Theory and applications of partial differential equations
I will talk in general about theory and applications of partial differential equations. A recent progress in the regularity theory for nonlinear problems will be also discussed, including uniform estimates of solutions in various function sp...
완전동형암호는 암호화된 상태에서 모든 계산을 지원하는 이상적인 암호로서 암호학계의 성배(holy grail)로 불리며 1978년 이후 오랫동안 미해결 문제로 알려져 있었다. 2009년 Gentry에 의해 처음 만들어진 후 많은 연구를 거쳐 실용화를 앞두고 있으며 2011...
A hyperplane arrangement is an arrangement of a finite set of hyperplanes in some vector space. Hyperplane arrangements generalize other famous combinatorial objects such as graphs and matroids. In this talk, we introduce a characteristic po...
Symplectic geometry has one of its origins in Hamiltonian dynamics. In the late 60s Arnold made a fundamental conjecture about the minimal number of periodic orbits of Hamiltonian vector fields. This is a far-reaching generalization of Poinc...
The general theory implies that the distribution of an irreducible Markov chain converges to its stationary distribution as time diverges to infinity. The speed of corresponding convergence is a significant issue in the study of mathematical...
We introduce the notion of congruences (modulo a prime number) between modular forms of different levels. One of the main questions is to show the existence of a certain newform of an expected level which is congruent to a given modular form...
<학부생을 위한 ɛ 강연> Convergence of Fourier series and integrals in Lebesgue spaces
Convergence of Fourier series and integrals is the most fundamental question in classical harmonic analysis from its beginning. In one dimension convergence in Lebesgue spaces is fairly well understood. However in higher dimensions the probl...
Elliptic curves defined over the rationals satisfy two finiteness properties; its group of rational points is a finitely generated abelian group and it has only finitely many points with integral coordinates. Bhargava and his collaborators e...
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, we briefly introduce how a combinatorial object, Integer partition, is related with number theoretic subjects : q-series and modular forms. In particular, we will focus on (1) combinatorial proof for q-series identities (2) ari...
We will show that the averaging formula for Nielsen numbers holds for continuous maps on infra-nilmanifolds: Let M be an infra-nilmanifold with a holonomy group Phi and f : M -> M be a continuous map. Then N(f ) = 1/| Phi | Sum_{A in Phi} | ...
Many aspects of the differential geometry of embedded Riemannian manifolds, including curvature, can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. For matrix analogues of embedded surfaces, one...
Among many different ways to introduce derived algebraic geometry is an interplay between ordinary algebraic geometry and homotopy theory. The infinity-category theory, as a manifestation of homotopy theory, supplies better descent results ...
※ 강연 뒷부분이 녹화되지 않았습니다. A symplectic manifold is a space with a global structure on which Hamiltonian equations are defined. A classical result by Darboux says that every symplectic manifold locally looks standard, so it has be...
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.
