Friday, February 12, 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.

2021-02-19 / 10:30 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by 신연종()

Modern machine learning (ML) has achieved unprecedented empirical success in many application areas. However, much of this success involves trial-and-error and numerous tricks. These result in a lack of robustness and reliability in ML. Foundational research is needed for the development of robust and reliable ML. This talk consists of two parts. The first part will present the first mathematical theory of physics informed neural networks (PINNs) -one of the most popular deep learning frameworks for solving PDEs. Linear second-order elliptic and parabolic PDEs are considered. I will show the consistency of PINNs by adapting the Schauderapproach and the maximum principle. The second part will focus on some recent mathematical understanding and development of neural network training. Specifically, two ML phenomena are analyzed --"Plateau Phenomenon" and "Dying ReLU."New algorithms are developed based on the insights gained from the mathematical analysis to improve neural network training.

2021-02-18 / 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]. Thursday, February 18, 2021 - 10:00 to 12:00 Exponential converence to the Gibbs equilibrium, and Poincare inequality for Gauss- ian measures (Gibbs measures).

2021-02-17 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 성기훈(카이스트)

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.

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