Tuesday, February 9, 2021

2021-02-16 / 17:00 ~ 18:00

by 박진형(서강대학교)

The double point divisor of an embedded smooth projective variety is an effective divisor that is (the divisorial component of) the non-isomorphic locus of a general projection to a hypersurface. Some positivity properties of double point divisors were studied by Mumford, Ilic, Noma, etc. in a variety of flavors. In this talk, we study the very-ampleness of double point divisor from outer projection and the bigness of double point divisor from inner projection.

2021-02-16 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학:

by 현윤석(인하대학교)

최근의 딥러닝 연구는 효율적인 알고리즘 설계, 더 높은 성능 도출, 알고리즘의 작동원리 분석등에 수학적 방법론을 적용하려는 시도들이 늘어나고 있지만, 아직 많은 수학자들에게는 조금은 낯선 영역이다. 이번 세미나에서는 수학을 연구하는 학생과 연구자들을 대상으로, Deep Learning Research에서 관심있는 주제와 연구 대상, 그리고 연구 방법들에 대한 일반적인 내용들을 소개하고, 최신 연구 동향에 대해 살펴봄으로써, 딥러닝 연구에 대해 이해하고, 수학이 이러한 연구에 어떻게 기여할 수 있을지에 대해 고민해 볼 수 있는 시간을 가져보려 한다. 특히 주로 이미지 데이터들을 처리하는 알고리즘 및 방법론과, 좀 더 빠르고 정확한 영상 인식알고리즘을 설계하기 위한 연구에 대해 소개하고, 관련 분야에서 최근 관심 있어 하는 연구 주제들은 무엇이 있는지에 대해서도 설명한다.

2021-02-09 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

Introduction: In this lecture series, we'll discuss algebro-geometric study on fundamental problems concerning tensors via higher secant varieties. We start by recalling definition of tensors, basic properties and small examples and proceed to discussion on tensor rank, decomposition, and X-rank for any nondegenerate variety $X$ in a projective space. Higher secant varieties of Segre (resp. Veronese) embeddings will be regarded as a natural parameter space of general (resp. symmetric) tensors in the lectures. We also review known results on dimensions of secants of Segre and Veronese, and consider various techniques to provide equations on the secants. In the end, we'll finish the lectures by introducing some open problems related to the theme such as syzygy structures and singularities of higher secant varieties.

2021-02-16 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 성기훈(카이스트)

The purpose of this reading seminar is to study the following: (1) Bourgain's invariant measure argument in stochastic PDE, (2) Uniqueness of the invariant measure (Gibbs measure) and its ergodicity, (3) Exponential converence to the Gibbs equilibrium. This seminar is mainly based on [1, 2, 3]. Tuesday, February 16, 2021 - 10:00 to 12:00 Main structure theorems of the set of invariant measures, the uniqueness of the invariant measure and its ergodicity.

2021-02-09 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 성기훈(카이스트)

The purpose of this reading seminar is to study the following: (1) Bourgain's invariant measure argument in stochastic PDE, (2) Uniqueness of the invariant measure (Gibbs measure) and its ergodicity, (3) Exponential converence to the Gibbs equilibrium. This seminar is mainly based on [1, 2, 3]. Tuesday, February 9, 2021 - 14:00 to 16:00 Bourgain's invariant measure argument in stochastic PDE and almost sure global existence of stochastic Gross-Pitaevskii equation

2021-02-09 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 대수기하학: The Green-Tao theorem for number fields II

by Wataru Kai(Tohoku University, Japan)

In the latter one hour, I will explain our generalization of their work to the general number fields based on my joint work with my Tohoku colleagues Masato Mimura, Akihiro Munemasa, Shin-ichiro Seki and Kiyoto Yoshino (arxiv:2012.15669). Time permitting, I will also touch upon its positive characteristic analog (arxiv:2101.00839). The case of the polynomial rings had also been conjectured by Green-Tao in the same paper and settled by Lê in 2011.

2021-02-09 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: The Green-Tao theorem for number fields I

by Wataru Kai(Tohoku University, Japan)

A famous theorem of Green and Tao says there are arbitrarily long arithmetic progressions consisting of prime numbers. In that 2008 paper, they predicted that similar statements should hold for prime elements of other number fields and the case of the Gaussian integers $Z[i]$ was subsequently settled by Tao. In the first of my two talks, I would like to share my (limited) knowledge about the background and history underlying their work.

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