Friday, March 22, 2024

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.

2024-03-22 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by 박노성(카이스트 전산학부)

Scientific knowledge, written in the form of differential equations, plays a vital role in various deep learning fields. In this talk, I will present a graph neural network (GNN) design based on reaction-diffusion equations, which addresses the notorious oversmoothing problem of GNNs. Since the self-attention of Transformers can also be viewed as a special case of graph processing, I will present how we can enhance Transformers in a similar way. I will also introduce a spatiotemporal forecasting model based on neural controlled differential equations (NCDEs). NCDEs were designed to process irregular time series in a continuous manner and for spatiotemporal processing, it needs to be combined with a spatial processing module, i.e., GNN. I will show how this can be done.

2024-03-26 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Erdős-Pósa Dualities for Minors

by Evangelos Protopapas(University of Montpellier)

Let $\mathcal{G}$ and $\mathcal{H}$ be minor-closed graphs classes. The class $\mathcal{H}$ has the Erdős-Pósa property in $\mathcal{G}$ if there is a function $f : \mathbb{N} \to \mathbb{N}$ such that every graph $G$ in $\mathcal{G}$ either contains (a packing of) $k$ disjoint copies of some subgraph minimal graph $H \not\in \mathcal{H}$ or contains (a covering of) $f(k)$ vertices, whose removal creates a graph in $\mathcal{H}$. A class $\mathcal{G}$ is a minimal EP-counterexample for $\mathcal{H}$ if $\mathcal{H}$ does not have the Erdős-Pósa property in $\mathcal{G}$, however it does have this property for every minor-closed graph class that is properly contained in $\mathcal{G}$. The set $\frak{C}_{\mathcal{H}}$ of the subset-minimal EP-counterexamples, for every $\mathcal{H}$, can be seen as a way to consider all possible Erdős-Pósa dualities that can be proven for minor-closed classes. We prove that, for every $\mathcal{H}$, $\frak{C}_{\mathcal{H}}$ is finite and we give a complete characterization of it. In particular, we prove that $|\frak{C}_{\mathcal{H}}| = 2^{\operatorname{poly}(\ell(h))}$, where $h$ is the maximum size of a minor-obstruction of $\mathcal{H}$ and $\ell(\cdot)$ is the unique linkage function. As a corollary of this, we obtain a constructive proof of Thomas' conjecture claiming that every minor-closed graph class has the half-integral Erdős-Pósa property in all graphs. This is joint work with Christophe Paul, Dimitrios Thilikos, and Sebastian Wiederrecht.

2024-03-26 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 서성미(충남대학교)

In this talk, I will discuss recent results on the free energy of logarithmically interacting charges in the plane in an external field. Specifically, at a particular inverse temperature $\beta=2$, this system exhibits the distribution of eigenvalues of certain random matrices, forming a determinantal point process. I will explain how the large N expansion of the free energy depends on the geometric and topological properties of the region where particles condensate, considering the disk, annulus, and sphere cases. I will further discuss the conditional Ginibre ensemble as a non-radial example confirming the Zabrodin-Wiegmann conjecture regarding the spectral determinant emerging at the O(1) term in the free energy expansion. This talk is based on joint works with Sung-Soo Byun, Meng Yang, and Nam-Gyu Kang.

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.

2024-03-22 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학:

by 채석주(KAIST 수리과학과 & IBS 의생명수학그룹)

“Transcriptome-wide analysis of cell cycle-dependent bursty gene expression from single-cell RNA-seq data using mechanistic model-based inference”, bioRxiv (2024) will be discussed in this Journal Club. Bursty gene expression is quantified by two intuitive parameters: the burst frequency and the burst size. While these parameters are known to be cell-cycle dependent for some genes, a transcriptome-wide picture remains missing. Here we address this question by fitting a suite of mechanistic models of gene expression to mRNA count data for thousands of mouse genes, obtained by sequencing of single cells for which the cell-cycle position has been inferred using a deep-learning approach. This leads to the estimation of the burst frequency and size per allele in the G1 and G2/M cell-cycle phases, hence providing insight into the global patterns of transcriptional regulation. In particular, we identify an interesting balancing mechanism: on average, upon DNA replication, the burst frequency decreases by ≈ 50%, while the burst size increases by the same amount. We also show that for accurate estimation of the ratio of burst parameters in the G1 and G2/M phases, mechanistic models must explicitly account for gene copy number differences between cells but, surprisingly, additional corrections for extrinsic noise due to the coupling of transcription to cell age within the cell cycle or technical noise due to imperfect capture of RNA molecules in sequencing experiments are unnecessary. 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()

2024-03-26 / 16:30 ~ 15:30

학과 세미나/콜로퀴엄 - 정수론:

by 조성윤()

The Kudla-Rapoport conjecture predicts a relation between the arithmetic intersection numbers of special cycles on a unitary Shimura variety and the derivative of representation densities for hermitian forms at a place of good reduction. In this talk, I will present a variant of the Kudla-Rapoport conjecture at a place of bad reduction. Additionally, I will discuss a proof of the conjecture in several new cases in any dimension. This is joint work with Qiao He and Zhiyu Zhang.

2024-03-22 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #2

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