Wednesday, March 27, 2024

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

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.

2024-04-01 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 강성경()

We introduce bordered Floer theory and its involutive version, as well as their applications to knot complements. We will sketch the proof that invariant splittings of CFK and those of CFD correspond to each other under the Lipshitz-Ozsvath-Thurston correspondence, via invariant splitting principle, which is an ongoing work with Gary Guth.

2024-03-28 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: The Renormalization of Volume and Chern-Simons Invariant for Hyperbolic 3-Manifolds

by 이동하(KAIST)

For hyperbolic manifolds, many interesting results support a deep relationship between hyperbolic volume and the Chern-Simons invariant. In this talk, we consider noncompact hyperbolic 3-manifolds having infinite volume. For these manifolds, there is a well-defined invariant called the renormalized volume which replaces classical volume. The talk will start from a gentle introduction to hyperbolic geometry and reach the renormalization of the Chern-Simons invariant, which has a close relationship with the renormalized hyperbolic volume.

2024-03-29 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 기타:

by 김지수(서울대학교)

Geometric and topological structures can aid statistics in several ways. In high dimensional statistics, geometric structures can be used to reduce dimensionality. High dimensional data entails the curse of dimensionality, which can be avoided if there are low dimensional geometric structures. On the other hand, geometric and topological structures also provide useful information. Structures may carry scientific meaning about the data and can be used as features to enhance supervised or unsupervised learning. In this talk, I will explore how statistical inference can be done on geometric and topological structures. First, given a manifold assumption, I will explore the minimax rate for estimating the dimension of the manifold. Second, also under the manifold assumption, I will explore the minimax rate for estimating the reach, which is a regularity quantity depicting how a manifold is smooth and far from self-intersecting. Third, I will investigate inference on cluster trees, which is a hierarchy tree of high-density clusters of a density function. Fourth, I will investigate inference on persistent homology, which quantifies salient topological features that appear at different resolutions of the data.

2024-03-29 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학:

by 임동주(KAIST 수리과학과 & IBS 의생명수학그룹)

"Anti-Windup Protection Circuits for Biomolecular Integral Controllers", bioRxaiv. (2023) will be discussed in this Journal Club. In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the eigenfunctions of the generating function solution of the CME are Heun functions, while the eigenvalues can be determined by solving a continued fraction equation. Our solution generalizes and corrects a previous time-dependent solution for the CME of a gene circuit describing non-bursty protein expression in the presence of negative autoregulation [Ramos et al., Phys. Rev. E 83, 062902 (2011)]. In particular, we clarify that the eigenvalues are generally not real as previously claimed. We also investigate the relationship between different types of dynamic behavior and the type of feedback, the protein burst size, and the gene switching rate. If you want to participate in the seminar, you need to enter IBS builiding (https://www.ibs.re.kr/bimag/visiting/). Please contact if you first come IBS to get permission to enter IBS building.

2024-03-29 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to étale cohomology 2

by 이제학(KAIST)

This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.

2024-03-28 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 변순식()

2024-04-02 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: On graphs without cycles of length 0 modulo 4

by Casey Tompkins(Alfréd Rényi Institute of Mathematics)

Bollobás proved that for every $k$ and $\ell$ such that $k\mathbb{Z}+\ell$ contains an even number, an $n$-vertex graph containing no cycle of length $\ell \bmod k$ can contain at most a linear number of edges. The precise (or asymptotic) value of the maximum number of edges in such a graph is known for very few pairs $\ell$ and $k$. We precisely determine the maximum number of edges in a graph containing no cycle of length $0 \bmod 4$. This is joint work with Ervin Győri, Binlong Li, Nika Salia, Kitti Varga and Manran Zhu.

Events for the 취소된 행사 포함