Tuesday, May 7, 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.

2024-05-08 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

The Tomas-Stein inequality is a fundamental inequality in Fourier Analysis. It measures the L^4 norm of the Fourier transform of the sphere surface measure in terms of the L^2 norm. It is possible because the sphere has a positive Gaussian curvature. In this talk we will present what is an extremizer problem to this inequality and what is the progress of this problem.

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.

2024-05-10 / 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.

2024-05-07 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Aharoni’s rainbow cycle conjecture holds up to an additive constant

by Tony Huynh(Sapienza Università di Roma)

In 2017, Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture for digraphs. If G is a simple n-vertex edge-colored graph with n color classes of size at least r, then G contains a rainbow cycle of length at most ⌈n/r⌉. In this talk, we prove that Aharoni’s conjecture holds up to an additive constant. Specifically, we show that for each fixed r, there exists a constant c such that if G is a simple n-vertex edge-colored graph with n color classes of size at least r, then G contains a rainbow cycle of length at most n/r+c. This is joint work with Patrick Hompe.

2024-05-07 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 대수기하학:

by 황준묵(IBS-CCG)

We introduce a general equivalence problems for geometric structures arising from minimal rational curves on uniruled complex projective manifolds. To study these problems, we need approaches fusing differential geometry and algebraic geometry. Among such geometric structures, those associated to homogeneous manifolds are particularly accessible to differential-geometric methods of Cartan geometry. But even in these cases, only a few cases have been worked out so far. We review some recent developments.

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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