Thursday, May 9, 2024

2024-05-10 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나: The qualitative theory of dynamical systems for deep learning

by Woochul Jung()

The qualitative theory of dynamical systems mainly provides a mathematical framework for analyzing the long-time behavior of systems without necessarily finding solutions for the given ODEs. The theory of dynamical systems could be related to deep learning problems from various perspectives such as approximation, optimization, generalization, and explainability. In this talk, we first introduce the qualitative theory of dynamical systems. Then, we present numerical results as the application of the qualitative theory of dynamical systems to deep learning problems.

2024-05-10 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 정수론:

by ()

EO strata are subvarieties in the moduli space of g-dimensional abelian varieties in characterstic p which classify points with given isomorphism type of p-torson subgroups. We are interested in how automorphism groups of points vary in supersingular EO strata. We show that when g is even and p>3, there is an open dense of the maximal supersingular EO stratum in which every point has automorphism group {\pm 1}, and prove Oor's conjecture in this case. This is joint work in progress with Valentijn Karemaker.

2024-05-16 / 16:30 ~ 18:30

학과 세미나/콜로퀴엄 - 기타:

by 김준범, 김정섭 (Samsung Research), 심규석(행정안전부)()

1. 데이터 분석 업무의 이해(김준범)- 데이터 분석가의 역할 소개 2. 초거대 언어 모델 동향(김정섭)-GPT-3 부터 Llama-3까지 이미 우리 삶 속에 깊숙이 자리잡은 초거대 언어 모델의 동향 3. 데이터 분석가에서 공직으로 오게된 과정과 앞으로의 계획(심규석)- 삼성화재에서의 데이터 분석 및 AI 모델링 업무, 행정안전부에서의 데이터 분석과제 기획·관리 및 공무원의 데이터 분석 역량지원 업무 전반에 관한 설명과 함께 각 기관을 지원하게 된 동기, 지원방법, 준비사항 등

2024-05-10 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #5

by 김재홍(KAIST)

This is part of an informal seminar series to be given by Mr. Jaehong Kim, who has been studying the book "Hodge theory and Complex Algebraic Geometry Vol 1 by Claire Voisin" for a few months. There will be 6-8 seminars during Spring 2024, and it will summarize about 70-80% of the book.

2024-05-14 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Cross-cap drawings and signed reversal distance

by Niloufar Fuladi(Inria center of Université de Lorraine)

A cross-cap drawing of a graph G is a drawing on the sphere with g distinct points, called cross-caps, such that the drawing is an embedding except at the cross-caps, where edges cross properly. A cross-cap drawing of a graph G with g cross-caps can be used to represent an embedding of G on a non-orientable surface of genus g. Mohar conjectured that any triangulation of a non-orientable surface of genus g admits a cross-cap drawing with g cross-caps in which each edge of the triangulation enters each cross-cap at most once. Motivated by Mohar’s conjecture, Schaefer and Stefankovic provided an algorithm that computes a cross-cap drawing with a minimal number of cross-caps for a graph G such that each edge of the graph enters each cross-cap at most twice. In this talk, I will first outline a connection between cross-cap drawings and an algorithm coming from computational biology to compute the signed reversal distance between two permutations. This connection will then be leveraged to answer two computational problems on graphs embedded on surfaces. First, I show how to compute a “short” canonical decomposition for a non-orientable surface with a graph embedded on it. Such canonical decompositions were known for orientable surfaces, but the techniques used to compute them do not generalize to non-orientable surfaces due to their more complex nature. Second, I explain how to build a counter example to a stronger version of Mohar’s conjecture that is stated for pseudo-triangulations. This is joint work with Alfredo Hubard and Arnaud de Mesmay.

2024-05-16 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: Deformations of Coxeter orbifolds

by 박승열(KAIST)

Given a smooth manifold or orbifold M and a Lie group G acting transitively on a space X, we consider the space of all (G, X)-structures on M up to an appropriate equivalence relation. This space, known as the deformation space of (G, X)-structures on M, encodes information about how one can "deform" the (G, X)-manifold M. In this talk, I will provide a general definition of deformation spaces and character varieties, which capture the local structure of the deformation space. Additionally, I will introduce a class of orbifolds called the Coxeter orbifolds, for which deformation spaces can be computed using an approach due to the foundational work of E. Vinberg.

2024-05-10 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

2024-05-09 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 홍영준()

This lecture explores the topics and areas that have guided my research in computational mathematics and machine learning in recent years. Numerical methods in computational science are essential for comprehending real-world phenomena, and deep neural networks have achieved state-of-the-art results in a range of fields. The rapid expansion and outstanding success of deep learning and scientific computing have led to their applications across multiple disciplines, ranging from fluid dynamics to material sciences. In this lecture, I will focus on bridging machine learning with applied mathematics, specifically discussing topics such as scientific machine learning, numerical PDEs, and mathematical approaches of machine learning, including generative models and adversarial examples.

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