In this talk, we derive second-order expressions for both the one- and two-particle reduced density matrices of the Gibbs state at fixed positive temperatures. We consider a translation-invariant system of N bosons in a three-dimensional torus. These bosons interact through a repulsive two-body potential with a scattering length of order 1/N in the large N limit. This analysis provides a justification of Bogoliubov's prediction regarding the fluctuations around the condensate. The talk will primarily introduce basic concepts and settings, ensuring accessibility for all attendees. This work is a joint effort with Christian Brennecke and Phan Thành Nam.

In this talk, I will describe a new approach to general relativistic initial data gluing based on explicit solution operators for the linearized constraint equation with prescribed support properties. In particular, we retrieve and optimize -- in terms of positivity, regularity, size and/or spatial decay requirements -- obstruction-free gluing originally put forth by Czimek-Rodnianski. Notably, our proof of the strengthened obstruction-free gluing theorem relies on purely spacelike techniques, rather than null gluing as in the original approach.

A graph is $H$-Ramsey if every two-coloring of its edges contains a monochromatic copy of $H$. Define the $F$-Ramsey number of $H$, denoted by $r_F(H)$, to be the minimum number of copies of $F$ in a graph which is $H$-Ramsey. This generalizes the Ramsey number and size Ramsey number of a graph. Addressing a question of Spiro, we prove that \[r_{K_3}(K_t)=\binom{r(K_t)}3\] for all sufficiently large $t$.  Our proof involves a combination of results on the chromatic number of triangle-sparse graphs. Joint work with Jacob Fox and Jonathan Tidor.

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심사위원장: 박철우, 심사위원: 정연승, 전현호, 안정연(산업및시스템공학과), 전용호(연세대학교)

In this talk, we will discuss nonlocal elliptic and parabolic equations on C^{1,τ} open sets in weighted Sobolev spaces, where τ ∈ (0, 1). The operators we consider are infinitesimal generators of symmetric stable Levy processes, whose Levy measures are allowed to be very singular. Additionally, for parabolic equations, the measures are assumed to be merely measurable in the time variable. This talk is based on a joint work with Hongjie Dong (Brown University).

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ID: 853 0775 9189, PW: 342420

In this talk, I will present the recent progress of understanding adversarial multiclass classification problems, motivated by the empirical observation of the sensitivity of neural networks by small adversarial attacks. Based on 'distributional robust optimization' framework, we obtain reformulations of adversarial training problem: 'generalized barycenter problem' and a family of multimarginal optimal transport problems. These new theoretical results reveal a rich geometric structure of adversarial training problems in multiclass classification and extend recent results restricted to the binary classification setting. From this optimal transport perspective understanding, we prove the existence of robust classifiers by using the duality of the reformulations without so-called 'universal sigma algebra'. Furthermore, based on these optimal transport reformulations, we provide two efficient approximate methods which provide a lower bound of the optimal adversarial risk. The basic idea is the truncation of effective interactions between classes: with small adversarial budget, high-order interactions(high-order barycenters) disappear, which helps consider only lower order tensor computations.

Given a set of lines in $\mathbb R^d$, a joint is a point contained in d linearly independent lines. Guth and Katz showed that N lines can determine at most $O(N^{3/2})$ joints in $\mathbb R^3$ via the polynomial method. Yu and I proved a tight bound on this problem, which also solves a conjecture proposed by Bollobás and Eccles on the partial shadow problem. It is surprising to us that the only known proof of this purely extremal graph theoretic problem uses incidence geometry and the polynomial method.

Abstract: In 1993, Demeyer and Ford computed the Brauer group of a smooth toric variety over an algebraically closed field of characteristic zero. One may pose the same question to the toric varieties over any field of positive characteristic. Another interesting question is what will happen if we replace the base field by a discrete valuation ring, thereby replacing smooth toric varieties by smooth toric schemes over a discrete valuation ring in the sense of Kempf-Knudsen-Mumford-Saint-Donat. In this talk. I am going to discuss the answers to these questions. This is joint work with Roy Joshua.

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Zoom info: meeting ID is 352 730 6970 with the password 1778. It will be open about 10-15 minutes before the scheduled talk. The talk time is in Korean Standard Time.

TBD

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ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234) + Google Map

Distributed optimization is a concept that multi-agent systems find a minimal point of a global cost functions which is a sum of local cost functions known to the agents. It appears in diverse fields of applications such as federated learning for machine learning problems and the multi-robotics systems. In this talk, I will introduce motivations for distributed optimization and related algorithms with their theoretical issues for developing efficient and robust algorithms.

We prove that the zero function is the only solution to a certain degenerate PDE defined in the upper half-plane under some geometric assumptions. This result implies that the Euclidean metric is the only adapted compactification of the standard half-plane model of hyperbolic space when the scalar curvature of the compactified metric has a certain sign. These Liouville-type theorems are expected to handle the boundary curvature blow-up to prove compactness results of CCE(conformally compact Einstein) manifolds with positive scalar curvature on the conformal infinity.

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심사위원장: 김동수, 심사위원:안드레아스 홈슨, 엄상일, 이주영(전산학부), 서승현(강원대학교)

We investigate the global existence and optimal time decay rate of solution to the one dimensional (1D) two-phase flow described by compressible Euler equations coupled with compressible Navier-Stokes equations through the relaxation drag force on the momentum equations (Euler-Navier-Stokes system). First, we prove the global existence of strong solution and the stability of the constant equilibrium state to 1D Cauchy problem of compressible Euler-Navier-Stokes system by using the standard continuity argument for small $H^{1}$ data while its second order derivative can be large. Then we derive the optimal time decay rate to the constant equilibrium state. Compared with multi-dimensional case, it is much harder to get optimal time decay rate by direct spectrum method due to a slower convergence rate of the fundamental solution in 1D case. To overcome this main difficulty, we need to first carry out time-weighted energy estimates (not optimal) for higher order derivatives, and based on these time-weighted estimates, we can close a priori assumptions and get the optimal time decay rate by spectrum analysis method. Moreover, due to non-conserved form and insufficient decay rate of the coupled drag force terms between the two-phase flows, we essentially need to use momentum variables $(m= \rho u, M=n\omega)$, rather than velocity variables $(u, \omega)$ in the spectrum analysis, to fully cancel out those non-conserved and insufficiently time-decay drag force terms. Finally, we study the singularity formation of the two-phase flow. We consider the blow-up of Euler equations in Euler-Navier-Stokes system. For Euler equations, we use Riemann invariants to construct decoupled Riccati type ordinary differential equations for smooth solutions and provide some sufficient conditions under which the classical solutions must break down in finite time.

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

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Lecture to be recorded by KAI-X

In this talk, I will discuss how the fundamental concepts in probability theory—the law of large numbers, the central limit theorem, and the large deviation principle—are developed in the study of real eigenvalues of asymmetric random matrices.

The Nagata Conjecture governs the minimal degree required for a plane algebraic curve to pass through a collection of $r$ general points in the projective plane $P^2$ with prescribed multiplicities. The "SHGH" Conjecture governs the dimension of the linear space of these polynomials. We formulate transcendental versions of these conjectures in term of pluripotential theory and we're making some progress.

For $d\ge 2$ and an odd prime power $q$, let $\mathbb{F}_q^d$ be the $d$-dimensional vector space over the finite field $\mathbb{F}_q$. The distance between two points $(x_1,\ldots,x_d)$ and $(y_1,\ldots,y_d)$ is defined to be $\sum_{i=1}^d (x_i-y_i)^2$. An influential result of Iosevich and Rudnev is: if $E \subset \mathbb{F}_q^d$ is sufficiently large and $t \in \mathbb{F}_q$, then there are a pair of points $x,y \in E$ such that the distance between $x$ and $y$ is $t$. Subsequent works considered embedding graphs of distances, rather than a single distance. I will discuss joint work with Debsoumya Chakraborti, in which we show that every sufficiently large subset of $\mathbb{F}_q^d$ contains every nearly spanning tree of distances with bounded degree in each distance. The main novelty in this result is that the distance graphs we find are nearly as large as the set $S$ itself, but even for smaller distance trees our work leads to quantitative improvements to previously known bounds. A key ingredient in our proof is a new colorful generalization of a classical result of Haxell on finding nearly spanning bounded-degree trees in expander graphs. This is joint work with Debsoumya Chakraborti.

The study of gradient flows has been extensive in the fields of partial differential equations, optimization, and machine learning. In this talk, we aim to explore the relationship between gradient flows and their discretized formulations, known as De Giorgi's minimizing movements, in various spaces. Our discussion begins with examining the backward Euler method in Euclidean space, and mean curvature flow in the space of sets. Then, we investigate gradient flows in the space of probability measures equipped with the distance arising in the Monge-Kantorovich optimal transport problem. Subsequently, we provide a theoretical understanding of score-based generative models, demonstrating their convergence in the Wasserstein distance.

While deep neural networks (DNNs) have been widely used in numerous applications over the past few decades, their underlying theoretical mechanisms remain incompletely understood. In this presentation, we propose a geometrical and topological approach to understand how deep ReLU networks work on classification tasks. Specifically, we provide lower and upper bounds of neural network widths based on the geometrical and topological features of the given data manifold. We also prove that irrespective of whether the mean square error (MSE) loss or binary cross entropy (BCE) loss is employed, the loss landscape has no local minimum.

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering hypergraph matchings and Hamiltonian cycles. We consider another natural generalization of the perfect matchings, Steiner triple systems. As a Steiner triple system can be viewed as a partition of pairs of vertices, it is a natural high-dimensional analogue of a perfect matching in graphs. We prove that for sufficiently large integer $n$ with $n \equiv 1 \text{ or } 3 \pmod{6},$ any $n$-vertex $3$-uniform hypergraph $H$ with minimum codegree at least $\left(\frac{3 + \sqrt{57}}{12} + o(1) \right)n = (0.879... + o(1))n$ contains a Steiner triple system. In fact, we prove a stronger statement by considering transversal Steiner triple systems in a collection of hypergraphs. We conjecture that the number $\frac{3 + \sqrt{57}}{12}$ can be replaced with $\frac{3}{4}$ which would provide an asymptotically tight high-dimensional generalization of Dirac's theorem.

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심사위원장: 이지운, 심사위원: 남경식, 황강욱, 양홍석(전산학부), 폴정(Fordham University)

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

In the analysis of singularities, uniqueness of limits often arises as an important question: that is, whether the geometry depends on the scales one takes to approach the singularity. In his seminal work, Simon demonstrated that Lojasiewicz inequalities, originally known in real algebraic geometry in finite dimensions, can be applied to show uniqueness of limits in geometric analysis in infinite dimensional settings. We will discuss some instances of this very successful technique and its applications.

Finite path integral is a finite version of Feynman’s path integral, which is a mathematical methodology to construct TQFT’s (topological quantum field theories) from finite gauge theory. It was introudced by Dijkgraaf and Witten in 1990. We study finite path integral model by replacing finite gauge theory with homological algebra based on bicommutative Hopf algebras. It turns out that Mayer-Vietoris functors such as homology theories extend to TQFT which preserves compositions up to a scalar. This talk concerns the second cohomology class of cobordism (more generally, cospan) categories induced by such scalars. In particular, we will explain that the obstruction class is described purely by homological algebra, not via finite path integral.

I will report on some recent results on modelling the heart, the external circulation, and their application to problems of clinical relevance. I will show that a proper integration between PDE-based and machine-learning algorithms can improve the computational efficiency and enhance the generality of our iHEART simulator.

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ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234) + Google Map

Zeta functions and zeta values play a central role in Modern Number Theory and are connected to practical applications in codes and cryptography. The significance of these objects is demonstrated by the fact that two of the seven Clay Mathematics Million Dollar Millennium Problems are related to these objects, namely the Riemann hypothesis and the Birch and Swinnerton-Dyer conjecture. We first recall results and well-known conjectures concerning these objects over number fields. If time permits, we will present recent developments in the setting of function fields. This is a joint work with Im Bo-Hae and Kim Hojin among others.

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There will be a tea time at 15:30 before the lecture.
Contact: Professor Bo-Hae Im ()

https://mathsci.kaist.ac.kr/bk21four/index.php/boards/view/board_seminar/3/

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심사위원장: 김용정, 심사위원: 권순식, 강문진, 김재경, 윤창욱(충남대학교)

The Stefan problem is a free boundary problem describing the interface between water and ice. It has PDE and probabilistic aspects. We discuss an approach to this problem, based on optimal transport theory. This approach is related to the Skorokhod problem, a classical problem in probability regarding the Brownian motion.

The mapping class group Map(S) of a surface S is the group of isotopy classes of diffeomorphisms of S. When S is a finite-type surface, the classical mapping class group Map(S) has been well understood. On the other hand, there are recent developments on mapping class groups of infinite-type surfaces. In this talk, we discuss mapping class groups of finite-type and infinite-type surfaces and elements of these groups. Also, we define surface Houghton groups, which are subgroups of mapping class groups of certain infinite-type surfaces. Then we discuss finiteness properties of surface Houghton groups, which is a joint work with Aramayona, Bux, and Leininger.

For a uniformly supersonic flow past a convex cornered wedge with the pressure being given for the surrounding quiescent gas at the downstream, as shown in experimental results, it is expected to form a shock followed by a contact discontinuity, which is also called the jet flow. By the shock polar analysis, it is well-known that there are two possible shocks, one a strong shock and the other one a weak shock. The strong shock is always transonic, while the weak shock could be transonic or supersonic. We prove the global existence, asymptotic behaviors, uniqueness, and stability of the subsonic jet with a strong transonic shock under the perturbation of the upstream flow and the pressure of the surrounding quiescent gas, for the two-dimensional steady full Euler equations.

Given a hypergraph $H=(V,E)$, we say that $H$ is (weakly) $m$-colorable if there is a coloring $c:V\to [m]$ such that every hyperedge of $H$ is not monochromatic. The (weak) chromatic number of $H$, denoted by $\chi(H)$, is the smallest $m$ such that $H$ is $m$-colorable. A vertex subset $T \subseteq V$ is called a transversal of $H$ if for every hyperedge $e$ of $H$ we have $T\cap e \ne \emptyset$. The transversal number of $H$, denoted by $\tau(H)$, is the smallest size of a transversal in $H$. The transversal ratio of $H$ is the quantity $\tau(H)/|V|$ which is between 0 and 1. Since a lower bound on the transversal ratio of $H$ gives a lower bound on $\chi(H)$, these two quantities are closely related to each other. Upon my previous presentation, which is based on the joint work with Joseph Briggs and Michael Gene Dobbins (https://www.youtube.com/watch?v=WLY-8smtlGQ), we update what is discovered in the meantime about transversals and colororings of geometric hypergraphs. In particular, we focus on chromatic numbers of $k$-uniform hypergraphs which are embeddable in $\mathbb{R}^d$ by varying $k$, $d$, and the notion of embeddability and present lower bound constructions. This result can also be regarded as an improvement upon the research program initiated by Heise, Panagiotou, Pikhurko, and Taraz, and the program by Lutz and Möller. We also present how this result is related to the previous results and open problems regarding transversal ratios. This presentation is based on the joint work with Eran Nevo.

We consider a family of nonlocal diffusion equations with a prescribed equilibrium state, which includes the fractional heat equation as well as a nonlocal equation of Fokker-Planck type. This family of equations will be shown to arise as the gradient flow of the relative entropy with respect to a version of the nonlocal Wasserstein metric introduced by Erbar. Such equations may also be viewed as the evolutionary Gamma-limit of a certain sequence of heat flows on discrete Markov chains. I will discuss criteria for existence, uniqueness, and stability of solutions, and sufficient criteria on the equilibrium state which ensure fast convergence to equilibrium.

TBD

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ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234) + Google Map

In this talk, we consider a group-sparse matrix estimation problem. This problem can be solved by applying the existing compressed sensing techniques, which either suffer from high computational complexities or lack of algorithm robustness. To overcome the situation, we propose a novel algorithm unrolling framework based on the deep neural network to simultaneously achieve low computational complexity and high robustness. Specifically, we map the original iterative shrinkage thresholding algorithm (ISTA) into an unrolled recurrent neural network (RNN), thereby improving the convergence rate and computational efficiency through end-to-end training. Moreover, the proposed algorithm unrolling approach inherits the structure and domain knowledge of the ISTA, thereby maintaining the algorithm robustness, which can handle non-Gaussian preamble sequence matrix in massive access. We further simplify the unrolled network structure with rigorous theoretical analysis by reducing the redundant training parameters. Furthermore, we prove that the simplified unrolled deep neural network structures enjoy a linear convergence rate. Extensive simulations based on various preamble signatures show that the proposed unrolled networks outperform the existing methods regarding convergence rate, robustness, and estimation accuracy.

In this talk, we consider nonlinear elliptic equations of the $p$-Laplacian type with lower order terms which involve nonnegative potentials satisfying a reverse H\"older type condition. We establish interior and boundary $L^q$ estimates for the gradient of weak solutions and the lower order terms, independently, under sharp regularity conditions on the coefficients and the boundaries. In addition, we prove interior estimates for Hessian of strong solutions and the lower order terms for nondivergence type elliptic equations. The talk is based on joint works with Jihoon Ok and Yoonjung Lee.

In this talk, we will primarily discuss the theoretical analysis of knowledge distillation based federated learning algorithms. Before we explore the main topics, we will introduce the basic concepts of federated learning and knowledge distillation. Subsequently, we will understand a nonparametric view of knowledge distillation based federated learning algorithms and introduce generalization analysis of these algorithms based the theory of regularized kernel regression methods.

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

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심사위원장: 백상훈, 심사위원: 곽시종, 김완수, 이용남, 쾨니히 요아힘(한국교원대학교)

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심사위원장: 임보해, 심사위원: 김완수, 박진형, 쾨니히 요아힘(한국교원대학교), 조재현(UNIST)

Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally efficient likelihood-based workflow that addresses all three steps in a unified way. Recently developed methods for constructing profile-wise prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters, and then combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well. We apply our methods to a range of synthetic data and real-world ecological data describing re-growth of coral reefs on the Great Barrier Reef after some external disturbance, such as a tropical cyclone or coral bleaching event.

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ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234) + Google Map

In this talk, I will introduce the use of deep neural networks (DNNs) to solve high-dimensional evolution equations. Unlike some existing methods (e.g., least squares method/physics-informed neural networks) that simultaneously deal with time and space variables, we propose a deep adaptive basis approximation structure. On the one hand, orthogonal polynomials are employed to form the temporal basis to achieve high accuracy in time. On the other hand, DNNs are employed to create the adaptive spatial basis for high dimensions in space. Numerical examples, including high-dimensional linear parabolic and hyperbolic equations and a nonlinear Allen–Cahn equation, are presented to demonstrate that the performance of the proposed DABG method is better than that of existing DNNs. zoom link: https://kaist.zoom.us/j/3844475577 zoom ID: 384 447 5577

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https://kaist.zoom.us/j/3844475577 회의 ID: 384 447 5577

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

In this talk, we address a question whether a mean-field approach for a large particle system is always a good approximation for a large particle system or not. For definiteness, we consider an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row (or columm)-summable network topology, we show that a homogeneous ensemble exhibits complete synchronization, and the infinite Kuramoto model can cast as a gradient flow, whereas we obtain a weak synchronization estimate, namely practical synchronization for a heterogeneous ensemble. Unlike with the finite Kuramoto model, phase diameter can be constant for some class of network topologies which is a novel feature of the infinite model. We also consider a second class of network topology (so-called a sender network) in which coupling strengths are proportional to a constant that depends only on sender's index number. For this network topology, we have a better control on emergent dynamics. For a homogeneous ensemble, there are only two possible asymptotic states, complete phase synchrony or bi-cluster configuration in any positive coupling strengths. In contrast, for a heterogeneous ensemble, complete synchronization occurs exponentially fast for a class of initial configuration confined in a quarter arc. This is a joint work with Euntaek Lee (SNU) and Woojoo Shim (Kyungpook National University).

The spectrum of a general non-Hermitian (non-normal) matrix is unstable; a tiny perturbation of the matrix may result in a huge difference in its eigenvalues. This instability is often quantified as eigenvalue condition numbers in numerical linear algebra or as eigenvector overlap in random matrix theory. In this talk, we show that adding a smoothly random noise matrix regularizes this instability, by proving a nearly optimal upper bound of eigenvalue condition numbers. If time permits, we will also discuss the effect of the noise matrix on a macroscopic scale in terms of the Brown measure of free circular Brownian motion. This talk is based on joint works with László Erdős.

Determining the density required to ensure that a host graph G contains some target graph as a subgraph or minor is a natural and well-studied question in extremal combinatorics. The celebrated 50-year-old Erdős-Sós conjecture states that for every k, if G has average degree exceeding k-2 then it contains every tree T with k vertices as a subgraph. This is tight as the clique with k-1 vertices contains no tree with k vertices as a subgraph. We present some variants of this conjecture. We first consider replacing bounds on the average degree by bounds on the minimum and maximum degrees. We then consider replacing subgraph by minor in the statement.

In this talk, I will introduce twistor theory, which connects complex geometry, Riemannian geometry, and algebraic geometry by producing a complex manifold, called the twistor space, from a quaternionic Kähler manifold. First, I will explain why quaternionic Kähler manifolds have to be studied in view of holonomy theory in Riemannian geometry, and how twistor theory enables us to use algebraic geometry in studying their geometry. Next, based on the realization of homogeneous twistor spaces as adjoint varieties, I will present a description of the compactified spaces of conics in adjoint varieties, which is motivated by twistor theory.

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심사위원장:이지운, 심사위원:남경식, 황강욱, 윤세영(김재철AI대학원), 서성미(충남대학교)

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

(KAI-X Distinguished Lecture Series) We have multiple approaches to vanishing theorems for the cohomology of Shimura varieties, via either algebraic geometry or automorphic forms. Such theorems have been of interest with either complex or torsion coefficients. Recently, results have been obtained under various genericity hypotheses by Caraiani-Scholze, Koshikawa, Hamann-Lee et al. I will survey different approaches. If time permits, I may discuss an ongoing project with Koshikawa to understand the non-generic case.

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KAI-X Distinguished lecture

The Hypothalamic-Pituitary-Adrenal (HPA) axis is the key regulatory pathway responsible for maintaining homeostasis under conditions of real or perceived stress. Endocrine responses to stressors are mediated by adrenocorticotrophic hormone (ACTH) and corticosteroid (CORT) hormones. In healthy, non-stressed conditions, ACTH and CORT exhibit highly correlated ultradian pulsatility with an amplitude modulated by circadian processes. Disruption of these hormonal rhythms can occur as a result of stressors or in the very early stages of disease. Despite the fact that misaligned endocrine rhythms are associated with increased morbidity, a quantitative understanding of their mechanistic origin and pathogenicity is missing. Mathematically, the HPA axis can be understood as a dynamical system that is optimised to respond and adapt to perturbations. Normally, the body copes well with minor disruptions, but finds it difficult to withstand severe, repeated or long-lasting perturbations. Whilst a healthy HPA axis maintains a certain degree of robustness to stressors, its fragility in diseased states is largely unknown, and this understanding constitutes a critical step toward the development of digital tools to support clinical decision-making. This talk will explore how these challenges are being addressed by combining high-resolution biosampling techniques with mathematical and computational analysis methods. This interdisciplinary approach is helping us quantify the inter-individual variability of daily hormone profiles and develop novel “dynamic biomarkers” that serve as a normative reference and to signal endocrine dysfunction. By shifting from a qualitative to a quantitative description of the HPA axis, these insights bring us a step closer to personalised clinical interventions for which timing is key.

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ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234) + Google Map