Thursday, March 21, 2024

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2024-03-28 / 11:50 ~ 12:40
대학원생 세미나 - 대학원생 세미나: The Renormalization of Volume and Chern-Simons Invariant for Hyperbolic 3-Manifolds 인쇄
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.
2024-03-22 / 11:00 ~ 12:00
학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나: 인쇄
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 인쇄
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: 인쇄
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.
2024-03-22 / 14:00 ~ 16:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
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.
2024-03-28 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by 변순식()

2024-03-21 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by 차재춘()
In dimension 4, the works of Freedman and Donaldson led us to the striking discovery that the smooth category is drastically different from the topological category, compared to other dimensions. Since then, it has been extraordinarily successful in investigating the difference in various contexts. In contrast, our understanding of when smooth and topological categories would exhibit similarity in dimension 4 remained, at best, minimal. In this talk, we will introduce some recent progress on new “topological = smooth” results in dimension 4, focusing on embedded disks.
2024-03-26 / 16:30 ~ 15:30
학과 세미나/콜로퀴엄 - 정수론: 인쇄
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 인쇄
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.
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