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)

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

TBA

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.

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.

Quantitative characterization of biomolecular networks is important for the analysis and design of network functionality. Reliable models of such networks need to account for intrinsic and extrinsic noise present in the cellular environment. Stochastic kinetic models provide a principled framework for developing quantitatively predictive tools in this scenario. Calibration of such models requires an experimental setup capable of monitoring a large number of individual cells over time, automatic extraction of fluorescence levels for each cell and a scalable inference approach. In the first part of the talk we will cover our microfluidic setup and a deep-learning based approach to cell segmentation and data extraction. The second part will introduce moment-based variational inference as a scalable framework for approximate inference of kinetic models based on single cell data.

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

Transport properties of Gibbs and Gaussian measures under different transformations have been studied in probability theory. In this talk, I will discuss the invariance and quasi-invariance of Gaussian type measures on functions/distributions under the flow of Hamiltonian PDEs.

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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 : 전현호, 심사위원 : 김용정, 박철우, 정연승, 이주호(김재철AI대학원)

심사위원장 : 최건호, 심사위원 : 곽도영(명예교수), 김동석(경영공학부), 권순식, 김완수

One of the important work in graph theory is the graph minor theory developed by Robertson and Seymour in 1980-2010. This provides a complete description of the class of graphs that do not contain a fixed graph H as a minor. Later on, several generalizations of H-minor free graphs, which are sparse, have been defined and studied. Also, similar topics on dense graph classes have been deeply studied. In this talk, I will survey topics in graph minor theory, and discuss related topics in structural graph theory.

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

논문은 저자와 독자 사이의 학문적 소통을 위한 논리적인 글이다. 이번 강연을 통해 논문을 작성하기 위한 기본 원리를 배울 수 있다. 특히, 연구가 거의 마무리되는 시점에 (After completing your research), 연구 결과를 그림과 표로 잘 정리한 다음에 (Based on well-organized figures and tables), 본격적으로 논문 작성을 시작하는 (Compose your manuscript from a title to a conclusion) ‘ABC 논문 작성법’을 소개한다. 논문 작성의 준비 과정으로 (A와 B의 과정), 연구 노트 작성 방법, 저널 클럽 운영 방법, 한 페이지 활용 방법을 설명한다. 논문 작성 준비가 완료되면, 제목부터 결론까지 순서대 로 논문 원고를 작성할 수 있다 (C의 과정). 이렇게 하면, 단기간에 집중하여 효율적으 로 논문을 작성할 수 있다. *참고: 원병묵 교수의 과학 논문 쓰는 법

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2022년 6월 3일 오후 4시 – 5시, 성균관대 신소재공학부의 원병묵 교수님의 논문 글쓰기 워크샵 강의가 있습니다.

이 ‘영어 논문 쓰기’ 워크숍은 현재의 영어 수준이나 과거의 영어 학습 경험과 상관 없이 누구나 영어 논문 쓰기를 시작할 수 있는 방법에 관한 것입니다. 우선 영어에 대한 막연한 두려움, 과거 경험으로 인한 자신감 부족, 게다가 ‘쓰기’라는 쉽지 않은 인지 활동, 심지어 논문이라는 큰 벽, 혹은 섣부른 자신감 등 ‘영어 논문 쓰기’를 방해하는 요인을 생각해 봅니다. 이런 요인을 자세하게 들여다보면 각각의 걸림돌을 넘어갈 방법도 명쾌하게 발견할 수 있습니다. 이 세미나에서 다룰 구체적 내용은 다음과 같습니다. - 한국인들이 ‘영어’와 ‘영어 쓰기’를 어렵게 느끼는 원인 이해하고 극복하기 - ‘읽기’와 ‘쓰기’의 서로 다른 두 가지 인지활동의 관련성 이해하고 적용하기 - 논문에 적합한 단어, 시제, 구두점 선택하고 사용하기 - 영문초록, 제목, 소제목 스타일 이해하고 작성하기 - 영어논문 쓰기를 돕는 디지털 도구 선택하고 활용하기 이 워크숍에서 안내될 몇 가지 방법은 영어 논문 쓰기가 더 이상 두려운 것이 아닌 연구자로서의 목표를 이루는 디딤돌이 되도록 할 것입니다.

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2022년 6월 3일 오후 5시 – 6시, 부산교육정책연구소 박영민 연구원님의 논문 글쓰기 워크샵 강의가 있습니다.

TBA

심사위원장 : 이창옥, 심사위원 : 임미경, 김동환, 예종철(겸임교수), 김윤호(UNIST 자연과학부)

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.