Wednesday, April 3, 2024

2024-04-09 / 16:00 ~ 17:00

by ()

I will discuss some recent progress on the freeness problem for groups of 2x2 rational matrices generated by two parabolic matrices. In particular, I will discuss recent progress on determining the structural properties of such groups (beyond freeness) and when they have finite index in the finitely presented group SL(2,Z[1/m]), for appropriately chosen m.

2024-04-05 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by 전동석(서울대학교)

The size and complexity of recent deep learning models continue to increase exponentially, causing a serious amount of hardware overheads for training those models. Contrary to inference-only hardware, neural network training is very sensitive to computation errors; hence, training processors must support high-precision computation to avoid a large performance drop, severely limiting their processing efficiency. This talk will introduce a comprehensive design approach to arrive at an optimal training processor design. More specifically, the talk will discuss how we should make important design decisions for training processors in more depth, including i) hardware-friendly training algorithms, ii) optimal data formats, and iii) processor architecture for high precision and utilization.

2024-04-03 / 17:00 ~ 17:50

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

In this talk, we consider some polynomials which define Gaussian Graphical models in algebraic statistics. First, we briefly introduce background materials and some preliminary on this topic. Next, we regard a conjecture due to Sturmfels and Uhler concerning generation of the prime ideal of the variety associated to the Gaussian graphical model of any cycle graph and explain how to prove it. We also report a result on linear syzygies of any model coming from block graphs. The former work was done jointly with A. Conner and M. Michalek and the latter with J. Choe.

2024-04-03 / 16:00 ~ 16:50

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

One of the classical and most fascinating problems at the intersection between combinatorics and number theory is the study of the parity of the partition function. Even though p(n) in widely believed to be equidistributed modulo 2, progress in the area has proven exceptionally hard. The best results available today, obtained incrementally over several decades by Serre, Soundarajan, Ono and many otehrs, do not even guarantee that, asymptotically, p(n) is odd for /sqrt{x} values of n/neq x, In this talk, we present a new, general conjectural framework that naturally places the parity of p(n) into the much broader, number-theoretic context of eta-eqotients. We discuss the history of this problem as well as recent progress on our "master conjecture," which includes novel results on multi-and regular partitions. We then show how seemingly unrelated classes of eta-equotients carry surprising (and surprisingly deep) connections modulo 2 to the partition function. One instance is the following striking result: If any t-multiparition function, with t/neq 0(mod 3), is odd with positive density, then so is p(n). (Note that proving either fact unconditionally seems entirely out of reach with current methods.) Throughout this talk, we will give a sense of the many interesting mathematical techniques that come into play in this area. They will include a variety of algebraic and combinatorial ideas, as well as tools from modular forms and number theory.

2024-04-09 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Positive discrepancy, MaxCut and eigenvalues of graphs

by Eero Räty(Umeå University)

The positive discrepancy of a graph $G$ of edge density $p$ is defined as the maximum of $e(U) - p|U|(|U|-1)/2$, where the maximum is taken over subsets of vertices in G. In 1993 Alon proved that if G is a $d$-regular graph on $n$ vertices and $d = O(n^{1/9})$, then the positive discrepancy of $G$ is at least $c d^{1/2}n$ for some constant $c$. We extend this result by proving lower bounds for the positive discrepancy with average degree d when $d < (1/2 - \epsilon)n$. We prove that the same lower bound remains true when $d < n^(2/3)$, while in the ranges $n^{2/3} < d < n^{4/5}$ and $n^{4/5} < d < (1/2 - \epsilon)n$ we prove that the positive discrepancy is at least $n^2/d$ and $d^{1/4}n/log(n)$ respectively. Our proofs are based on semidefinite programming and linear algebraic techniques. Our results are tight when $d < n^{3/4}$, thus demonstrating a change in the behaviour around $d = n^{2/3}$ when a random graph no longer minimises the positive discrepancy. As a by-product, we also present lower bounds for the second largest eigenvalue of a $d$-regular graph when $d < (1/2 - \epsilon)n$, thus extending the celebrated Alon-Boppana theorem. This is joint work with Benjamin Sudakov and István Tomon.

2024-04-08 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 강성경()

Using the invariant splitting principle, we construct an infinite family of exotic pairs of contractible 4-manifolds which survive one stabilization. We argue that some of them are potential candidates for surviving two stabilizations.

2024-04-05 / 17:00 ~ 18:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Convex integration and applications to PDEs II

by 김성학(경북대학교)

In the second talk of the series, we exhibit several examples of application of convex integration to important PDE problems. In particular, we shall sketch some ideas of proof such as in the p-Laplace equation and its parabolic analogue, Euler-Lagrange equation of a polyconvex energy, gradient flow of a polyconvex energy and polyconvex elastodynamics.

2024-04-09 / 17:00 ~ 18:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Evolution of Crystalline Mean Curvature Flow with a Volume Constraint: Part 2

by 권도현(서울시립대학교)

In this talk, we focus on the global existence of volume-preserving mean curvature flows. In the isotropic case, leveraging the gradient flow framework, we demonstrate the convergence of solutions to a ball for star-shaped initial data. On the other hand, for anisotropic and crystalline flows, we establish the global-in-time existence for a class of initial data with the reflection property, utilizing explicit discrete-in-time approximation methods.

2024-04-05 / 16:00 ~ 17:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Convex integration and applications to PDEs I

by 김성학(경북대학교)

We begin the first talk by introducing the concept of an h-principle that is mostly accessible through the two important methods. One of the methods is the convex integration that was successfully used by Mueller and Sverak and has been applied to many important PDEs. The other is the so-called Baire category method that was mainly studied by Dacorogna and Marcellini. We compare these methods in applying to a toy example.

2024-04-04 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: The Asymptotic Iteration Method and Hanh Difference Equations

by Lucas MacQuarrie(KAIST, IBS 의생명 수학 그룹)

TBA

2024-04-09 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 권도현(서울시립대학교)

Atoms and molecules aim to minimize surface energy, while crystals exhibit directional preferences. Starting from the classical isoperimetric problem, we investigate the evolution of volume-preserving crystalline mean curvature flow. Defining a notion of viscosity solutions, we demonstrate the preservation of geometric properties associated with the Wulff shape. We establish global-in-time existence and regularity for a class of initial data. Furthermore, we discuss recent findings on the long-time behavior of the flow towards the critical point of the anisotropic perimeter functional in a planar setting.

2024-04-05 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

2024-04-04 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

After a brief review of the history, some applications of these models will be reviewed. This will include descriptions of rogue waves, tsunami propagation, internal waves and blood flow. Some of the theory emanaging from these applications will then be sketched.

2024-04-05 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #3

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.

Events for the 취소된 행사 포함