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.

---

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).

---

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.

---

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.

---

[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.

---

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.

---

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

TBA

---

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.

---

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.

---

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.

---

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.

---

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.

---

[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.

---

[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.

---

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)

We will discuss hormone circuits and their dynamics using new models that take into account timescales of weeks due to growth of the hormone glands. This explains some mysteries in diabetes and autoimmune disease.

---

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

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.

---

https://us06web.zoom.us/j/83876347559?pwd=SVZoUzZkUkMyZno0Vk1pS0pkTEdZQT09 ID: 838 7634 7559 PW: 8XahHQ

Suppose that $E$ is a subset of $\mathbb{F}_q^n$, so that each point is contained in $E$ with probability $\theta$, independently of all other points. Then, what is the probability that there is an $m$-dimensional affine subspace that contains at least $\ell$ points of $E$? What is the probability that $E$ intersects all $m$-dimensional affine subspaces? We give Erdős-Renyi threshold functions for these properties, in some cases sharp thresholds. Our results improve previous work of Chen and Greenhill. This is joint work with Jeong Han Kim, Thang Pham, and Semin Yoo.

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.

---

Zoom 회의 ID: 352 730 6970, 암호: 7178 대기실에서 개별 승인하오니, 실명으로 접속하시기 바랍니다.

Random simple and multigraph models based on exchangeable random measures, sometimes named graphexprocesses or generalisedgraphonmodels, have recently been proposed as a flexible class of sparse random graph models. This class of models can be seen as a generalisationof the popular graphonmodels. I will present this class of models, discuss some of their asymptotic properties, in particular the asymptotic behaviourof the degree distribution and of the clustering coefficients. I will also present some particular parametric models within this class and their use for discovering latent communities in sparse real-world networks.

In this talk, we present a short history of L^p-theories for partial differential equations. In particular, we introduce recent developments handling fractional derivatives and degenerate estimates in weighted spaces.

Random simple and multigraph models based on exchangeable random measures, sometimes named graphex processes or generalised graphon models, have recently been proposed as a flexible class of sparse random graph models. This class of models can be seen as a generalisation of the popular graphon models. I will present this class of models, discuss some of their asymptotic properties, in particular the asymptotic behaviour of the degree distribution and of the clustering coefficients. I will also present some particular parametric models within this class and their use for discovering latent communities in sparse real-world networks.

I will give an introduction to topological data analysis (TDA), in which one uses ideas from algebraic topology to study the “shape” of data. I will focus on persistent homology (PH), which is the most common approach in TDA.

---

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

From the venation patterns of leaves to spider webs, roads in cities, social networks, and the spread of COVID-19 infections and vaccinations, the structure of many systems is influenced significantly by space. In this talk, I will discuss the application of topological data analysis (specifically, persistent homology) to spatial systems. I will present a few examples, such as voting in presidential elections, city street networks, spatiotemporal dynamics of COVID-19 infections and vaccinations, and webs that were spun by spiders under the influence of various drugs.

---

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

A ruled surface is a fibration over a smooth curve with fibers being isomorphic to the projective line. If a ruled surface is assumed to not have any section with negative self-intersection, then it is known that there is no curve with negative self-intersection on the ruled surface. Moreover, if the ruled surface is “sufficiently” general in its moduli, then the surface does not admit a curve with zero self-intersection. So, it is natural to ask the questions of which ruled surface admits a curve with zero self-intersection, and how many such ruled surfaces exist in the moduli. In this talk, I will introduce some answers to the questions.

---

[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.

Finding a given graph in a large host graph is a very essential problem in graph theory. One main variant of this is coloring edges of a host graph with many colors and trying to find a 'rainbow' subgraph, whose edges have distinct colors. I will explain some history, and introduce my recent result which searches for a rainbow color-critical graph.

---

[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.

When a biological system is modeled using a mathematical procedure, the following step is normally to estimate the system parameters. Despite the numerous computational and statistical techniques, estimating parameters for complex systems can be a difficult task. As a result, one can think of revealing parameter-independent dynamical properties of a system. More precisely, rather than estimating parameters, one can focus on the underlying structure of a biochemical system to derive the qualitative behavior of the associated mathematical process. In this talk, we will discuss introduce reaction network theory. A reaction network is a graphical configuration of a biochemical system. One of the most important problems in this field is to relate dynamical properties and the underlying reaction network structure. When abundances of biochemical species (variables) in the system are small, then the randomness inherent in the molecular interactions is crucial to the system dynamics, and the abundances are modeled stochastically as a jump by jump fashion continuous-time Markov chain. The goal of this talk is to 1. walk you through the basic modeling aspect of the stochastically modeled reaction networks, and 2. to show how to derive stability (ergodicity) of the associated Markov process solely based on the underlying network structure.

---

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

In this talk we will discuss a Hirzebruch-Riemann-Roch (HRR) type theorem for matrix factorization categories of Deligne-Mumford stacks. We will first discuss a proof of a Hochschild-Kostant-Rosenberg type isomorphism and show how it can be used to define a Chern character formula which allows us to prove the HRR type theorem. This talk is based on a joint work with Dongwook Choa and Bumsig Kim.

---

Zoom details: ID: 352 730 6970 Password: 1098. Please come with your real names.

The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains a copy of $F$ or its complement contains $H$. Burr in 1981 proved a pleasingly general result that for any graph $H$, provided $n$ is sufficiently large, a natural lower bound construction gives the correct Ramsey number involving cycles: $R(C_n,H)=(n-1)(\chi(H)-1)+\sigma(H)$, where $\sigma(H)$ is the minimum possible size of a colour class in a $\chi(H)$-colouring of $H$. Allen, Brightwell and Skokan conjectured that the same should be true already when $n\geq |H|\chi(H)$. We improve this 40-year-old result of Burr by giving quantitative bounds of the form $n\geq C|H|\log^4\chi(H)$, which is optimal up to the logarithmic factor. In particular, this proves a strengthening of the Allen-Brightwell-Skokan conjecture for all graphs $H$ with large chromatic number. This is joint work with John Haslegrave, Joseph Hyde and Hong Liu

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.

---

Zoom 회의 ID: 352 730 6970 암호: 4114 대기실에서 개별 승인하니, 실명으로 접속하시기 바랍니다.

We prove global Holder gradient estimates for bounded positive weak solutions of fast diffusion equations in smooth bounded domains with homogeneous Dirichlet boundary condition, which then leads us to establish their optimal global regularity. It solves a problem raised by Berryman and Holland in 1980. This is joint work with Jingang Xiong.

This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between dimensionality-reduced conditional distributions of different protected classes. The incorporation of MMD naturally leads to an exact and tractable mathematical formulation of fairness with good statistical properties. We formulate the problem of fair PCA subject to MMD constraints as a non-convex optimization over the Stiefel manifold and solve it using the Riemannian Exact Penalty Method with Smoothing (REPMS; Liu and Boumal, 2019). Importantly, we provide local optimality guarantees and explicitly show the theoretical effect of each hyperparameter in practical settings, extending previous results. Experimental comparisons based on synthetic and UCI datasets show that our approach outperforms prior work in explained variance, fairness, and runtime. This paper is accepted to the 36th AAAI Conference on Artificial Intelligence (AAAI 2022).

This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between dimensionality-reduced conditional distributions of different protected classes. The incorporation of MMD naturally leads to an exact and tractable mathematical formulation of fairness with good statistical properties. We formulate the problem of fair PCA subject to MMD constraints as a non-convex optimization over the Stiefel manifold and solve it using the Riemannian Exact Penalty Method with Smoothing (REPMS; Liu and Boumal, 2019). Importantly, we provide local optimality guarantees and explicitly show the theoretical effect of each hyperparameter in practical settings, extending previous results. Experimental comparisons based on synthetic and UCI datasets show that our approach outperforms prior work in explained variance, fairness, and runtime. This paper is accepted to the 36th AAAI Conference on Artificial Intelligence (AAAI 2022).

---

[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.

The Gordon-Bender-Knuth identities are determinant formulas for the sum of Schur functions of partitions with bounded length. There are interesting combinatorial consequences of the Gordon-Bender-Knuth identities, for instance, connections between standard Young tableaux of bounded height, lattice walks in a Weyl chamber, and noncrossing matchings. In this talk we prove an affine analog of the Gordon-Bender-Knuth identities and study their combinatorial properties. As a consequence we obtain an unexpected connection between cylindric standard Young tableaux and r-noncrossing and s-nonnesting matchings. This is joint work with JiSun Huh, Christian Krattenthaler, and Soichi Okada.

---

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

It is known that the rank- and tree-width of the random graph G(n,p) undergo a phase transition at p=1/n; whilst for subcritical p, the rank- and tree-width are bounded above by a constant, for supercritical p, both parameters are linear in n. The known proofs of these results use as a black box an important theorem of Benjamini, Kozma, and Wormald on the expansion of supercritical random graphs. We give a new, short, and direct proof of these results, leading to more explicit bounds on these parameters, and also consider the rank- and tree-width of supercritical random graphs closer to the critical point, showing that this phase transition is smooth. This is joint work with Joshua Erde and Mihyun Kang.

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.

---

Zoom 회의 ID: 352 730 6970 암호: 0971 대기실에서 개별승인을 하오니 실명으로 접속하시기 바랍니다.

This talk follows on from the recent talk of Pascal Gollin in this seminar series, but will aim to be accessible for newcomers. Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. By relaxing `packing’ to `half-integral packing’, Reed obtained an analogous result for odd cycles, and gave a structural characterisation of when the (integral) packing version fails. We prove some far-reaching generalisations of these theorems. First, we show that if the edges of a graph are labelled by finitely many abelian groups, then the cycles whose values avoid a fixed finite set for each abelian group satisfy the half-integral Erdős-Pósa property. Similarly to Reed, we give a structural characterisation for the failure of the integral Erdős-Pósa property in this setting. This allows us to deduce the full Erdős-Pósa property for many natural classes of cycles. We will look at applications of these results to graphs embedded on surfaces, and also discuss some possibilities and obstacles for extending these results. This is joint work with Kevin Hendrey, Ken-ichi Kawarabayashi, O-joung Kwon, Sang-il Oum, and Youngho Yoo.

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.

---

Zoom info: 352 730 6970 암호: 2032 대기실에서 개별 승인을 하니 실명으로 접속하시기 바랍니다.

Cells make fate decisions in response to dynamic environments and multicellular structure emerges from interplays among cells in space and time. The recent single-cell genomics technology provides an unprecedented opportunity to profile cells. However, those measurements are taken as snapshots for groups of individual cells with only static information. Can one infer interactions among cells from such datasets? Is it possible to recover spatial information from non-spatial datasets? How to obtain temporal relationships of cells from the static measurements? In this talk I will present our newly developed computational tools that reconstruct interactions and spatiotemporal relationships for cells using single-cell RNA-seq, ATAC-seq, and spatial transcriptomics datasets. Through applications of those methods to systems in development and regeneration, we show the discovery power of such methods and identify areas for further development in spatiotemporal reconstruction.

---

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

I present a version of the Moser-Trudinger inequality in the setting of complex geometry. As a very particular case, the result already gives a new Moser-Trudinger inequality for functions in the Sobolev space W1,2 of a domain in R2. As an application, we deduce a new necessary condition for the complex Monge-Ampere equation for a given measure on a compact Kahler manifold to admit a Holder continuous solution. This is a joint work with Tien-Cuong Dinh and George Marinescu.