SATNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SATNet has been successfully applied to learn, among others, the rules of a complex logical puzzle, such as Sudoku, just from input and output pairs where inputs are given as images. In this paper, we show how to improve the learning of SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We present SymSATNet, a variant of SATNet that translates the given symmetries of the target rules to a condition on the parameters of SATNet and requires that the parameters should have a particular parametric form that guarantees the condition. The requirement dramatically reduces the number of parameters to learn for the rules with enough symmetries, and makes the parameter learning of SymSATNet much easier than that of SATNet. We also describe a technique for automatically discovering symmetries of the target rules from examples. Our experiments with Sudoku and Rubik’s cube show the substantial improvement of SymSATNet over the baseline SATNet. This is joint work with Sangho Lim and Eungyeol Oh.

Offline reinforcement learning (RL) refers to the problem setting where the agent aims to optimize the policy solely from the pre-collected data without further environment interactions. In offline RL, the distributional shift becomes the primary source of difficulty, which arises from the deviation of the target policy being optimized from the behavior policy used for data collection. This typically causes overestimation of action values, which poses severe problems for model-free algorithms that use bootstrapping. To mitigate the problem, prior offline RL algorithms often used sophisticated techniques that encourage underestimation of action values, which introduces an additional set of hyperparameters that need to be tuned properly. In this talk, I present OptiDICE, an offline RL algorithm that prevents overestimation in a more principled way. OptiDICE directly estimates the stationary distribution corrections of the optimal policy and does not rely on policy-gradients, unlike previous offline RL algorithms. Using an extensive set of benchmark datasets for offline RL, OptiDICE is shown to perform competitively with the state-of-the-art methods. This is a joint work with Jongmin Lee (UC Berkeley), Wonseok Jeon (Qualcomm), Byung-Jun Lee (Korea U.), and Joelle Pineau (MILA)

The law of iterated logarithm (LIL) is a crowning achievement in classical probability theory that gives the sharp upper bound for the magnitude of fluctuations of a random walk. If each step has mean zero and variance one, then the upper bound (in certain sense) is given by \sqrt{2n\log\log n}, hence the name “iterated logarithm.” Despite being considered the “third fundamental limit theorem in probability” by some probabilists after the law of large numbers and the central limit theorem, its proof is not so accessible to non-experts. For instance, most textbooks either only consider special cases or use sophisticated machineries in their proofs. The purpose of this talk is to provide a relatively simple and elementary proof of the so-called Hartman—Wintner LIL. The idea is to generalize a proof of the central limit theorem (CLT), which will be also presented, to obtain a result on the rate of convergence in the CLT. First principles in probability (e.g. the second Borel—Cantelli lemma) are the only technical prerequisites.

Around early 2010, there was a huge success in understanding the spectrum of large random matrices, in other words, large random graphs. It was only for large but dense random graphs at first. However, as random matrix theory has been developed, there is some progress in sparse cases. In this short talk, I will review a series of results for spectral statistics of sparse random graphs and explain their implications.

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[Zoom 링크] Zoom 회의 참가 https://kaist.zoom.us/j/2655728482?pwd=OXpJeFdDcWliSG51WUp0N1Nad2JHdz09 회의 ID: 265 572 8482 암호: 2AHRKr [Gather Town 링크] https://gather.town/app/ffr2PVibAWRIyXWO/kaistmath 두 발표 세션이 끝나면 Gather Town으로 옮겨와 대학원생들간에 자유롭게 이야기를 나누는 시간을 가질 계획입니다. Gather Town은 크롬이 깔려있는 기기(노트북, 패드, 스마트폰 등)에서 모두 접속 가능합니다. 별도의 회원가입 없이도 개별 캐릭터 설정 후 접속하면 주변의 다른 캐릭터들과 대화할 수 있는 플랫폼입니다.

Randomness of biochemical reactions is inherent in various biological systems, from DNA to organs and the human body. These stochastic dynamics are frequently modeled using a continuous-time Markov chain (CTMC). Its long-term behavior is described by a stationary distribution, corresponding to its deterministic counterpart called a steady state. Stationary distribution can be derived analytically only in limited systems such as linear or finite-state systems. In this talk, I will introduce a recent result by Anderson, Craciun, and Kurtz deriving stationary distribution from the underlying graph structure of a reaction network and how we can extend it. For those who are first told the word 'Mathematical Biology,' I will briefly introduce mathematical biology before going into the detailed topic.

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[Zoom 링크] Zoom 회의 참가 https://kaist.zoom.us/j/2655728482?pwd=OXpJeFdDcWliSG51WUp0N1Nad2JHdz09 회의 ID: 265 572 8482 암호: 2AHRKr [Gather Town 링크] https://gather.town/app/ffr2PVibAWRIyXWO/kaistmath 두 발표 세션이 끝나면 Gather Town으로 옮겨와 대학원생들간에 자유롭게 이야기를 나누는 시간을 가질 계획입니다. Gather Town은 크롬이 깔려있는 기기(노트북, 패드, 스마트폰 등)에서 모두 접속 가능합니다. 별도의 회원가입 없이도 개별 캐릭터 설정 후 접속하면 주변의 다른 캐릭터들과 대화할 수 있는 플랫폼입니다.

심사위원장 : 권순식, 심사위원 : 배명진, 남경식, Yoshio Tsutsumi(Kyoto University), Mamoru Okamoto(Osaka University)

Inside living cells, chemical reactions form a large web of networks and they are responsible for physiological functions. Understanding the behavior of complex reaction networks is a challenging and interesting task. In this talk, I would like to illustrate how the methods of algebraic topology can shed light on the properties of chemical reaction systems. In particular, we discuss the following two problems: (1) response of reaction systems to external perturbations and (2) simplification of complex reaction networks without altering the behavior of the system.

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ZOOM Meeting ID: 868 7549 9085 Direct link: https://kaist.zoom.us/j/86875499085

We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian’s partial C0-estimate.

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https://zoom.us/j/98194255942?pwd=cWpLM0c1T2U2OG9MR0VJNHpOTFBrdz09 아이디: 981 9425 5942 비밀번호: 373452

I will introduce mathematical and computational methods for spatio-temporal modelling in molecular and cell biology, including all-atom and coarse-grained molecular dynamics (MD), Brownian dynamics (BD), stochastic reaction-diffusion models and macroscopic mean-field equations. Microscopic (BD, MD) models are based on the simulation of trajectories of individual molecules and their localized interactions (for example, reactions). Mesoscopic (lattice-based) stochastic reaction-diffusion approaches divide the computational domain into a finite number of compartments and simulate the time evolution of the numbers of molecules in each compartment, while macroscopic models are often written in terms of mean-field reaction-diffusion partial differential equations for spatially varying concentrations.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

I will discuss the development, analysis and applications of multi-resolution methods for spatio-temporal modelling of intracellular processes, which use (detailed) Brownian dynamics or molecular dynamics simulations in localized regions of particular interest (in which accuracy and microscopic details are important) and a (less-detailed) coarser model in other regions in which accuracy may be traded for simulation efficiency. I will discuss the error analysis and convergence properties of the developed multi-resolution methods, their software implementation and applications of these multiscale methodologies to modelling of intracellular calcium dynamics, actin dynamics and DNA dynamics. I will also discuss the development of multiscale methods which couple molecular dynamics and coarser stochastic models in the same dynamic simulation.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대학교)

심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대학교)

This talk is concerned with the bifurcation and stability of the compresible Taylor vortex. Consider the compressible Navier-Stokes equations in a domain between two concentric infinite cylinders. If the outer cylinder is at rest and the inner one rotates with sufficiently small angular velocity, a laminar flow, called the Couette flow, is stable. When the angular velocity of the inner cylinder increases, beyond a certain value of the angular velocity, the Couette flow becomes unstable and a vortex pattern, called the Taylor vortex, bifurcates and is observed stably. This phenomena is mathematically formulated as a bifurcation and stability problem. In this talk, the compressible Taylor vortex is shown to bifurcate near the criticality for the incompressible problem when the Mach number is sufficiently small. The localized stability of the compressible Taylor vortex is considered under sufficiently small axisymmetric perturbations; and it is shown that the large time behavior of solutions around the Taylor vortex is described by solutions of a system of diffusion equations.

Despite of great progress over the last decades in simulating complex problems with the numerical discretization of (stochastic) partial differential equations (PDEs), solving high-dimensional problems governed by parameterized PDEs remains challenging. Machine learning has emerged as a promising alternative in scientific computing community by enforcing the physical laws. We review some of machine learning approaches and present a novel algorithm based on variational inference to solve (stochastic) systems. Numerical examples are provided to illustrate the proposed algorithm.

Modular curves for Hecke congruence groups, or more generally, for Fuchsian groups of the first kind can be seen as the moduli spaces of the isomorphism classes of elliptic curves with torsion data in some sense. In this talk, I will introduce the notion of modular curves and modular forms. If time permits, I will also introduce their applications to some transcendental questions.

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[Zoom 링크] Zoom 회의 참가 https://kaist.zoom.us/j/2655728482?pwd=OXpJeFdDcWliSG51WUp0N1Nad2JHdz09 회의 ID: 265 572 8482 암호: 2AHRKr [Gather Town 링크] https://gather.town/app/ffr2PVibAWRIyXWO/kaistmath 두 발표 세션이 끝나면 Gather Town으로 옮겨와 대학원생들간에 자유롭게 이야기를 나누는 시간을 가질 계획입니다. Gather Town은 크롬이 깔려있는 기기(노트북, 패드, 스마트폰 등)에서 모두 접속 가능합니다. 별도의 회원가입 없이도 개별 캐릭터 설정 후 접속하면 주변의 다른 캐릭터들과 대화할 수 있는 플랫폼입니다.

Helly-type theorems and problems form a nice area of discrete geometry. I will start with the notable theorems of Radon and Tverberg and mention the following conjectural extension.

For a set X of points x(1), x(2),...,x(n) in some real vector space V we denote by T(X,r) the set of points in X that belong to the convex hulls of r pairwise disjoint subsets of X.
We let t(X,r) = 1 + dim(T(X,r)).

Radon's theorem asserts that
If t(X,1) < |X| then t(X, 2) > 0.

The first open case of the cascade conjecture asserts that
If t(X,1) + t(X,2) < | X | then t(X,3) >0.

In the lecture I will discuss connections with topology and with various problems in graph theory.
I will also mention questions regarding dimensions of intersection of convex sets.

Some related material:
1) A lecture (from 1999): An invitation to Tverberg Theorem: https://youtu.be/Wjg1_QwjUos
2) A paper on Helly type problems by Barany and me https://arxiv.org/abs/2108.08804
3) A link to Barany's book: Combinatorial convexity https://www.amazon.com/Combinatorial-Convexity-University-Lecture-77/dp/1470467097

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ZOOM Meeting ID: 868 7549 9085 Direct link: https://kaist.zoom.us/j/86875499085

심사위원장 : 임미경, 심사위원 : 김동환, 김용정, 권기운(동국대 수학과), 이현대(인하대 수학과)

Counting the number of points on a variety is a historical method for investigating the variety, for example, in the Weil conjecture. Nowadays, it is known that the point count helps us determine the E-polynomial. This E-polynomial, in turn, gives arithmetic-geometric information on the variety such as the dimension, the number of irreducible components and Euler characteristic. In this talk, we will consider a specific type of variety, the character variety associated to the fundamental group of a surface. In short, we will discuss this variety for a punctured surface, with regular semisimple or regular unipotent monodromy at the punctures. This variety plays a crucial role in diverse areas of mathematics, including non-abelian Hodge theory, geometric Langlands program and mathematical physics. The complex representation theory of finite groups will be used to compute the number of points on such a variety.

Hadwiger’s transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals in R d by Goodman, Pollack, and Wenger. Here we establish a colorful extension of their theorem, which proves a conjecture of Arocha, Bracho, and Montejano. The proof uses topological methods, in particular the Borsuk-Ulam theorem. The same methods also allow us to generalize some colorful transversal theorems of Montejano and Karasev.

9:30-10:30am Title: Equations in Simple Groups Abstract: Given a word w in a free group on variables x_1,...,x_n, a finite group G, and an element g in G, we consider the question of whether the equation w = g has solutions where the x_i take values in G, and if so, how many. I am particularly interested in what happens when the word is fixed and G is a large finite simple groups. I will say something about the ideas which have led to progress for certain families of words, with emphasis on open problems. 10:50-11:50 Title: Elliptic curves and field arithmetic Abstract: Let E be an elliptic curve over a field K. When K is a number field, Mordell's theorem says that the points of E over K form a finitely generated group. We say a field is "anti-Mordellic" if the opposite is true for all E/K. I will discuss what is known about anti-Mordellic fields, with emphasis on a longterm joint project with Bo-Hae Im to understand the relation between the anti-Mordellic property and the absolute Galois group of K.

The boundary of melting ice forms a random interface. So does the frontier of slowing burning pieces of paper. As time changes, the interface evolves in a random fashion. In probability theory, a collection of models often exhibits universal behaviors when the system size or time becomes large. The KPZ universality class comprises 1+1 dimensional probability models that mimic the random growth behavior mentioned above and display particular universal fluctuations.We will overview some of the development in this class that started about two decades ago.

Ellipsoidal BGK model (ES-BGK) is a generalized version of the Boltzmann-BGK model. In this model, the local Maxwellian in the relaxation operator is extended to an ellipsoidal Gaussian with a Prandtl parameter ν, so that the correct Prandtl number can be computed in the Navier-Stokes limit. In this talk, we review some of the recent results on ES-BGK model, such as the existence (stationary or non-stationary) theory and the entropy-entropy production estimates. A dichotomy is observed between −1/2 < v < 1 and ν=−1/2. In the former case, an equivalence relation between the local temperature and the temperature tensor enables one to apply theories developed for the original BGK model in a modified form. In the critical case (ν=−1/2), where the correct Prandtl number is achieved, such equivalence breaks down, and the structure of the flow has to be incorporated to estimate the temperature tensor from below. This is from joint works with Stephane Brull, Doheon Kim, and Son Sung Jun.

The idea of balance between excitation and inhibition is central in the theory of biological neural networks. I will give a brief introduction to the concept of such balance, and an overview of the mathematical ideas that can be used to study it.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

I will first describe how to extend the theory of balanced networks to account for synaptic plasticity. This theory can be used to show when a plastic network will maintain balance, and when it will be driven into an unbalanced state. I will next discuss how this approach provides evidence for a novel form of rapid compensatory inhibitory plasticity. Experimental evidence for such plasticity comes from optogenetic activation of excitatory neurons in primate visual cortex (area V1) which induces a population-wide dynamic reduction in the strength of neuronal interactions over the timescale of minutes during the awake state, but not during rest. I will shift gears in the final part of the talk, and discuss how community detection algorithms can help uncover the large scale organization of neuronal networks from connectome data.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

심사위원장 : 황강욱, 심사위원 : 강완모, 정연승, 전현호, 문일철(산업및시스템공학과)

심사위원장 : 이지운, 심사위원 : 강남규(겸직교수), 서인석(서울대학교 수리과학부), 폴정, 남경식

A subset V of a domain Ω has the extension property if for every holomorphic function p on V there is a bounded holomorphic function φ on Ω that agrees with p on V and whose sup-norm on Ω equals the sup-norm of p on V. Within the talk, we shall study mutual relations between extension property and interpolations problems.

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Zoom link https://zoom.us/j/95969402165?pwd=MUhVTUQ5azZSOW1EdkRMMFRVM1R4QT09 ID: 959 6940 2165 PW: 962685

The upper tail problem for subgraph counts in the Erdos-Renyi graph, introduced by Janson-Ruciński, has attracted a lot of attention. There is a class of Gibbs measures associated with subgraph counts, called exponential random graph model (ERGM). Despite its importance, lots of fundamental questions have remained unanswered owing to the lack of exact solvability. In this talk, I will talk about a brief overview on the upper tail problem and the concentration of measure results for the ERGM. Joint work with Shirshendu Ganguly and Ella Hiesmayr.

심사위원장 : 폴정, 심사위원 : 이지운, 남경식, 강남규(겸직교수), 서인석(서울대학교)

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https://us02web.zoom.us/j/2793681958?pwd=SVF2OHNkbFZweWwwK0tZb2FEU2dIdz09

We investigate in depth the behaviour of Monge-Ampère volumes of quasi-psh functions on a given compact hermitian manifold. We prove that the property for these Monge-Ampère volumes to stay bounded away from zero or infinity is a bimeromorphic invariant. We show in particular that a conjecture of Demailly-Paun holds true if and only if such Monge-Ampère volumes stay bounded away from infinity. This is a joint work with Vincent Guedj.

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Zoom link https://zoom.us/j/95121528401?pwd=SXd2bnVFNW1veEJEZUJuNUhVaUdJZz09 ID: 951 2152 8401 PW: 641513

In this talk, we introduce homomorphisms between binary matroids that generalize graph homomorphisms. For a binary matroid $N$, we prove a complexity dichotomy for the problem $\rm{Hom}_\mathbb{M}(N)$ of deciding if a binary matroid $M$ admits a homomorphism to $N$. The problem is polynomial-time solvable if $N$ has a loop or has no circuits of odd length, and is otherwise $\rm{NP}$-complete. We also get dichotomies for the list, extension, and retraction versions of the problem. This is joint work with Hyobin Kim and Mark Siggers at Kyungpook National University.

TBA

Asymptoticswith consideration of ultra-high dimensional data must consider an increasing number of variables, i.e., dimensions, rather than growing the number of observations. High-dimensional asymptotic studies have revealed some unexpected characteristics of data with an exceedingly large number of variables, such as gene expressions. In the context of binary classification, i.e., supervised learning with dichotomous labels, data piling refers to the phenomenon that training data vectors from each class project to a single point for classification. This interesting phenomenon has been a key to understanding many distinctive properties of high-dimensional discrimination. In this talk, high-dimensional asymptoticsof data piling is investigated under equal covariance assumption, which reveals its close connection to the well-known ridged linear classifier. In particular, we show that a negatively ridged discriminant vector can asymptotically achieve data piling of independent test data, essentially yielding a perfect classification. Double data pilingis generalized to heterogeneous covariance models and we propose a data-splitting approach to estimate the direction for the second data piling of test data.

Outputs from health biological systems display complex fluctuations that are not random but display robust and often self-similar (fractal) temporal correlations at different time scales— scaling behaviors. The scaling behaviors in the fluctuations of biological outputs such as neural activities, cardiac dynamics, motor activity are believed to be originated from feedbacks within the complex biological networks, reflecting the system adaptability to internal and external inputs. Supporting this concept, our studies have demonstrated a mechanistic link between the scaling regulation of physiological fluctuations and the circadian control system— a result of evolutionary adaptation to daily environmental light-dark cycles on the earth. In this talk, I will discuss certain evidence for this ‘scaling-circadian’ link and its related implications. Moreover, I will review some recent studies, in which we examined how the scaling patterns of human motor activity fluctuations change with aging and in Alzheimer’s disease. Our results showed that (1) alterations in scaling activity patterns occur before the clinical manifestation of Alzheimer’s disease (i.e., cognitive impairment) and predict cognitive decline and the risk for Alzheimer’s dementia; and (2) the progression of Alzheimer’s disease accelerates the aging effect on the scaling activity patterns. Our work provides strong evidence that altered scaling activity patterns may also be a risk factor for neurodegeneration, playing a role in the development and progression of Alzheimer’s disease.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

We study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit solution of the three-dimensional incompressible Euler equations. The flow is axi-symmetric with no swirl, the vortex core is simply a ball sliding on the axis of symmetry with a constant speed, and the vorticity in the core is proportional to the distance from the symmetry axis. We use the variational setting introduced by A. Friedman and B. Turkington (Trans. Amer. Math. Soc., 1981). As a consequence, the stability up to a translation is obtained by using a concentrated compactness method. As an application, we prove linear in time filamentation near Hill’s vortex: there exists an arbitrary small outward perturbation growing linearly for all times. These results rigorously confirm numerical simulations by Pozrikidis in 1986. The second part is joint work with In-Jee Jeong(SNU).

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ZOOM Meeting ID: 868 7549 9085 Direct link: https://kaist.zoom.us/j/86875499085

In this talk, we will discuss a complete classification of proper holomorphic maps from the unit ball in complex two dimensional space into the Cartan’s classical domain of type IV in complex three dimensional space that extend smoothly to some boundary point. This classification (which is a consequence of a classification of CR maps from the 3-sphere into the tube over the future light cone) consists of 4 algebraic maps. Among them, two previously known maps are isometric with respect to the canonical Bergman metrics and two other maps give counterexamples to a recent conjecture of Xiao-Yuan for the case of maps from the complex 2-ball. This is a joint work with Michael Reiter.

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Zoom link https://zoom.us/j/91925812463?pwd=bnRWQnhQKzRsV1Q3VnJiRjZFMFVxQT09 ID: 919 2581 2463PW: 958065

I will present how to apply for the abroad postdoc position. Basically, I will explain how to prepare the CV, recommendation letters, research statement, teaching statement, diversity statement, etc., which are necessary documents to apply postdoc. The timelines for the postdoc application of the universities in the U.S. and Europe are very different from Korean universities. I will share a variety of information about when, where, and who you can apply for the postdoc position.

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[Zoom 링크] Zoom 회의 참가 https://kaist.zoom.us/j/2655728482?pwd=OXpJeFdDcWliSG51WUp0N1Nad2JHdz09 회의 ID: 265 572 8482 암호: 2AHRKr [Gather Town 링크] https://gather.town/app/ffr2PVibAWRIyXWO/kaistmath 두 발표 세션이 끝나면 Gather Town으로 옮겨와 대학원생들간에 자유롭게 이야기를 나누는 시간을 가질 계획입니다. Gather Town은 크롬이 깔려있는 기기(노트북, 패드, 스마트폰 등)에서 모두 접속 가능합니다. 별도의 회원가입 없이도 개별 캐릭터 설정 후 접속하면 주변의 다른 캐릭터들과 대화할 수 있는 플랫폼입니다.

We introduce an odd coloring of a graph, which was introduced very recently, motivated by parity type colorings of graphs. A proper vertex coloring of graph $G$ is said to be odd if for each non-isolated vertex $x \in V (G)$ there exists a color $c$ such that $c$ is used an odd number of times in the neighborhood of $x$. The recent work on this topic will be presented, and the work is based on Eun-Kyung Cho, Ilkyoo Choi, and Hyemin Kown.

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2011~현재 미국 국립 과학원 회원 2005~현재 수학 연보(Annals of Mathematics) 편집자/감사관 2010, 1990 국제 수학자 회의 초청 연사 2009 클레이상 2004 오스왈드 베블렌 기하학상 전 고등연구소 회원

Metastasis and therapy resistance cause over 90% of cancer-related deaths. Despite extensive ongoing efforts, no unique genetic or mutational signature has emerged for metastasis. Instead, the ability of genetically identical cells to adapt reversibly by exhibiting multiple phenotypes (phenotypic/non-genetic heterogeneity) and switch among them (phenotypic plasticity) is proposed as a hallmark of metastasis. Also, drug resistance can emerge from such non-genetic adaptive cellular changes. However, the origins of such non-genetic heterogeneity in most cancers are poorly understood. I will present our findings on a) how non-genetic heterogeneity emerges in a population of cancer, and b) what design principles underlie regulatory networks enabling non-genetic heterogeneity across multiple cancers. Our results unravel how systems-levels approaches integrating mechanistic mathematical modeling with in vitro and in vivo data can identify causes and consequences of such non-genetic heterogeneity.

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This talk will be presented online. Zoom link: 997 8258 4700 (pw: 1234)

TBA

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

Tuberculosis (TB) is one of the world’s deadliest infectious diseases. Caused by the pathogen Mycobacterium tuberculosis (Mtb), the standard regimen for treating TB consists of treatment with multiple antibiotics for at least six months. There are a number of complicating factors that contribute to the need for this long treatment duration and increase the risk of treatment failure. The structure of granulomas, lesions forming in lungs in response to Mtb infection, create heterogeneous antibiotic distributions that limit antibiotic exposure to Mtb. We can use a systems biology approach pairing experimental data from non-human primates with computational modeling to represent and predict how factors impact antibiotic regimen efficacy and granuloma bacterial sterilization. We utilize an agent-based, computational model that simulates granuloma formation, function and treatment, called GranSim. A goal in improving antibiotic treatment for TB is to find regimens that can shorten the time it takes to sterilize granulomas while minimizing the amount of antibiotic required. We also created a whole host model, called HOSTSIM, to study Mtb dynamics within a human host. Overall, we use these models to help better understand TB treatment and strengthen our ability to predict regimens that can improve clinical treatment of TB.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

Ordinary differential equations are useful in modeling the periodic behavior of organisms, such as circadian rhythm, based on known biological knowledge and researchers' hypotheses. The theoretical mathematical models are calibrated to the experimental measurements by estimating a set of unknown model parameters. Traditional parameter estimation with mathematical models often focuses only on the point estimation relying on an optimization method such as simulated annealing, but it often neglects the uncertainty in point estimates and suffers from the local trap issue. This talk provides a gentle introduction to Bayesian analysis focusing on its usefulness in uncertainty quantification; introduces a Bayesian computing method with an advanced Markov chain Monte Carlo called the generalized multiset sampler; and illustrates the proposed Bayesian inference with circadian oscillations observed in a model filamentous fungus, Neurospora crassa.

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ZOOM Meeting ID: 868 7549 9085 Direct link: https://kaist.zoom.us/j/86875499085

Extension problems through a small singular set appear throughout complex analysis. After a short reminder of some classical results we shall focus on problems of extending (pluri)subharmonic functions. In particular we shall focus on new techniques coming from PDEs that lead to resolutions of several questions in the field. The talk is partially based on joint works with Zywomir Dinew.

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https://us06web.zoom.us/j/82764115688?pwd=N2NzWjFDQ2FpQXJnRGdGNnFacnl2Zz09 ID: 827 6411 5688 PW: wrEH3p

그래프 신경망은 그래프에서 높은 표현 능력과 함께 특징 정보를 추출하는 방법론으로 학계와 산업체에서 최근 폭발적인 관심을 받고 있다. 본 세미나에서는 그래프 신경망의 개요 및 주요 동작 원리를 다룬다. 구체적으로, message passing의 원리를 이해하고 state-of-the-art 알고리즘에서 사용한 다양한 message passing 함수를 소개한다. 그리고, 협업 필터링에 기반한 추천 시스템을 소개하고, 이러한 추천 시스템 설계에 그래프 신경망의 응용에 대해 학습한다. 경량화된 그래프 신경망을 사용한 state-of-the-art 추천 알고리즘을 소개하고, 해당 방법들이 가지는 challenge를 이해한다. 마지막으로, 발표자 연구실에서 제안한 그래프 신경망을 활용한 새로운 추천 시스템 방법을 간단히 소개한다.

In 1975, Szemerédi proved that for every real number $\delta > 0 $ and every positive integer $k$, there exists a positive integer $N$ such that every subset $A$ of the set $\{1, 2, \cdots, N \}$ with $|A| \geq \delta N$ contains an arithmetic progression of length $k$. There has been a plethora of research related to Szemerédi's theorem in many areas of mathematics. In 1990, Cameron and Erdős proposed a conjecture about counting the number of subsets of the set $\{1,2, \dots, N\}$ which do not contain an arithmetic progression of length $k$. In the talk, we study a natural higher dimensional version of this conjecture, and also introduce recent extremal problems related to Szemerédi's theorem.

TBA

수학모델은 역사적으로 오래 전부터 다양한 자연현상과 사회현상을 이해하기 위해 고안되어 왔고 순수와 응용에 걸쳐 활발하게 연구되어 온 분야 중 하나이다. 데이터는 4차 산업혁명의 핵심분야인 인공지능과 머신러닝, IoT에 필수 아이템이며 실제 산업이나 일상 속에서 무수히 쏟아져 나오는 핵심 자원이다. 그렇다면 수학모델을 다루는 수학자와 공학자의 시각에서나 데이터를 다루어야 하는 실제 산업현장에서는 이 두 가지가 만났을 때의 시너지를 상상해 볼 수 있을 것이다. 본 강연에서는 데이터와 수학모델이 공존할 수 있을지, 그리고 공존 가능하다면 인공지능분야에서 수학이 풀어야 하는 숙제를, 나아가 다양한 현장의 문제를 해결할 수 있는 중요한 단초를 제공하는 데이터와 수학모델의 공존법을 소개하려고 한다.

A macroscopic theory for cellular states with steady-growth is presented, based on consistency between cellular growth and molecular replication, together with robustness of phenotypes against perturbations. Adaptive changes in high-dimensional phenotypes are shown to be restricted within a low-dimensional slow manifold, from which a macroscopic law for cellular states is derived, as is confirmed by adaptation experiments of bacteria under stress. The theory is extended to phenotypic evolution, leading to proportionality between phenotypic responses against genetic evolution and by environmental adaptation, which explains the evolutionary fluctuation-response relationship previously uncovered.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

We prove the time-asymptotic stability of composite wave consisting of superposition of a viscous shock and a rarefaction for the 1-dimensional compressible barotropic Navier Stokes equations. This problem first mentioned in 1986 by Matsumura and Nishihara. This problem has unsolved between 1986 and 2021. The main difficulty is due to the incompatibility of the standard anti-derivative method, often used to study this area. In 2021, MOON-JIN KANG, ALEXIS F. VASSEUR, and YI WANG solve this problem using ground-breaking technic. But this has a little limits which make generalization to difficult. So, HO-BIN LEE and SUNG-HO HAN little change the proof.

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[Zoom 링크] Zoom 회의 참가 https://kaist.zoom.us/j/2655728482?pwd=OXpJeFdDcWliSG51WUp0N1Nad2JHdz09 회의 ID: 265 572 8482 암호: 2AHRKr [Gather Town 링크] https://gather.town/app/ffr2PVibAWRIyXWO/kaistmath 두 발표 세션이 끝나면 Gather Town으로 옮겨와 대학원생들간에 자유롭게 이야기를 나누는 시간을 가질 계획입니다. Gather Town은 크롬이 깔려있는 기기(노트북, 패드, 스마트폰 등)에서 모두 접속 가능합니다. 별도의 회원가입 없이도 개별 캐릭터 설정 후 접속하면 주변의 다른 캐릭터들과 대화할 수 있는 플랫폼입니다.

Let $S := S_{g, n}$ be a surface of genus $g$ with $n$ punctures. We collect all isotopy classes of homeomorphisms of $S$, call it as a "Mapping class group" and denote it as $Mod(S)$ or $MCG(S)$. In this talk I will introduce (1) classification of elements in $Mod(S)$, (2) Actions on some spaces such as moduli space or Teichmuller space, (3) Topological entropy followed by my recent work. This is a joint work with my advisor Harry Hyungryul Baik, Changsub Kim, and Philippe Tranchida.

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[Zoom 링크] Zoom 회의 참가 https://kaist.zoom.us/j/2655728482?pwd=OXpJeFdDcWliSG51WUp0N1Nad2JHdz09 회의 ID: 265 572 8482 암호: 2AHRKr [Gather Town 링크] https://gather.town/app/ffr2PVibAWRIyXWO/kaistmath 두 발표 세션이 끝나면 Gather Town으로 옮겨와 대학원생들간에 자유롭게 이야기를 나누는 시간을 가질 계획입니다. Gather Town은 크롬이 깔려있는 기기(노트북, 패드, 스마트폰 등)에서 모두 접속 가능합니다. 별도의 회원가입 없이도 개별 캐릭터 설정 후 접속하면 주변의 다른 캐릭터들과 대화할 수 있는 플랫폼입니다.

Morihiko Saito's theory of mixed Hodge modules is a far generalisation of classical Hodge theory, which is based on the theory of perverse sheaves, D-modules, variations of Hodge structures. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. Naturally they are accompanied by perverse sheaves via the Riemann–Hilbert correspondence. This guide consists of about 8 talks, which may cover: review of classical Hodge theory, D-modules and filtered D-modules, nearby and vanishing cycles, etc. The main goal is to understand the notion of mixed Hodge modules and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry.

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Zoom 회의 ID: 352 730 6970; 암호: 1778 ; 실명으로 들어오시면 대기실에서 개별 승인해 드립니다.

심사위원장: 이용남, 심사위원 : 곽시종, 백상훈, 최영욱(영남대 수학교육과), 최인송(건국대 수학과)