INU Colloquium
INU Colloquium
Speaker: Insuk Seo (Seoul National University)
Date & Time: Thursday, 5 December 2024, 16:30-18:00
제목: 확률론의 여러 난제들
초록: 본 강연에서는 확률론에서 다루는 여러 대상 중 수리물리학과 관련이 깊은 Self-avoiding walk, percolation, random-cluster model들을 소개하고, 이들 모델에서 수학자들이 그간 알아낸 것과 알아내지 못한 것들이 무엇인지 소개한다. 강연은 앞서 언급된 모델은 물론, 확률론에 대한 별도의 지식이 없이도 충분히 이해할 수 있도록 진행된다.
Speaker: Takwon Kim (Sungshin Women's University)
Date & Time: Thursday, 17 October 2024, 16:30-18:00
Title: Making Decisions in Financial Markets
Abstract: Financial markets are inherently uncertain, making decision-making processes closely tied to stochastic optimization. In this talk, I will introduce several stochastic optimization problems that arise in financial markets and present techniques used to solve them. We will then examine how these optimization problems provide a framework for making decisions in uncertain financial environments.
Speaker: Dohyun Kwon (University of Seoul)
Date & Time: Thursday, 12 September 2024, 16:30-18:00
Title: Applications of Optimal Transport in Machine Learning
Abstract: Over the past few decades, optimal transport theory has gained increasing interest across multiple fields, including partial differential equations, probability, and machine learning. In this talk, we explore the diverse applications of optimal transport theory within various machine learning problems, with a specific focus on generative models. Our discussion begins by examining gradient flows in the space of probability measures equipped with the distance arising from the Monge-Kantorovich optimal transport problem. We then analyze a score-based generative model based on the Fokker-Planck equations that underlie both the forward and reverse processes of the model.
Speaker: Jaeyong Lee (Chung-Ang University)
Date & Time: Thursday, 13 June 2024, 16:30-18:00
Title: Deep Learning and Partial Differential Equations
Abstract: Many differential equations and partial differential equations (PDEs) are being studied to model physical phenomena in nature with mathematical expressions. Recently, new numerical approaches using machine learning and deep learning have been actively studied. There are two mainstream deep learning approaches to approximate solutions to the PDEs, i.e., using neural networks directly to parametrize the solution to the PDE and learning operators from the parameters of the PDEs to their solutions. As the first direction, Physics-Informed Neural Network was introduced in (Raissi, Perdikaris, and Karniadakis 2019), which learns the neural network parameters to minimize the PDE residuals in the least-squares sense. On the other side, operator learning using neural networks has been studied to approximate a PDE solution operator, which is nonlinear and complex in general. In this talk, I will introduce these two ways to approximate the solution of PDE and my research related to them.
Speaker: Daejun Kim (Korea University)
Date & Time: Thursday, 23 May 2024, 17:15-18:45
Title: Theta series and representations by integral quadratic forms
Abstract: The representation of integers by quadratic forms has been a subject of interest in number theory for a long time. One crucial tool in this study is the theta series of a positive-definite quadratic form, which establishes a connection between algebraic and analytic theories of quadratic forms. In this talk, we will explore this connection and their applications in studying integer representations by quadratic forms.
Speaker: Sung-Soo Byun (Seoul National University)
Date & Time: Thursday, 25 April 2024, 16:30-18:00
Title: Random Matrix Theory Through the Lens of the Universality Principle
Abstract: As a fundamental concept in modern probability theory, universality asserts that the outcome of a system is largely independent of its specific structural details, provided there are sufficiently many different sources of randomness. In this talk, I will present recent progress on the universality principle in the context of the non-Hermitian random matrix theory. In particular, I will introduce the local universality problem of the planar symplectic ensembles and present my contributions to this topic.
Speaker: Sin-Myung Lee (Korea Institute for Advanced Study)
Date & Time: Thursday, 5 October 2023, 16:30~18:00
Title: Representation theory: An algebraic study of symmetries
Abstract: One of the most significant and effective way to understand a given object is to investigate its symmetries, which usually form an algebraic structure such as finite group, Lie group or Lie algebra. Representation theory is a study of how such algebraic structures can be realized as symmetries of vector spaces, namely how to represent them in terms of matrices. In this talk, we first formalize and generalize the rotational symmetry of the sphere through representations of the Lie algebra sl(2). Then we briefly review the representation theory of simple Lie algebras, and finally discuss how to describe supersymmetry or quantum symmetry by introducing corresponding algebraic structures called Lie superalgebras or quantum groups, respectively.
Speaker: Euiyong Park (University of Seoul)
Date & Time: Thursday, 27 April 2023, 16:30~18:00
Title: Monoidal categorification for cluster algebras
Abstract: In this talk, I will explain about the notion of categorification using module categories. I will deal with quantum group examples to explain how cluster algebra structures arise in the categorification setting. The monoidal seeds and their mutations, which can be viewed as lifts of usual seeds and mutations, will be explained with examples using quantum groups and quiver Hecke algebras. If time permits, then I will explain recent research results on categorification of quantum groups.
Speaker: Se-jin Oh (Ewha Womans University)
Date & Time: Thursday, 13 October 2022, 16:00~17:30
Title: Canonical basis and positivity phenomena (자연기저와 양성현상)
Abstract: In this talk, we discuss the canonical basis appearing in the symmetric group, its q-deformations on one side, and Lie algebra and its deformation
on the other side. For this talk, understanding linear algebra is enough. We welcome undergraduate students!
last updated: October 10, 2024