The driving passion of molecular cell biologists is to understand the molecular mechanisms that control important aspects of cell physiology, but this ambition is – paradoxically – limited by the very wealth of molecular details currently known about these mechanisms. Their complexity overwhelms our intuitive notions of how molecular regulatory networks might respond under normal and stressful conditions. To make progress we need a new paradigm for connecting molecular biology to cell physiology. I will outline an approach that uses precise mathematical methods to associate the qualitative features of dynamical systems, as conveyed by ‘bifurcation diagrams’, with ‘signal–response’ curves measured by cell biologists.

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

Cell growth, DNA replication, mitosis and division are the fundamental processes by which life is passed on from one generation of eukaryotic cells to the next. The eukaryotic cell cycle is intrinsically a periodic process but not so much a ‘clock’ as a ‘copy machine’, making new daughter cells as warranted. Cells growing under ideal conditions divide with clock-like regularity; however, if they are challenged with DNA-damaging agents or mitotic spindle disruptors, they will not progress to the next stage of the cycle until the damage is repaired. These ‘decisions’ (to exit and re-enter the cell cycle) are essential to maintain the integrity of the genome from generation to generation. A crucial challenge for molecular cell biologists in the 1990s was to unravel the genetic and biochemical mechanisms of cell cycle control in eukaryotes. Central to this effort were biochemical studies of the clock-like regulation of ‘mitosis promoting factor’ during synchronous mitotic cycles of fertilized frog eggs and genetic studies of the switch-like regulation of ‘cyclin-dependent kinases’ in yeast cells. The complexity of these control systems demands a dynamical approach, as described in the first lecture. Using mathematical models of the control systems, I will uncover some of the secrets of cell cycle ‘clocks’ and ‘switches’.

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

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This lecture explores a list of topics and areas that have led my research in computational mathematics and deep learning in recent years. Numerical approaches in computational science are crucial for understanding real-world phenomena, and deep neural networks have achieved state-of-the-art performance in a variety of fields. The exponential growth and the extreme success of deep learning and scientific computing have seen application across a multitude of disciplines. In this lecture, I will focus on recent advancements in scientific computing and deep learning such as adversarial examples, nanophotonics, and numerical PDEs.

We determine the maximum number of copies of $K_{s,s}$ in a $C_{2s+2}$-free $n$-vertex graph for all integers $s \ge 2$ and sufficiently large $n$. Moreover, for $s\in\{2,3\}$ and any integer $n$ we obtain the maximum number of cycles of length $2s$ in an $n$-vertex $C_{2s+2}$-free bipartite graph. This is joint work with Ervin Győri (Renyi Institute), Zhen He (Tsinghua University), Zequn Lv (Tsinghua University), Casey Tompkins (Renyi Institute), Kitti Varga (Technical University of Budapest BME), and Xiutao Zhu (Nanjing University).

Order types are a combinatorial classification of finite point sets used in discrete and computational geometry. This talk will give an introduction to these objects and their analogue for the projective plane, with an emphasis on their symmetry groups. This is joint work with Emo Welzl: https://arxiv.org/abs/2003.08456

Wigner's jellium is a model for a gas of electrons. The model consists of unit negatively charged particles lying in a sea of neutralizing homogeneous positive charges spread out according to Lebesgue measure. The key challenge in analyzing this system stems from the long-range Coulomb interactions. While the motivation for the jellium stems from physics, Coulomb systems appear in a variety of different research fields such as random matrix theory. In the first part of this talk, I will review key limit results for classical Coulomb systems in large domains. In the second part, I will present some recent advances for quantum Coulomb systems.

In computer science, random expressions are commonly used to analyze algorithms, either to study their average complexity, or to generate benchmarks to test them experimentally. In general, these approaches only consider the expressions as purely syntactic trees, and completely ignore their semantics — i.e. the mathematical object represented by the expression. However, two different expressions can be equivalent (for example “0*(x+y)” and “0” represent the same expression, the null expression). Can these redundancies question the relevance of the analyses and tests that do not take into account the semantics of the expressions? I will present how the uniform distribution over syntactic expression becomes completely degenerate when we start taking into account their semantics, in a very simple but common case where there is an absorbing element. If time permits it, I will briefly explain why the BST distribution offers more hope. This is a joint work with Cyril Nicaud and Pablo Rotondo.

TBA

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

Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the “species”). If the counts of the species are low, then these systems are often modeled as continuous-time Markov chains on the d-dimensional integer lattice (with d being the number of species), with transition rates determined by stochastic mass-action kinetics. A natural (broad) mathematical question is: how do the qualitative properties of the dynamical system relate to the graph properties of the network? For example, it is of particular interest to know which graph properties imply that the stochastically modeled reaction network is positive recurrent, and therefore admits a stationary distribution. After a general introduction to the models of interest, I will discuss this problem, giving some of the known results. I will also discuss recent progress on the Chemical Recurrence Conjecture, which has been open for decades, which is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent.

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

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서울대학교 법과대학 학사 사법시험 32회 합격 판사(서울지방법원 등) 현) 김&장 법률사무소

We’re all familiar with sleep, but how can we mathematically model it? And what determines how long and when we sleep? In this talk I’ll introduce the nonsmooth coupled oscillator systems that form the basis of current models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we are using models to unravel environmental, societal and physiological factors that determine sleep timing and outline how we are using models to inform the quantitative design of light interventions for mental health disorders and address contentious societal questions such as whether to move school start time for adolescents.

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

TBA

In this talk, we will first review some recent results on the eigenvectors of random matrices under fixed-rank deformation, and then we will focus on the limit distribution of the leading eigenvectors of the Gaussian Unitary Ensemble (GUE) with fixed-rank (aka spiked) external source, in the critical regime of the Baik-Ben Arous-Peche (BBP) phase transition. The distribution is given in terms of a determinantal point process with extended Airy kernel. Our result can be regarded as an eigenvector counterpart of the BBP eigenvalue phase transition. The derivation of the distribution makes use of the recently rediscovered eigenvector-eigenvalue identity, together with the determinantal point process representation of the GUE minor process with external source. This is a joint work with Dong Wang (UCAS).

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서울대학교 산업공학과 학사/석사 소만사 창업 (주)소만사 대표이사 소프트웨어 산업협회 이사 한국정보보호 산업협회 부회장

In recent years, community detection has been an active research area in various fields including machine learning and statistics. While a plethora of works has been published over the past few years, most of the existing methods depend on a predetermined number of communities. Given the situation, determining the proper number of communities is directly related to the performance of these methods. Currently, there does not exist a golden rule for choosing the ideal number, and people usually rely on their background knowledge of the domain to make their choices. To address this issue, we propose a community detection method that is equipped with data-adaptive methods of finding the number of the underlying communities. Central to our method is fused l-1 penalty applied on an induced graph from the given data. The proposed method shows promising results.

Stochastic finite-sum optimization problems are ubiquitous in many areas such as machine learning, and stochastic optimization algorithms to solve these finite-sum problems are actively studied in the literature. However, there is a major gap between practice and theory: practical algorithms shuffle and iterate through component indices, while most theoretical analyses of these algorithms assume uniformly sampling the indices. In this talk, we talk about recent research efforts to close this theory-practice gap. We will discuss recent developments in the theoretical convergence analysis of shuffling-based optimization methods. We will first consider minimization algorithms, mainly focusing on stochastic gradient descent (SGD) with shuffling; we will then briefly talk about some new progress on minimax optimization methods.

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서울대학교 산업공학과 학/석사 삼성전자 연구원 조지아텍 박사 삼성전자 종합기술원 전문연구원 현) 삼성전자 종합기술원 머신러닝 랩장

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서울대학교 산업공학과 학사 행정고시 37회 재경직 합격 KDI 국제정책대학원 석사 서울지방국세청 조사과장 국세청 기획재정담당관

TBA

Deep generative models (DGM) have been an intersection between the probabilistic modeling and the machine learning communities. Particularly, DGM has impacted the field by introducing VAE, GAN, Flow, and recently Diffusion models with its capability to learn the data density of datasets. While there are many model variations in DGM, there are also common fundamental theories, assumptions and limitations to study from the theoretic perspectives. This seminar provides such general and fundamental challenges in DGMs, and later we particularly focus on the key developments in diffusion models and their mathematical properties in detail.

The disjoint paths logic, FOL+DP,  is an extension of First Order Logic (FOL) with the extra atomic predicate $\mathsf{dp}_k(x_1,y_1,\ldots,x_k,y_k),$ expressing the existence of internally vertex-disjoint paths between $x_i$ and $y_i,$ for $i\in \{1,\ldots, k\}$. This logic can express a wide variety of problems that escape the expressibility potential of FOL. We prove that for every minor-closed graph class, model-checking for FOL+DP can be done in quadratic time. We also introduce an extension of FOL+DP, namely the scattered disjoint paths logic, FOL+SDP, where we further consider the atomic predicate $\mathsf{s-sdp}_k(x_1,y_1,\ldots,x_k,y_k),$ demanding that the disjoint paths are within distance bigger than some fixed value $s$. Using the same technique we prove that model-checking for FOL+SDP can be done in quadratic time on classes of graphs with bounded Euler genus. Joint work with Petr A. Golovach and Dimitrios M. Thilikos.

This talk is about the complex dynamics, which cares the iteration of holomorphic map (usually a rational map on the Riemann sphere), and the shift locus is a nice set of polynomials that all critical points escape to infinity under iteration. Understanding the shape and topology of shift locus is a challenge for decades, and accumulated works are done by Blanchard, Branner, Hubbard, Keen, McMullen, and recently Calegari introduce a nice lamination model. In this talk I will explain the basic complex dynamics and introduce the topology of the shift locus of cubic polynomials done by Calegari's paper 'Sausages and Butcher paper' and if time allows, I will end this talk with the connection to the Big mapping class group, the MCG of Sphere - Cantor set.

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서울대 의학 학사/박사 한국학중앙연구원 철학 박사 현) 이화여대 의과대학교수

This series of talks is intended to be a gentle introduction to the random walk theory on infinite groups and hyperbolic spaces. We will touch upon keywords including hyperbolicity, stationary measure, boundaries and limit laws. Those who are interested in geometric group theory or random walks are welcomed to join.

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This is a casual seminar among TARGET students, but other graduate students are also welcomed.

For a graph $F$, the Turán number is the maximum number of edges in an $n$-vertex simple graph not containing $F$. The celebrated Erdős-Stone-Simonovits Theorem gives that \[ \text{ex}(n,F)=\bigg(1-\frac{1}{\chi(F)-1}+o(1)\bigg)\binom{n}{2},\] where $\chi(F)$ is the chromatic number of $H$. This theorem asymptotically solves the problem when $\chi(F)\geqslant 3$. In case of bipartite graphs $F$, not even the order of magnitude is known in general. In this talk, I will introduce some recent progress on Turán numbers of bipartite graphs and related generalizations and discuss several methods developed in recent years. Finally, I will introduce some interesting open problems on this topic.