Wednesday, March 26, 2025

2025-03-31 / 16:00 ~ 17:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Singular limit problems of Maxwell-Euler and Boussinesq equations

by 이지훈(중앙대학교)

The singular limit problem is an important issue in various forms of ODEs and PDEs, and it is particularly known as a fundamental problem in equations derived from fluid dynamics. In this presentation, I will introduce some general phenomena of the singular limit problem through several examples. Subsequently, I will examine how the solution of the Euler-Maxwell equations converges to the MHD equations under the assumption that the speed of light approaches infinity, and how the Boussinesq equations converge to the QG equations in certain regimes.

2025-04-01 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Reconstructing hypergraph matching polynomials

by Hyunwoo Lee(KAIST & IBS Extremal Combinatorics and Probabi)

By utilizing the recently developed hypergraph analogue of Godsil’s identity by the second author, we prove that for all $n \geq k \geq 2$, one can reconstruct the matching polynomial of an $n$-vertex $k$-uniform hypergraph from the multiset of all induced sub-hypergraphs on $\lfloor \frac{k-1}{k}n \rfloor + 1$ vertices. This generalizes the well-known result of Godsil on graphs in 1981 to every uniform hypergraph. As a corollary, we show that for every graph $F$, one can reconstruct the number of $F$-factors in a graph under analogous conditions. We also constructed examples that imply the number $\lfloor \frac{k-1}{k}n \rfloor + 1$ is the best possible for all $n\geq k \geq 2$ with $n$ divisible by $k$. This is joint work Donggyu Kim.

2025-03-26 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 서동균(서울대학교)

A surface can be decomposed into a union of pairs of pants, a construction known as a pants decomposition. This fundamental observation reveals many important properties of surfaces. By forming a simplicial graph whose vertices represent pants decompositions, connecting two vertices with an edge whenever the corresponding decompositions differ by a simple move, we obtain a graph that is quasi-isometric to the Weil–Petersson metric on Teichmüller space. Meanwhile, topologists often study a structure called a rose, formed by attaching multiple circles at a single point. A rose is homotopy equivalent to a compact surface with boundary. Consequently, we can define a pants decomposition of a rose as the pants decomposition of a surface homotopy equivalent to it. In this talk, we will explore the concept of pants decompositions specifically in the context of roses.

2025-03-27 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 허영미(연세대학교 수학과)

Wavelets provide a versatile framework for signal representation and analysis, integrating ideas from harmonic analysis, approximation theory, and practical algorithm design. In this talk, we introduce foundational concepts in wavelet theory, focusing on classical results regarding wavelet expansions and approximations. Building on these basics, we explore modern developments and discuss how these approaches can balance theoretical rigor with practical convenience. The presentation aims to offer both a solid introduction to classical wavelet theory and a glimpse into current and future research directions. Part of the talk is based on joint work with Hyojae Lim.

2025-03-28 / 11:00 ~ 12:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

Individual human cancer cells often show different responses to the same treatment. In this talk I will share the quantitative experimental approaches my lab has developed for studying the fate and behavior of human cells at the single-cell level. I will focus on the tumor suppressor protein p53, a transcription factor controlling genomic integrity and cell survival. In the last several years we have established the dynamics of p53 (changes in its levels over time) as an important mechanism controlling gene expression and guiding cellular outcomes. I will present recent studies from the lab demonstrating how studying p53 dynamics in response to radiation and chemotherapy in single cells can guide the design and schedule of combinatorial therapy, and how the p53 oscillator can be used to study the principles and function of entertainment in Biology. I will also present new findings suggesting that p53’s post-translational modification state is altered between its first and second pulses of expression, and the effects these have on gene expression programs over time.

2025-04-02 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 정수론: Representing Some Number Sequences as Products of Fibonacci-like Sequences

by İLKER İNAM(Bilecik Şeyh Edebali Üniversitesi)

Diophantine equations involving specific number sequences have attracted considerable attention. For instance, studying when a Tribonacci number can be expressed as the product of two Fibonacci numbers is an interesting problem. In this case, the corresponding Diophantine equation has only two nontrivial integer solutions. While finding these solutions is relatively straightforward, proving that no further solutions exist requires a rigorous argument-this is where Baker’s method plays a crucial role. After conducting a comprehensive literature review on the topic, we present our recent results on Diophantine equations involving Fibonacci, Tribonacci, Jacobsthal, and Perrin numbers. Furthermore, as an application of Baker’s method, we will briefly demonstrate how linear forms in logarithms can be effectively applied to Diophantine equations involving Fibonacci-like sequences. This is joint work with Zeynep Demirkol Ozkaya (Van), Zekiye Pinar Cihan (Bilecik) and Meltem Senadim (Bilecik).

2025-04-02 / 14:30 ~ 15:30

학과 세미나/콜로퀴엄 - 정수론: Fast Computation of Half-Integral Weight Modular Forms and a Sato-Tate Like Problem

by İLKER İNAM(Bilecik Şeyh Edebali Üniversitesi)

Modular forms continue to attract attention for decades with many different application areas. To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to be able to compute a large number of Fourier coefficients. In this talk, firstly, we will show that this can be achieved in level 4 for a large range of half-integral weights by making use of one of three explicit bases, the elements of which can be calculated via fast power series operations. After having "many" Fourier coefficients, it is time to ask the following question: Can the dis- tribution of normalised Fourier coefficients of half-integral weight level 4 Hecke eigenforms with bounded indices be approximated by a distribution? We will suggest that they follow the generalised Gaussian distribution and give some numerical evidence for that. Finally, we will see that the appar- ent symmetry around zero of the data lends strong evidence to the Bruinier- Kohnen Conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently. This is joint work with Gabor Wiese (Luxembourg), Zeynep Demirkol Ozkaya (Van) and Elif Tercan (Bilecik).

Events for the 취소된 행사 포함