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...
Spectral Analysis for the Anomalous Localized Resonance by Plasmonic Structures
We present a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrizati...
<학부생을 위한 ɛ 강연> Self-Supervised Learning in Computer Vision
In recent years, artificial intelligence has made remarkable progress in developing algorithms that can learn from vast amounts of carefully labeled data. This paradigm of supervised learning has made great success in training specialist mo...
There are basically two approaches for solving linear systems: one is to exactly solve the linear sytem such as Gaussian-elimination. The other approximates the solution in the Krylov spaces; Conjugate-gradient and General minimum residual m...
In late 1970's John McKay discovered the astonishing identity 196884=196883+1, which lead Conway and Norton to formulate the famous Monstrous Moonshine conjectures about the Monster group, the largest sporadic finite simple group. The simple...
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.
학부생을 위한 강연: Choi's orthogonal Latin Squares is at least 61 years earlier than Euler's
조선시대 영의정을 지낸 최석정(1646-1715)은 그의 저서 구수략에 여러 크기의 직교라틴방진을 남겼는데 이는 combinatorial mathematics의 효시로 알려진 Leonhard Euler(1707?1783) 의 직교라틴방진보다도 적어도 61년이 앞서는 기록이다. 놀랍게도 최석정이...
Birational Geometry of varieties with effective anti-canonical divisors
Fano varieties are fundamental objects in algebraic geometry. These can be considered as the unique output of the -K -minimal model program on the varieties with effective anticanonical divisors. Thus the initial models should encode the in...
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...
Symplectic Geometry, Mirror symmetry and Holomorphic Curves
Symplectic geometry arose from the study of classical mechanics, and later many interesting symplectic invariants has been found since Gromov introduced techniques of J-holomorphic curves. Miraculously, such invariants are closely related wi...
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...
