Saturday, October 21, 2023

2023-10-27 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by ()

The talk will focus on a part of the frontier of our current understanding of nonlinear stability of traveling waves of partial differential equations, especially on how spectral stability implies nonlinear stability and which kind of dynamics may be expected. We shall highlight main expected difficulties related to the stability of discontinuous waves of hyperbolic systems, and show a few significant steps obtained by the speaker with respectively Vincent Duchêne (Rennes), Gregory Faye (Toulouse) and Louis Garénaux (Karslruhe).

2023-10-23 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by ()

In this talk, we study the non-cutoff Boltzmann collision kernel for the inverse power law potentials $U_s(r)=1/r^{s-1}$ for $s>2$ in dimension $d=3$. We will study the formal derivation of the non-cutoff collision kernel. Then we will prove the limit of the non-cutoff kernel to the hard-sphere kernel and check the angular singularity would vanish. We will also see precise asymptotic formulas of the singular layer near $\theta\simeq 0$ in the limit $s\to \infty$. Consequently, we will also see that solutions to the homogeneous Boltzmann equation converge to the respective solutions weakly in $L^1$ globally in time as $s\to \infty$.

2023-10-24 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Powers of planar graphs, product structure, and blocking partitions

by Robert Hickingbotham(Monash University)

Graph product structure theory describes complex graphs in terms of products of simpler graphs. In this talk, I will introduce this subject and talk about some of my recent results in this area. The focus of my talk will be on a new tool in graph product structure theory called `blocking partitions.’ I’ll show how this tool can be used to prove stronger product structure theorems for powers of planar graphs as well as k-planar graphs, resolving open problems of Dujmović, Morin and Wood, and Ossona de Mendez.

2023-10-26 / 14:30 ~ 15:45

학과 세미나/콜로퀴엄 - 기타:

by ()

2023-10-25 / 15:00 ~ 16:00

학과 세미나/콜로퀴엄 - 미분기하 세미나:

by (포항공대)

The Gauss-Bonnet theorem implies that the two dimensional torus does not have nonnegative Gauss curvature unless it is flat, and that the two dimensional sphere does not a metric which has Gaussian curvature bounded below by one and metric bounded below by the standard round metric. Gromov proposed a series of conjectures on generalizing the Gauss-Bonnet theorem in his four lectures. I will report my work with Gaoming Wang (now Tsinghua) on Gromov dihedral rigidity conjecture in hyperbolic 3-space and scalar curvature comparison of rotationally symmetric convex bodies with some simple singularities.

2023-10-24 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나: Colloquium: On The Power of Foundation Models and Mathematics in the New Era

by 유재준(UNIST AI대학원)

In this lecture, we aim to delve deep into the emerging landscape of 'Foundation Models'. Distinct from traditional deep learning models, Foundation Models have ushered in a new paradigm, characterized by their vast scale, versatility, and transformative potential. We will uncover the key differences between these models and their predecessors, delving into the intricate mechanisms through which they are trained and the profound impact they are manifesting across various sectors. Furthermore, the talk will shed light on the invaluable role of mathematics in understanding, optimizing, and innovating upon these models. We will explore the symbiotic relationship between Foundation Models and mathematical principles, elucidating how the latter not only underpins their functioning but also paves the way for future advancements.

Events for the 취소된 행사 포함