Root multiplicities of hyperbolic Kac-Moody algebras and Fourier coefficients of modular forms
In this talk, we will consider the hyperbolic Kac-Moody algebra associated to a certain rank 3 Cartan matrix and generalized Kac-Moody algebras that contain the hyperbolic Kac-Moody algebra. The denominator funtions of the generalized Kac-Mo...
It is usually a difficult problem to characterize precisely which elements of a given integral domain can be written as a sum of squares of elements from the integral domain. Let R denote the ring of integers in a quadratic number field. Thi...
Unconditional results without an unproved hypothesis such as the generalized Riemann hypothesis (GRH) are very weak for an individual number field. But if we consider a family of number fields, one can prove just as strong results as we woul...
Category수학강연회소속Univ. of Toronto / KIAS강연자Kim, Henry
A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold M2 which can be realized as isometric immersions into R3. This problem can be formulated as initial and/or boundary ...
Category수학강연회소속Univ. of Wisconsin강연자Marshall Slemrod
We survey work on a class of nonlinear elliptic PDEs that was initiated by Moser. Methods from PDE, dynamical systems, and geometry set in the framework of the calculus of variations are used to construct a rich collection of solutions.
Category수학강연회소속Univ. of Wisconsin/포항공대강연자Paul Rabinowitz
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 ...
Category수학강연회소속University of Bielefeld강연자Walter Hoh
Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients
In this talk I will first give a survey of recent recent results SDEs with singular coefficients. Then I will report some recent results, jointly with Longjie Xie, on critical and supercritical SDEs with singular coefficients.
Category수학강연회소속University of Illinois강연자Renming Song
There are three Bieberbach theorems on flat Riemannian manifolds; characterization, rigidity and finiteness. These extend to almost flat manifolds. We discuss characterization, rigidity and finiteness of infra-nilmanifolds (almost flat manif...
For the irreducible representations of the Hecke algebras, the minimal elements in each conjugacy class play an important role. In this talk, we try to review the minimal length elements and characterize in a more efficient way to find the m...
Category수학강연회소속University of Picardie Jules-Verne, Amiens강연자김성순
Unprojection or "constructing bigger Gorenstein ideals from smaller one" is an algebraic device for constructing Gorenstein varieties in codimension 4, 5, ..., beyond the range of standard structure theorems; it has a large number of fairly ...
Category수학강연회소속University of Warwick / 서강대강연자Miles Reid
Brownian motion with darning and conformal mappings
Brownian motion with darning (BMD) is a diffusion process obtained from Brownian motion by shorting each hole in the space into one point. In this talk, I will present a quick introduction to BMD and its basic properties including the zero p...
Category수학강연회소속University of Washington강연자Zhen-Qing Chen
Anomalous diffusions and fractional order differential equations
Anomalous diffusion phenomenon has been observed in many natural systems, from the signalling of biological cells, to the foraging behaviour of animals, to the travel times of contaminants in groundwater. In this talk, I will first discuss t...
Category수학강연회소속University of Washington강연자Zhen-Qing Chen
A classical theorem of Jacobs, de Leeuw and Glicksberg shows that a representation of a group on a reflexive Banach space may be decomposed into a returning subspace and a weakly mixing subspace. This may be realized as arising from the idem...
Category수학강연회소속University of Waterloo강연자Nico Spronk
Hamiltonian dynamics, Floer theory and symplectic topology
In this lecture, I will convey subtle interplay between dynamics of Hamiltonian flows and La-grangian intersection theory via the analytic theory of Floer homology in symplectic geometry. I will explain how Floer homology theory (`closed str...
A dissipative effect on some PDEs with physical singularity
초록: In this lecture, we study various dissipative effect in a phase space from either entropy dissipation or boundary. We see how this effect leads mathematical studies on long time behavior and scale-uniform estimate of kinetic PDEs in g...
Category수학강연회소속University of Wisconsin-Madison강연자김찬우