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...
CategoryMath ColloquiaDept.Univ. of KentuckyLecturerDavid Leep
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.
CategoryMath ColloquiaDept.Univ. of Wisconsin/포항공대LecturerPaul Rabinowitz
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 ...
CategoryMath ColloquiaDept.Univ. of WisconsinLecturerMarshall Slemrod
We will introduce the behavior of zeros of linear combinations of zeta functions. Those linear combinations are related to the Riemann zeta function, the Eisenstein series, Periods, etc.
Limit computations in algebraic geometry and their complexity
Given a one-parameter family of algebraic varieties, its point-wise limit is usually too small whereas its algebraic limit is usually too big. I will introduce a notion of meaningful geometric limit and explain how it can be effectively comp...
Ward's identities and the related concept of the stress-energy tensor are standard tools in conformal field theory. I will present a mathematical overview of these concepts and outline relations between conformal field theory and Schramm-Loe...
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...
CategoryMath ColloquiaDept.University of WisconsinLecturer오용근