍

  • @johnbourke1697
    @johnbourke1697 11 місяців тому

    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!

  • @lcyken
    @lcyken 11 місяців тому

    Please keep doing this! Thank you

  • @marcosmartinezwagner8505
    @marcosmartinezwagner8505 11 місяців тому

    That moment you realize your teacher (Cortiñas) proved an amazing conjecture

  • @davidenriquegarciazelada9543
    @davidenriquegarciazelada9543 11 місяців тому

    Very clear and nicely motivated, I enjoyed the ideas a lot, thank you Hari and Mura! 🎉

  • @alexandershapiro28
    @alexandershapiro28 Рік тому

    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.

    • @saadslaoui8831
      @saadslaoui8831 10 місяців тому

      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!

  • @ProfessorJohnSmith
    @ProfessorJohnSmith Рік тому

    I dont see any previous video he refers to?

    • @math-life-balance
      @math-life-balance Рік тому

      oh, sorry, let me add a link

    • @math-life-balance
      @math-life-balance Рік тому

      he refers to the video "the magic of group completion", where K-theory space was introduced

  • @RohitSingh-nm9wd
    @RohitSingh-nm9wd Рік тому

    Just amazing.

  • @ligmamale4389
    @ligmamale4389 Рік тому

    This is great

  • @PeakMathLandscape
    @PeakMathLandscape Рік тому

    Incredible!

  • @wagnersgobbi7246
    @wagnersgobbi7246 Рік тому

    Thank you. That was the first time in my life that I understood more than 2% of any K-theory material hahahaha

  • @DMVMedien
    @DMVMedien Рік тому

    Great idea! And so nicely drawn und presented! Thank you! 👌

  • @okoyoso
    @okoyoso Рік тому

    We need more videos bringing down advanced topics back to Earth like these. The RH series coming out now is also amazing.