# Department Seminars & Colloquia

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A major trajectory in the development of statistical learning has been the expansion of mathematical spaces underlying observed data, extending from numbers to vectors, functions, and beyond. This expansion has fostered significant theoretical and computational breakthroughs. One notable direction involves analyzing sets where each set becomes an object of interest for inference. This perspective accommodates the intrinsic and non-ignorable heterogeneity inherent in data-generating processes. Among various theoretical frameworks to analyze sets, a principled approach is viewing a set as an empirical measure. In this talk, I revisit the concept of the median - a robust alternative to the mean as a centroid - and introduce a novel extension of this concept within the space of probability measures under the framework of optimal transport. I will present theoretical results and a generic computational pipeline that leverages existing algorithmic developments in the field, with examples. Furthermore, the potential benefits of this novel approach for scalable inference and scientific discovery will be explored.

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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Room B232, IBS
IBS-KAIST Seminar
Brenda Gavina (IBS BIMAG)
[Journal Club] Computational screen for sex-specific drug effects in a cardiac fibroblast signaling network model

Room B232, IBS

IBS-KAIST Seminar

In this talk, we will discuss the paper, “Computational screen for sex-specific drug effects in a cardiac fibroblast signaling network model”, by K.M. Watts, W. Nichols and W.J. Richardson, Scientific Reports, 2023.
Abstract
Heart disease is the leading cause of death in both men and women. Cardiac fibrosis is the uncontrolled accumulation of extracellular matrix proteins, which can exacerbate the progression of heart failure, and there are currently no drugs approved specifically to target matrix accumulation in the heart. Computational signaling network models (SNMs) can be used to facilitate discovery of novel drug targets. However, the vast majority of SNMs are not sex-specific and/or are developed and validated using data skewed towards male in vitro and in vivo samples. Biological sex is an important consideration in cardiovascular health and drug development. In this study, we integrate a cardiac fibroblast SNM with estrogen signaling pathways to create sex-specific SNMs. The sex-specific SNMs demonstrated high validation accuracy compared to in vitro experimental studies in the literature while also elucidating how estrogen signaling can modulate the effect of fibrotic cytokines via multi-pathway interactions. Further, perturbation analysis and drug screening uncovered several drug compounds predicted to generate divergent fibrotic responses in male vs. female conditions, which warrant further study in the pursuit of sex-specific treatment recommendations for cardiac fibrosis. Future model development and validation will require more generation of sex-specific data to further enhance modeling capabilities for clinically relevant sex-specific predictions of cardiac fibrosis and treatment.

In this talk we present homogeneous nonprime ideals that can be used to produce, via an unprojection process, homogeneous prime ideals of high Castelnuovo-Mumford regularity. We thus provide counterexamples to the Eisenbud-Goto regularity conjecture other than those given by the Rees-like algebra method of J. McCullough and I. Peeva. Their construction was inspired by G. Caviglia (2004), J. Beder et al. (2011), and K. Borna-A. Mohajer (2015, arXiv).

Let G be a numerical semigroup. We prove an upper bound for the Betti numbers of the semigroup ring of G which depends only on the width of G, that is, the difference between the largest and the smallest generators of G. In this way, we make progress towards a conjecture of Herzog and Stamate. Moreover, for 4-generated numerical semigroups, the first significant open case, we prove the Herzog-Stamate bound for all but finitely many values of the width.
This is a joint work with A. Moscariello and A. Sammartano.

This is a one-day workshop with young geometric topologists. Follow the link for more details

https://sites.google.com/site/hrbaik85/workshop-and-conferences-at-kaist/yggt-at-kaist?authuser=0

https://sites.google.com/site/hrbaik85/workshop-and-conferences-at-kaist/yggt-at-kaist?authuser=0

It has been well known that any closed, orientable 3-manifold can be obtained by performing Dehn surgery on a link in S^3. One of the most prominent problems in 3-manifold topology is to list all the possible lens spaces that can be obtained by a Dehn surgery along a knot in S^3, which has been solved by Greene. A natural generalization of this problem is to list all the possible lens spaces that can be obtained by a Dehn surgery from other lens spaces. Besides, considering surgeries between lens spaces is also motivated from DNA topology. In this talk, we will discuss distance one surgeries between lens spaces L(n, 1) with n ≥ 5 odd and lens spaces L(s, 1) for nonzero s and the corresponding band surgeries from T(2, n) to T(2, s), by using our Heegaard Floer d-invariant surgery formula, which is deduced from the Heegaard Floer mappping cone formula. We give an almost complete classification of the above surgeries.

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Wonwoo Kang (University of Illinois, Urbana-Champaign)
Skein relations for punctured surfaces

Room B332, IBS (기초과학연구원)

Discrete Mathematics

Since the introduction of cluster algebras by Fomin and Zelevinsky in 2002, there has been significant interest in cluster algebras of surface type. These algebras are particularly noteworthy due to their ability to construct various combinatorial structures like snake graphs, T-paths, and posets, which are useful for proving key structural properties such as positivity or the existence of bases. In this talk, we will begin by presenting a cluster expansion formula that integrates the work of Musiker, Schiffler, and Williams with contributions from Wilson, utilizing poset representatives for arcs on triangulated surfaces. Using these posets and the expansion formula as tools, we will demonstrate skein relations, which resolve intersections or incompatibilities between arcs. Topologically, a skein relation replaces intersecting arcs or arcs with self-intersections with two sets of arcs that avoid the intersection differently. Additionally, we will show that all skein relations on punctured surfaces include a term that is not divisible by any coefficient variable. Consequently, we will see that the bangles and bracelets form spanning sets and exhibit linear independence. This work is done in collaboration with Esther Banaian and Elizabeth Kelley.

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Kisun Lee (Clemson University)
Symmetric Tropical Rank 2 Matrices

Room B332, IBS (기초과학연구원)

Discrete Mathematics

Tropical geometry replaces usual addition and multiplication with tropical addition (the min) and tropical multiplication (the sum), which offers a polyhedral interpretation of algebraic variety. This talk aims to pitch the usefulness of tropical geometry in understanding classical algebraic geometry. As an example, we introduce the tropicalization of the variety of symmetric rank 2 matrices. We discuss that this tropicalization has a simplicial complex structure as the space of symmetric bicolored trees. As a result, we show that this space is shellable and delve into its matroidal structure. It is based on the joint work with May Cai and Josephine Yu.

The analysis on the limiting behavior of solution is pivotal for equations in geometric analysis, mathematical physics and application in optimization. In 80s, Rene Thom conjectured that if an analytic gradient flow has a limit, then it approaches to the limit along a unique asymptotic direction. This represents a higher-order question following the seminal works by Lojasiewicz and L. Simon. In 2000, this conjecture was affirmatively proved by Kurdyka, Mostowski, and Parusinski for finite dimensional gradient flows. In this talk, we present a generalization of this to the class of PDEs which are gradient flows or equations with gradient structure. Our result reveals both the rate and the direction of convergence to the limit. This is a joint work with Pei-Ken Hung at UIUC.

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Hyunwoo Lee (KAIST & IBS Extremal Combinatorics and Probabi)
Random matchings in linear hypergraphs

Room B332, IBS (기초과학연구원)

Discrete Mathematics

For a given hypergraph $H$ and a vertex $v\in V(H)$, consider a random matching $M$ chosen uniformly from the set of all matchings in $H.$ In $1995,$ Kahn conjectured that if $H$ is a $d$-regular linear $k$-uniform hypergraph, the probability that $M$ does not cover $v$ is $(1 + o_d(1))d^{-1/k}$ for all vertices $v\in V(H)$. This conjecture was proved for $k = 2$ by Kahn and Kim in 1998.
In this paper, we disprove this conjecture for all $k \geq 3.$ For infinitely many values of $d,$ we construct $d$-regular linear $k$-uniform hypergraph $H$ containing two vertices $v_1$ and $v_2$ such that $\mathcal{P}(v_1 \notin M) = 1 – \frac{(1 + o_d(1))}{d^{k-2}}$ and $\mathcal{P}(v_2 \notin M) = \frac{(1 + o_d(1))}{d+1}.$ The gap between $\mathcal{P}(v_1 \notin M)$ and $\mathcal{P}(v_2 \notin M)$ in this $H$ is best possible. In the course of proving this, we also prove a hypergraph analog of Godsil’s result on matching polynomials and paths in graphs, which is of independent interest.

In the 1970's J. Levine produced a surjection from the knot concordance group to the so called algebraic concordance group. This captured the known features of the knot concordance group to that point and classifies high dimensional concordance. During this survey talk we will explore the construction of the algebraic concordance group and explain some of its consequences.

In the 1980's Casson and Gordon produced the first non slice knots which are trivial in Levine's algebraic concordance group, and in 2003 Cochran-Orr-Teichner produced the first no slice knots undetectable by Casson and Gordon's invariants. They do so by producing a filtration of the concordance group by subgroups a knot in the 1.5th term of this filtration has vanishing Casson-Gordon invariants. Since then this work has been central to the study of knot concordance. We will introduce this filtration and review just enough of the theory of L^2 homology to prove that the successive quotients of this filtration are nontrivial.

Knot homology theories revolutionized the study of knots and links, much like (simplicial or singular) homology theory revolutionized the study of topological spaces. One of the major knot homology theories, Khovanov homology, was introduced by M. Khovanov in 2000 as a "categorification of the Jones polynomial." One notable feature of Khovanov homology is its ability to detect the unknot, a feature not known to be possessed by the Jones polynomial. Recently, it has found notable applications in low-dimensional topology, including the detection of exotic surfaces in the 4-ball.
Day 1: Jones polynomial and its categorification.

Knot homology theories revolutionized the study of knots and links, much like (simplicial or singular) homology theory revolutionized the study of topological spaces. One of the major knot homology theories, Khovanov homology, was introduced by M. Khovanov in 2000 as a "categorification of the Jones polynomial." One notable feature of Khovanov homology is its ability to detect the unknot, a feature not known to be possessed by the Jones polynomial. Recently, it has found notable applications in low-dimensional topology, including the detection of exotic surfaces in the 4-ball.
Day 2: Numerical invariants from Khovanov homology and their applications.

Knot homology theories revolutionized the study of knots and links, much like (simplicial or singular) homology theory revolutionized the study of topological spaces. One of the major knot homology theories, Khovanov homology, was introduced by M. Khovanov in 2000 as a "categorification of the Jones polynomial." One notable feature of Khovanov homology is its ability to detect the unknot, a feature not known to be possessed by the Jones polynomial. Recently, it has found notable applications in low-dimensional topology, including the detection of exotic surfaces in the 4-ball.
Day 3: Recent developments of Khovanov homology and its applications to low-dimensional topology.

Pressure functions are key ideas in the thermodynamic formalism of dynamical systems. McMullen used the convexity of the pressure function to construct a metric, called a pressure metric, on the Teichmuller space and showed that it is a constant multiple of the Weil-Petersson metric. In the spirit of Sullivan's dictionary, McMullen applied the same idea to define a metric on the space of Blaschke products.
In this talk, we will discuss Bridgeman-Taylor and McMullen's earlier works on the pressure metric, as well as recent developments in more generic settings. Then we will talk about pressure metrics on hyperbolic components in complex dynamics, as well as unsolved problems.

When does a topological branched self-covering of the sphere enjoy a holomorphic structure? William Thurston answered this question in the 1980s by using a holomorphic self-map of the Teichmuller space known as Thurston's pullback map. About 30 years later, Dylan Thurston took a different approach to the same question, reducing it to a one-dimensional dynamical problem. We will discuss both characterizations and their applications to various questions in complex dynamics.

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Semin Yoo (IBS Discrete Mathematics Group)
Paley-like quasi-random graphs arising from polynomials

Room B332, IBS (기초과학연구원)

Discrete Mathematics

We provide new constructions of families of quasi-random graphs that behave like Paley graphs but are neither Cayley graphs nor Cayley sum graphs. These graphs give a unified perspective of studying various graphs defined by polynomials over finite fields, such as Paley graphs, Paley sum graphs, and graphs associated with Diophantine tuples and their generalizations from number theory. As an application, we provide new lower bounds on the clique number and independence number of general quasi-random graphs. In particular, we give a sufficient condition for the clique number of quasi-random graphs of order $n$ to be at least $(1-o(1))\log_{3.008}n$. Such a condition applies to many classical quasi-random graphs, including Paley graphs and Paley sum graphs, as well as some new Paley-like graphs we construct. If time permits, we also discuss some problems of diophantine tuples arising from number theory, which is our original motivation.
This is joint work with Seoyoung Kim and Chi Hoi Yip.

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Room B232, IBS
IBS-KAIST Seminar
Hyun Kim (IBS BIMAG)
[Journal Club] Powerful and accurate detection of temporal gene expression patterns from multi-sample multi-stage single-cell transcriptomics data wit

Room B232, IBS

IBS-KAIST Seminar

In this talk, we discuss the paper, “Powerful and accurate detection of temporal gene expression patterns from multi-sample multi-stage single-cell transcriptomics data with TDEseq” by Y. Fan, L. Li and S. Sun, Genome Biology, 2024.
Abstract
We present a non-parametric statistical method called TDEseq that takes full advantage of smoothing splines basis functions to account for the dependence of multiple time points in scRNA-seq studies, and uses hierarchical structure linear additive mixed models to model the correlated cells within an individual. As a result, TDEseq demonstrates powerful performance in identifying four potential temporal expression patterns within a specific cell type. Extensive simulation studies and the analysis of four published scRNA-seq datasets show that TDEseq can produce well-calibrated p-values and up to 20% power gain over the existing methods for detecting temporal gene expression patterns.
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.

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Maria Chudnovsky (Princeton University)
Anticomplete subgraphs of large treewidth

Room B332, IBS (기초과학연구원)

Discrete Mathematics

We will discuss recent progress on the topic of induced subgraphs and tree-decompositions. In particular this talk with focus on the proof of a conjecture of Hajebi that asserts that (if we exclude a few obvious counterexamples) for every integer t, every graph with large enough treewidth contains two anticomplete induced subgraphs each of treewidth at least t. This is joint work with Sepher Hajebi and Sophie Spirkl.

Deep learning has shown remarkable success in various fields, and efforts continue to develop investment methodologies using deep learning in the financial sector. Despite numerous successes, the fact is that the revolutionary results seen in areas such as image processing and natural language processing have not been seen in finance. There are two reasons why deep learning has not led to disruptive change in finance. First, the scarcity of financial data leads to overfitting in deep learning models, so excellent backtesting results do not translate into actual outcomes. Second, there is a lack of methodological development for optimizing dynamic control models under general conditions. Therefore, I aim to overcome the first problem by artificially augmenting market data through an integration of Generative Adversarial Networks (GANs) and the Fama-French factor model, and to address the second problem by enabling optimal control even under complex conditions using policy-based reinforcement learning. The methods of this study have been shown to significantly outperform traditional linear financial factor models such as the CAPM and value-based approaches such as the HJB equation.

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Room B232, IBS
IBS-KAIST Seminar
Olive Cawiding (IBS BIMAG)
[Journal Club] CausalXtract: a flexible pipeline to extract causal effects from live-cell time-lapse imaging data

Room B232, IBS

IBS-KAIST Seminar

"CausalXtract: a flexible pipeline to extract causal effects from live-cell time-lapse imaging data”, by Franck Simon et.al., bioRxiv, 2024, will be discussed in the Journal Club. The abstract is the following :
Live-cell microscopy routinely provides massive amount of time-lapse images of complex cellular systems under various physiological or therapeutic conditions. However, this wealth of data remains difficult to interpret in terms of causal effects. Here, we describe CausalXtract, a flexible computational pipeline that discovers causal and possibly time-lagged effects from morphodynamic features and cell-cell interactions in live-cell imaging data. CausalXtract methodology combines network-based and information-based frameworks, which is shown to discover causal effects overlooked by classical Granger and Schreiber causality approaches. We showcase the use of CausalXtract to uncover novel causal effects in a tumor-on-chip cellular ecosystem under therapeutically relevant conditions. In particular, we find that cancer associated fibroblasts directly inhibit cancer cell apoptosis, independently from anti-cancer treatment. CausalXtract uncovers also multiple antagonistic effects at different time delays. Hence, CausalXtract provides a unique computational tool to interpret live-cell imaging data for a range of fundamental and translational research applications.
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.

This talk presents a uniform framework for computational fluid dynamics in porous media based on finite element velocity and pressure spaces with minimal degrees of freedom. The velocity space consists of linear Lagrange polynomials enriched by a discontinuous, piecewise linear, and mean-zero vector function per element, while piecewise constant functions approximate the pressure. Since the fluid model in porous media can be seen as a combination of the Stokes and Darcy equations, different conformities of finite element spaces are required depending on viscous parameters, making it challenging to develop a robust numerical solver uniformly performing for all viscous parameters. Therefore, we propose a pressure-robust method by utilizing a velocity reconstruction operator and replacing the velocity functions with a reconstructed velocity. The robust method leads to error estimates independent of a pressure term and shows uniform performance for all viscous parameters, preserving minimal degrees of freedom. We prove well-posedness and error estimates for the robust method while comparing it with a standard method requiring an impractical mesh condition. We finally confirm theoretical results through numerical experiments with two- and three-dimensional examples and compare the methods' performance to support the need for our robust method.

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Room B332, IBS (기초과학연구원)
Discrete Mathematics
Jane Tan (University of Oxford)
Semi-strong colourings of hypergraphs

Room B332, IBS (기초과학연구원)

Discrete Mathematics

A vertex colouring of a hypergraph is $c$-strong if every edge $e$ sees at least $\min\{c, |e|\}$ distinct colours. Let $\chi(t,c)$ denote the least number of colours needed so that every $t$-intersecting hypergraph has a $c$-strong colouring. In 2012, Blais, Weinstein and Yoshida introduced this parameter and initiated study on when $\chi(t,c)$ is finite: they showed that $\chi(t,c)$ is finite whenever $t \geq c$ and unbounded when $t\leq c-2$. The boundary case $\chi(c-1, c)$ has remained elusive for some time: $\chi(1,2)$ is known to be finite by an easy classical result, and $\chi(2,3)$ was shown to be finite by Chung and independently by Colucci and Gyárfás in 2013. In this talk, we present some recent work with Kevin Hendrey, Freddie Illingworth and Nina Kamčev in which we fill in this gap by showing that $\chi(c-1, c)$ is finite in general.