1. Congruences between modular forms

    We introduce the notion of congruences (modulo a prime number) between modular forms of different levels. One of the main questions is to show the existence of a certain newform of an expected level which is congruent to a given modular form...
    Category수학강연회 소속서울대 강연자유화종
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  2. Conformal field theory in mathematics

    Since Belavin, Polyakov, and Zamolodchikov introduced conformal field theory as an operator algebra formalism which relates some conformally invariant critical clusters in two-dimensional lattice models to the representation theory of Viraso...
    Category수학강연회 소속고등과학원 강연자강남규
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  3. Conformal field theory and noncommutative geometry

    Conformal field theory and noncommutative geometry
    Category수학강연회 소속동경대학교 강연자Kawahigashi
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  4. Compressible viscous Navier-Stokes flows: Corner singularity, regularity

    In this talk I will talk about existence and regularity for solutions to the compressible viscous Navier-Stokes equations on nonsmooth domains, especially with corners. The solution is constructed by the decomposition of the corner singulari...
    Category수학강연회 소속POSTECH 강연자권재룡
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  5. Combinatorial Laplacians on Acyclic Complexes

    The main topic of the talk is a determinantal formula for high dimensional tree numbers of acyclic complexes via combinatorial Laplace operators . This result is a generalization of Temperley's tree number formula for graphs, motivated by a ...
    Category수학강연회 소속서울대학교 강연자국웅
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  6. Codimension Three Conjecture

    We proved the codimension three conjecture that says the micro-local perverse sheaves extend if it is defined outside odimension three (counting from Lagrangian subvarity). It is a joint work with Kari Vilonen.
    Category수학강연회 소속교토대학교/서울대학교 강연자Masaki Kashiwara
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  7. Cloaking via Change of Variables

    We consider the problem of identifying the material properties from boundary measurements. For the conductivity case, this is known as Calderon problem: “Is it possible to determine the electrical conductivity inside a domain from the bounda...
    Category수학강연회 소속KAIST 강연자임미경
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  8. Classical and Quantum Probability Theory

    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...
    Category수학강연회 소속충북대학교 강연자지운식
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  9. Class field theory for 3-dimensional foliated dynamical systems

    I will talk about arithmetic topology, in particular, some issues related to class field theory for 3-dimensional foliated dynamical systems.
    Category수학강연회 소속Kyushu University 강연자Morishita Masanori
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  10. 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...
    Category수학강연회 소속연세대 수학과 강연자김준일
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  11. Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds

    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...
    Category수학강연회 소속KIAS 강연자박진성
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  12. Categorification of Donaldson-Thomas invariants

    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...
    Category수학강연회 소속서울대학교 강연자김영훈
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  13. Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras

    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...
    Category수학강연회 소속Kyoto University/서울대학교 강연자Masaki Kashiwara
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  14. 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...
    Category수학강연회 소속University of Washington 강연자Zhen-Qing Chen
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  15. Brownian motion and energy minimizing measure in negative curvature

    Category수학강연회 소속서울대학교 강연자임선희
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  16. 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...
    Category수학강연회 소속연세대학교 강연자최성락
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  17. Averaging formula for Nielsen numbers

    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} | ...
    Category수학강연회 소속서강대학교 강연자이종범
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  18. Arithmetic of elliptic curves

    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...
    Category수학강연회 소속서울대 강연자김도형
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  19. 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...
    Category수학강연회 소속University of Washington 강연자Zhen-Qing Chen
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  20. Analytic torsion and mirror symmetry

    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 ...
    Category수학강연회 소속Kyoto University 강연자Ken-ichi Yoshikawa
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