- Видео 64
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University of Chicago Department of Mathematics
Добавлен 1 окт 2020
ZhengTong Chern-Weil Symposium Fall 2024: Camillo De Lellis (IAS)
Area-Minimizing Currents Mod an IntegerAbstract:
Currents mod p are a suitable generalization of classical chains mod p, i.e. of finite combinations of smooth submanifolds with coefficients in the cyclic group Zp. By the pioneering work of Federer and Fleming it is possible to minimize the area in this context and, for instance, represent mod p homology classes with area minimizers. For p greater than 2 typically (i.e. away from a small set of exceptional points) one would expect such minimizers to be a union of smooth minimal surfaces joining together ("in multiples of p’s") at some common boundary. This is however surprisingly challenging to prove, especially for even p’s, and up until r...
Currents mod p are a suitable generalization of classical chains mod p, i.e. of finite combinations of smooth submanifolds with coefficients in the cyclic group Zp. By the pioneering work of Federer and Fleming it is possible to minimize the area in this context and, for instance, represent mod p homology classes with area minimizers. For p greater than 2 typically (i.e. away from a small set of exceptional points) one would expect such minimizers to be a union of smooth minimal surfaces joining together ("in multiples of p’s") at some common boundary. This is however surprisingly challenging to prove, especially for even p’s, and up until r...
Просмотров: 342
Видео
ZhengTong Chern-Weil Symposium Fall 2024: Zhiwei Yun (MIT)
Просмотров 1,1 тыс.Месяц назад
Higher Derivatives of Zeta Functions and Volume of Moduli ShtukasAbstract:It is well-known that the volume of a locally symmetric space (quotient of a symmetric space by an arithmetic subgroup, with respect to a suitably normalized invariant measure) is essentially a product of special values of zeta functions. We give an extension of this result in the function field case, so far only for gene...
ZhengTong Chern-Weil Symposium Fall 2024: Dennis Gaitsgory (Max Planck Institute for Mathematics)
Просмотров 838Месяц назад
Proof of the Geometric Langlands Conjecture Abstract:In the talk we will explain the various contexts for the geometric Langlands conjecture (de Rham, Betti, l-adic), and the ideas that go into its proof.This is joint work with: Dima Arinkin, Dario Beraldo, Justin Campbell, Lin Chen, Joakim Faergeman, Kevin Lin and Nick Rozenblyum.
ZhengTong Chern-Weil Symposium: Otis Chodosh (Stanford)
Просмотров 2706 месяцев назад
Otis Chodosh of Stanford gives a talk titled "Generalizations of the Bernstein Problem" as part of the ZhengTong Chern-Weil Symposium in Mathematics. Abstract: Sergei Bernstein proved (in 1914) that an entire solution to the minimal surface equation on R^2 must be affine. This is a nonlinear version of the Liouville theorem for harmonic functions and turns out to have deep links with the regula...
ZhengTong Chern-Weil Symposium: Martin Hairer (Imperial College London)
Просмотров 2066 месяцев назад
Martin Hairer of Imperial College London gives a talk titled "Stochastic Quantisation of Yang-Mills" as part of the ZhengTong Chern-Weil Symposium in Mathematics. Abstract: We report on recent progress on the problem of building a stochastic process that admits the still hypothetical 3D Yang-Mills measure as its invariant measure. One interesting feature of our construction is that it preserves...
ZhengTong Chern-Weil Symposium: Aaron Naber (Northwestern)
Просмотров 1426 месяцев назад
Aaron Naber of Northwestern gives a talk titled "Nonlinear Harmonic Maps and the Energy Identity" as part of the first ZhengTong Chern-Weil Symposium in Mathematics. Abstract: We will begin this talk with a broad introduction to nonlinear harmonic maps with a discussion of some basic examples and background. We will then focus our attention on a type of singularity formulation, resulting in so ...
Colloquium: Francois Labourie (Cote d'Azure)
Просмотров 1176 месяцев назад
Francois Labourie gives a talk titled "Poisson Algebra, Combinatorics and Representations of Surface Groups" as part of the math department's colloquia series. Abstract: In this talk, I will start by recalling what a Poisson algebra is by first concentrating on the basic example of the algebra of polynomials in 2 variables. I will then briefly recall the relationship of Poisson algebras with Ha...
Colloquium: Anush Tserunyan (McGill)
Просмотров 1786 месяцев назад
Anush Tserunyan gives a talk titled "A Descriptive Approach To Pointwise Ergodic Theorems" as part of the math department's colloquia series. Abstract: Pointwise ergodic theorems provide a bridge between the global behaviour of a dynamical system and the local (combinatorial) statistics of the system at a point. These are powerful tools used in ergodic theory, probability, number theory, and ot...
Colloquium: Tasho Kaletha (Michigan)
Просмотров 1846 месяцев назад
Tasho Kaletha gives a talk titled "Representations of Reductive Groups Over Local and Global Fields" as part of the math department's colloquia series. Abstract: The pioneering work of Langlands has established the theory of reductive algebraic groups and their representations as a key part of modern number theory. I will survey classical and modern results in the representation theory of reduc...
Colloquium: Lek-Heng Lim (UChicago)
Просмотров 2516 месяцев назад
Lek-Heng Lim gives a talk titled "Mathematical Snippets From Developments In AI" as part of the math department's colloquia series. Abstract: Discuss some mathematical issues coming from observations of developments in AI
2024 Unni Namboodiri Lectures: Oscar Randal-Williams (Lecture 3)
Просмотров 1207 месяцев назад
Oscar Randal-Williams (University of Cambridge) concludes his lecture titled "Symmetries of Manifolds" as part of the 2024 Unni Namboodiri Lectures in Geometry and Topology. Abstract: Whenever one studies a mathematical object one ought also to study its symmetries. Manifolds spaces which look locally like ordinary Euclidean space but which can be globally complicated are the central objects of...
Unni Namboodiri Lectures: Oscar Randal-Williams (Lecture 2)
Просмотров 387 месяцев назад
Oscar Randal-Williams (University of Cambridge) continues his lecture titled "Symmetries of Manifolds" as part of the 2024 Unni Namboodiri Lectures in Geometry and Topology. Abstract: Whenever one studies a mathematical object one ought also to study its symmetries. Manifolds spaces which look locally like ordinary Euclidean space but which can be globally complicated are the central objects of...
2024 Unni Namboodiri Lectures: Oscar Randal-Williams (Lecture 1)
Просмотров 1997 месяцев назад
Oscar Randal-Williams (University of Cambridge) gives a lecture titled "Symmetries of Manifolds" as part of the 2024 Unni Namboodiri Lectures in Geometry and Topology. Abstract: Whenever one studies a mathematical object one ought also to study its symmetries. Manifolds spaces which look locally like ordinary Euclidean space but which can be globally complicated are the central objects of study...
Colloquium: Will Sawin (Princeton)
Просмотров 6508 месяцев назад
Will Sawin gives a talk titled “The Fundamental Group of Random 3-Manifolds and Other Random Objects” as part of the math department’s colloquia series. Abstract: The fundamental group of a 3-manifold varies greatly from one manifold to the next. But what do they typically look like? Dunfield and Thurston formulated a precise version of this question by giving a definition of a random 3-manifol...
Colloquium: Hannah Larson (Berkeley)
Просмотров 3268 месяцев назад
Hannah Larson (Berkeley) gives a talk titled “Cohomology of Moduli Spaces of Curves” as part of the math department’s colloquium series. Abstract: The moduli space M_g of genus g curves (or Riemann surfaces) is a central object of study in algebraic geometry. Its cohomology is important in many fields. For example, the cohomology of M_g is the same as the cohomology of the mapping class group, ...
Colloquium: Kirsten Wickelgren (Duke)
Просмотров 2708 месяцев назад
Colloquium: Kirsten Wickelgren (Duke)
Colloquium: Wieslawa Niziol (Jussieu)
Просмотров 1878 месяцев назад
Colloquium: Wieslawa Niziol (Jussieu)
Colloquium: Kathryn Mann (Cornell University)
Просмотров 223Год назад
Colloquium: Kathryn Mann (Cornell University)
Colloquium: Duncan Dauvergne (University of Toronto)
Просмотров 238Год назад
Colloquium: Duncan Dauvergne (University of Toronto)
Colloquium: Vera Fischer (University of Vienna)
Просмотров 258Год назад
Colloquium: Vera Fischer (University of Vienna)
Colloquium: Toby Gee (Imperial College London)
Просмотров 308Год назад
Colloquium: Toby Gee (Imperial College London)
ZhengTong Chern-Weil Symposium: Stefan Steinerberger (Washington)
Просмотров 131Год назад
ZhengTong Chern-Weil Symposium: Stefan Steinerberger (Washington)
ZhengTong Chern-Weil Symposium: Svitlana Mayboroda (University of Minnesota)
Просмотров 107Год назад
ZhengTong Chern-Weil Symposium: Svitlana Mayboroda (University of Minnesota)
ZhengTong Chern-Weil Symposium: Yaiza Canzani (UNC Chapel Hill)
Просмотров 88Год назад
ZhengTong Chern-Weil Symposium: Yaiza Canzani (UNC Chapel Hill)
ZhengTong Chern-Weil Symposium: Semyon Dyatlov (MIT)
Просмотров 155Год назад
ZhengTong Chern-Weil Symposium: Semyon Dyatlov (MIT)
Minicourse: Courant, Bezout, and Persistence - Lecture 2
Просмотров 95Год назад
Minicourse: Courant, Bezout, and Persistence - Lecture 2
Minicourse: Courant, Bezout, and Persistence - Lecture 1
Просмотров 213Год назад
Minicourse: Courant, Bezout, and Persistence - Lecture 1
First
The so-called ``Shoulder Serum'' entitling the section at 18:40 should be Schilder's Theorem. Likewise, the title ``Dirichlet Passion'' at 35:45 should be Dirichlet Laplacian. This mislabeling of sections is youtube's fault. Shame on you, youtube automated transcription!
California Institute of Technology - (How close are we to human teleportation? Successes in quantum teleportation experiments abound) In fact, a fun 2013 study by physics students at the University of Leicester came up with useful numbers to show how complex it would be to teleport a person, even if we approached it as sending information that is used to re-create the person elsewhere. They reasoned that the transferable data for a human would consist of the DNA pairs that make up genomes in each cell. As such, the total data for each human cell would be approximately 1010 bits (b), while the data for a full human would come in at about 2.6 x 1042 b. Sending this gigantic amount of data would need the kind of computing technology we didn’t invent yet. By 2013 tech standards the students used, transferring data for just one human (at the bandwidth of 29.5 to 30 GHz) would take up to 4.85×1015years, much longer than the age of the universe. "Teleporting humans presents technical and philosophical challenges. A recent experiment achieved tremendous accuracy in quantum teleportation over 27 miles. Human teleportation may be possible with advances in technology to process huge amounts of data." We ask technicians and engineers to use the DNA transfer experiment in the field of teleportation Then conduct experiments to transfer mice in the field of teleportation Mistakes must be studied in order to develop new plans for success, because failed experiences lead to a successful experience (Please send these suggestions to engineers and technicians in the field of quantum entanglement and quantum computing)
Might expand to 9 symmetries of a proton
Expand to a 9 ball isotopy