Weyl character formula and Kac-Wakimoto conjecture
The character of the finite-dimensional irreducible modules over a finite-dimensional simple Lie algebra is given by the celebrated Weyl character formula. However, such a formula does not hold in general for finite-dimensional irreducible m...
Empirical observations have shown that for an adequate description of many random phenomena non-Gaussian processes are needed. The paths of these Markov processes necessarily have jumps. Their generators are nonlocal operators which admit a ...
CategoryMath ColloquiaDept.University of BielefeldLecturerWalter Hoh
Green’s function for initial-boundary value problem
In this talk, we will present an approach to construct the Green’s function for an initial boundary value problem with precise pointwise structure in the space-time domain. This approach is given in terms of transform variable and physical v...
CategoryMath ColloquiaDept.National Univ. of SingaporeLecturerShih-Hsien Yu
Mechanization of proof: from 4-Color theorem to compiler verification
I will give a broad introduction to how to mechanize mathematics (or proof), which will be mainly about the proof assistant Coq. Mechanizing mathematics consists of (i) defining a set theory, (2) developing a tool that allows writing definit...
On the distributions of partition ranks and cranks
To explain Ramanujan's integer partition function congruences, Dyson's rank and Andrews-Garvan's crank have been introduced. The generating functions for these two partition statistics are typical examples of mock Jacobi forms and Jacobi for...
In this talk, I will talk about the definition Q-curvature and some of its properties. Then I will talk about the problem of prescribing Q-curvature, especially I will explain the ideas of studying the problem using flow approach.
Geometry, algebra and computation in moduli theory
I will explain the basic concepts of moduli and how moduli spaces can be constructed in algebraic geometry. Exploring the moduli spaces and issues arising from their construction lead to interesting interplay of geometry, algebra and computa...
Gromov-Witten-Floer theory and Lagrangian intersections in symplectic topology
Gromov introduced the analytic method of pseudoholomorphic curves into the study of symplectic topology in the mid 80's and then Floer broke the conformal symmetry of the equation by twisting the equation by Hamiltonian vector fields. We sur...
I will introduce the basic notions of model theory, a branch of mathematical logic, and survey its applications to other areas of mathematics such as analysis, algebra, combinatorics and number theory. If time permits I will present recent w...
The notion of essential dimension was introduced by Buhler and Reichstein in the late 90s. Roughly speaking, the essential dimension of an algebraic object is the minimal number of algebraically independent parameters one needs to define the...
We will talk about the Fourier restriction theorems for non-degenerate and degenerate curves in Euclidean space Rd. This problem was first studied by E. M. Stein and C. Fefferman for the circle and sphere, and it still remains an unsolved pr...
Recommendation system and matrix completion: SVD and its applications (학부생을 위한 강연)
이 강연에서는 최근 음악, 영화 추천 등 다양한 Recommendation System의 기본 아이디어인 Matrix Completion 문제와, 이를 해결하기 위해 Singular Value Decomposition을 통한 차원 축소 및 내재 공간 학습이 어떤 원리로 이루어 지는지 설명합니다. 그리고 ...
From 1980’s, the study of Kleinian groups has been carried out in the framework of the paradigm of “Thurston’s problems”. Now they are all solved, and we can tackle deeper problems; for instance to determine the topological types of the defo...