Wednesday, April 2, 2025

2025-04-07 / 16:00 ~ 17:30

편미분방정식 통합연구실 세미나 - 편미분방정식: Behaviors of a solution of the logistic diffusive model and its equilibrium

by 이유빈()

Abstract:The logistic diffusive model provides the population distribution of a species according to time under a fixed open domain in R^n, a dispersal rate, and a given resource distribution. In this talk, we discuss the solution of the model and its equilibrium. First, we show the existence, uniqueness, and regularity results of the solution and the equilibrium. Then, we investigate two contrasting behaviors of the equilibrium with respect to the dispersal rate by applying two methods for each case: sub-super solution method and asymptotic expansion. Finally, we introduce an optimizing problem of a total population of the equilibrium with respect to resource distribution and prove a significant property of an optimal control called bang-bang. References: [1] Cantrell, R.S., Cosner, C. Spatial ecology via reaction-diffusion equation. Wiley series in mathematical and computational biology, John Wiley & Sons Ltd (2003) [2] I. Mazari, G. Nadin, Y. Privat, Optimization of the total population size for logistic diffusive equations: Bang-bang property and fragmentation rate, Communications in Partial Differential Equation 47 (4) (Dec 2021) 797-828

2025-04-03 / 11:50 ~ 12:30

대학원생 세미나 - 대학원생 세미나: Coloring tournaments: Structures and algorithms

by 김석범(카이스트 수리과학과 & 기초과학연구원 이산수학그룹)

Graph coloring is one of the central topics in graph theory, and there have been extensive studies about graph coloring and its variants. In this talk, we focus on the structural and algorithmic aspects of graph coloring together with their interplay. Specifically, we explain how local information on graphs can be transformed into global properties and how these can be used to investigate coloring problems from structural and algorithmic perspectives. We also introduce the notion of dicoloring, a variant of coloring defined for directed graphs, and present our recent work on dicoloring for a special type of directed graph called tournaments.

2025-04-04 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학: [Journal Club] Accurate predictions on small data with a tabular foundation model

by 임동주(KAIST)

In this talk, we discuss the paper “Accurate predictions on small data with a tabular foundation model” by Noah Hollmann et al., Nature (2025).

2025-04-09 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 미분기하 세미나:

by 서검교(숙명여자대학교)

Serrin’s overdetermined problem is a famous result in mathematics that deals with the uniqueness and symmetry of solutions to certain boundary value problems. It is called "overdetermined" because it has more boundary conditions than usually required to determine a solution, which leads to strong restrictions on the shape of the domain. In this talk, we discuss overdetermined boundary value problems in a Riemannian manifold and discuss a Serrin-type symmetry result to the solution to an overdetermined Steklov eigenvalue problem on a domain in a Riemannian manifold with nonnegative Ricci curvature and it will be discussed about an overdetermined problems with a nonconstant Neumann boundary condition in a warped product manifold.

2025-04-03 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 박사논문심사: 고차 시컨트 다양체의 정규성과 특이성

by ()

2025-04-03 / 15:00 ~ 16:00

학과 세미나/콜로퀴엄 - 박사논문심사: 뤼나-뷔스트 이론의 관점으로 본 수반 다양체의 이차곡선 매개변수공간

by ()

2025-04-08 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 김승혁(한양대학교 수학과)

We present recent developments on the quantitative stability of the Sobolev inequalities, as well as the stability of critical points of their Euler–Lagrange equations. In particular, we introduce our recent joint work with H. Chen (Hanyang University) and J. Wei (The Chinese University of Hong Kong) on the stability of the Yamabe problem, the fractional Lane–Emden equation for all possible orders, and the Brezis-Nirenberg problem.

2025-04-03 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

TBD

2025-04-04 / 11:00 ~ 12:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

The advent of single-cell transcriptomics has brought a greatly improved understanding of the heterogeneity of gene expression across cell types, with important applications in developmental biology and cancer research. Single-cell RNA sequencing datasets, which are based on tags called universal molecular identifiers, typically include a large number of zeroes. For such datasets, genes with even moderate expression may be poorly represented in sequencing count matrices. Standard pipelines often retain only a small subset of genes for further analysis, but we address the problem of estimating relative expression across the entire transcriptome by adopting a multivariate lognormal Poisson count model. We propose empirical Bayes estimation procedures to estimate latent cell-cell correlations, and to recover meaningful estimates for genes with low expression. For small groups of cells, an important sampling procedure uses the full cell-cell correlation structure and is computationally feasible. For larger datasets, we propose a gene-level shrinkage procedure that has favorable performance for datasets with approximately compound symmetric cell-cell correlation. A fast procedure that incorporates matrix approximations is also promising, and extensible to very large datasets. We apply our approaches to simulated and real datasets, and demonstrate favorable performance in comparisons to competing normalization approaches. We further illustrate the applications of our approach in downstream analyses, including cell-type clustering and identification.

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