Nonlocal equations, often modeled using the fractional Laplacian, have received significant attention in recent years. In this talk, we will briefly overview how the classical regularity theory for second-order (elliptic) PDEs (in divergenc...
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...
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...
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 mapping class group of a surface S is the component group of orientation-preserving homeomorphisms on S. We survey geometric and algebraic aspects of this group, and introduce a technique of using right-angled Artin groups to find geomet...
For each natural number k, the C^k diffeomorphisms of the circle form a group with function compositions. This definition even extends to real numbers k no less than one by Hölder continuity. We survey algebraic properties of this grou...
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...
CategoryMath ColloquiaDept.University of Picardie Jules-Verne, AmiensLecturer김성순
Structural stability of meandering-hyperbolic group actions
Sullivan sketched a proof of his structural stability theorem for differentiabl group actions satisfying certain expansion-hyperbolicity axioms. We relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group a...
Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some r...
In 1980s, Donaldson discovered his famous invariant of 4-manifolds which was subsequently proved to be an integral on the moduli space of semistable sheaves when the 4-manifold is an algebraic surface. In 1994, the Seiberg-Witten invariant w...
Connectedness of a zero-level set as a geometric estimate for parabolic PDEs
Studies on PDEs are mostly focused on ?nding properties of PDEs within a speci?c discipline and on developing a technique specialized to them. However, ?nding a common structure over di?erent disciplines and unifying theories from di?erent s...
Symplectic topology and mirror symmetry of partial flag manifolds
Soon after Gromov’s applications of pseudo-holomorphic curves to symplectic topology, Floer invented an infinite-dimensional Morse theory by analyzing moduli spaces of pseudo-holomorphic curves to make substantial progress on Arnold&r...
The process of mathematical modelling for complex and stochastic biological systems
The revolution of molecular biology in the early 1980s has revealed complex network of non-linear and stochastic biochemical interactions underlying biological systems. To understand this complex system, mathematical models have been widely ...
Circular maximal functions on the Heisenberg group
The spherical average has been a source of many problems in harmonic analysis. Since late 90's, the study of the maximal spherical means on the Heisenberg group $mathbb{H}^n$ has been started to show the pointwise ergodic theorems on the gro...
