The field of operator algebras deals with suitable closed subalgebras of the algebra of bounded linear operators on a Hilbert space. There are two types of operator algebras: C*-algebras and von Neumann algebras. In the 1970s A. Connes obtai...

We start with the famous Heisenberg uncertainty principle to give the idea of the probability in quantum mechanics. The Heisenberg uncertainty principle states by precise inequalities that the product of uncertainties of two physical quantit...

I will talk about arithmetic topology, in particular, some issues related to class field theory for 3-dimensional foliated dynamical systems.

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...

In this talk, I will explain a relationship of the Chern-Simons invariant and the eta invariant for Schottky hyperbolic manifolds. The relating formula involves a defect term given by the Bergman tau function over the conformal boundary Riem...

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...

Representation theory is to study the actions of groups or algebras on vector spaces. Recently, its categorical version, categorical representation theory, attracts researchers in representation theory. In this theory we replace "vector spac...

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...

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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...

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} | ...

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...

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...

In the early 90's, physicists Bershadsky-Cecotti-Ooguri-Vafa conjectured that the analytic torsion was the counterpart in complex geometry of the counting problem of elliptic curves in Calabi-Yau threefolds. It seems that this conjecture is ...

Many mathematical and computational analyses have been performed for deterministic partial differential equations (PDEs) that have perfectly known input data. However, in reality, many physical and engineering problems involve some level of ...

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...

초록: SNU-abstract.pdf

양자컴퓨터와 양자암호로 대표되는 양자기술의 응용이 대두되면서 그 기반이 되는 양자정보학에 대한 관심이 그 어느때보다 높다. 양자정보학은 양자상태의 정보량 및 양자상태를 전송할 때 전달되는 정보량을 분석하고자 하는 목표를 가지고 있는데 많은 경우...

상산수리과학관 20주년 기념강연

Lagrangian Floer theory in symplectic manifold associate a category (A infinity category) to a symplectic manifold. More than 20 years ago a relation of a relation between Lagrangian Floer theory and Gauge theory was studied by Floer himself...