Martin Zirnbauer: Bott periodicity and the "Periodic Table" of topological insulators and ...
Full Title:Bott periodicity and the "Periodic Table" of topological insulators and superconductors Bott periodicity is said to be one the most surprising phenomena in topology. Perhaps even more surprising is its recent appearance in condensed matter physics. Invoking a twisted equivarian
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Strange Pattern in symmetries - Bott periodicity
A strange repeating pattern in the symmetries of circles, spheres and higher dimensional spheres called Bott periodicity. We will learn about symmetries of spheres, homotopy groups, the orthogonal groups and, finally, Bott periodicity. Produced by Connect films https://www.connectfi
From playlist Summer of Math Exposition Youtube Videos
Morse-Bott theory on singular analytic spaces and applications to the topology of… - Paul Feehan
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Morse-Bott theory on singular analytic spaces and applications to the topology of symplectic four-manifolds Speaker: Paul Feehan Affiliation: Rutgers University Date: November 29, 2021 We describe two extensions, called th
From playlist Mathematics
Convolution Theorem: Fourier Transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.
From playlist Partial differential equations
Math 139 Fourier Analysis Lecture 04: Uniqueness of Fourier Series
Uniqueness of Fourier Series: all Fourier coefficients vanish implies function vanishes at points of continuity; absolute convergence of Fourier series implies uniform convergence of Fourier series to the original (continuous) function; twice continuous differentiability implies absolute c
From playlist Course 8: Fourier Analysis
What Morse missed by not talking to Weyl - Raoul Bott
75th Anniversary Celebration School of Mathematics Raoul Bott Harvard University March 12, 2005 More videos on http://video.ias.edu
From playlist Mathematics
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
A Riemann-Roch theorem in Bott-Chern cohomology - Jean-Michel Bismut
Jean-Michel Bismut Université Paris-Sud April 21, 2014 If MM is a complex manifold, the Bott-Chern cohomology H(⋅,⋅)BC(M,C)HBC(⋅,⋅)(M,C) of MM is a refinement of de Rham cohomology, that takes into account the p,q p,q grading of smooth differential forms. By results of Bott and Chern, vect
From playlist Mathematics
Computing Embedded Contact Homology in the Morse-Bott Setting using Cascades - Yuan Yao
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Computing Embedded Contact Homology in the Morse-Bott Setting using Cascades Speaker: Yuan Yao Affiliation: University of California, Berkeley Date: November 28, 2022 I will first give an overview of ECH. Then I will desc
From playlist Mathematics
Theory of numbers: Fermat's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Fermat's theorem a^p = a mod p. We then define the order of a number mod p and use Fermat's theorem to show the order of a divides p-1. We apply this to testing some Fermat and Mersenne numbers to se
From playlist Theory of numbers
Sachchidanand Prasad: Morse-Bott Flows and Cut Locus of Submanifolds
Sachchidanand Prasad, Indian Institute of Science Education and Research Kolkata Title: Morse-Bott Flows and Cut Locus of Submanifolds We will recall the notion of cut locus of closed submanifolds in a complete Riemannian manifold. Using Morse-Bott flows, it can be seen that the complement
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Completion theorems in equivariant homotopy theory - Saul Glasman
Short Talks by Postdoctoral Members Saul Glasman - September 22, 2015 http://www.math.ias.edu/calendar/event/88164/1442944800/1442945700 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
G. Williamson - Character formulas in the modular representation theory of algebraic groups
I will review present two formulas for the characters of representations of reductive algebraic groups in positive characteristic p. Both formulas involve certain polynomials ("p-Kazhdan-Lusztig polynomials") which measure the failure of the decomposition theorem for resolutions of affine
From playlist Geordie Williamson external seminars
Fourier series + Fourier's theorem
Free ebook http://tinyurl.com/EngMathYT A basic lecture on how to calculate Fourier series and a discussion of Fourier's theorem, which gives conditions under which a Fourier series will converge to a given function.
From playlist Engineering Mathematics
Lecture 9.1 Periodic functions
Periodic functions are functions that repeat themselves at regular intervals. In this lecture, we discuss the properties of periodic functions.
From playlist MATH2018 Engineering Mathematics 2D
(ML 19.2) Existence of Gaussian processes
Statement of the theorem on existence of Gaussian processes, and an explanation of what it is saying.
From playlist Machine Learning
Positive loops and orderability in contact geometry - Peter Weigel
Peter Weigel Purdue University October 4, 2013 Orderability of contact manifolds is related in some non-obvious ways to the topology of a contact manifold Σ. We know, for instance, that if Σ admits a 2-subcritical Stein filling, it must be non-orderable. By way of contrast, in this talk I
From playlist Mathematics