Date/Time : 08 Feb 2024 15:00
Venue : S17-05-11 (SR 5)
Speaker : Tan Bui-Thanh, The University of Texas at Austin

Digital twins (DTs) are digital replicas of systems and processes. At the core of a DT is a  physical/mathematical model which captures the behavior of the real system across temporal and spatial scales. One of the key roles of DTs is enabling “what if” scenario testing of hypothetical simulations to understand the implications at any point throughout the life cycle of the process, to monitor the process, and to calibrate parameters to match the actual process. In this talk we will present various (faster than) real time Scientific Deep Learning (SciDL) approaches for forward, inverse, and UQ problems. Both theoretical and numerical results for various problems including transport, heat, Burgers, Euler, and Navier-Stokes equations will be presented.

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Date/Time : 07 Feb 2024 14:00
Venue : S17 #06-11 (SR6)
Speaker : Marco Badran, ETH Zurich

Given a closed manifold $N$ and a compact, non-degenerate minimal submanifold $M$ of codimension 2 we construct a collection of solutions $U_\varepsilon$ to the magnetic Ginzburg-Landau equations such that $U_\varepsilon$ concentrates around $M$ as $\varepsilon\to 0$, establishing a codimension two analogous of the celebrated result by Pacard and Ritoré in the Allen-Cahn setting. The construction is carried out via an asymptotic gluing technique, yielding precise asymptotic expansion of the concentration profile.

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Date/Time : 07 Feb 2024 16:00
Venue : S17 #05-11 (SR5)
Speaker : Didac Martinez-Granado, University of Luxembourg and National University of Singapore

We define a notion of hyperplane for a hyperbolic group G and study G-invariant measures on the space of hyperplanes of its Gromov boundary, which we call “co-geodesic currents´´. Co-geodesic currents are induced by many classical objects such as geodesic currents for surface groups, certain cocompact actions of hyperbolic groups on CAT(0) cube complexes, quasi-fuchsian representations on a surface group, etc. Moreover, there is a natural intersection pairing between co-geodesic currents and the more classical geodesic currents, introduced by Bonahon, i.e. G-invariant measures on the square of the boundary of G. This pairing generalizes Bonahon’s intersection number when G is a surface group. Furthermore, every co-geodesic current \mu induces natural dual pseudo-metric space, in the sense that the intersection of \mu with the current determined by the conjugacy class of an element g in G recovers the stable length of g in the pseudo-metric space. This is joint work in progress with Eduardo Reyes.

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Date/Time : 07 Feb 2024 17:00
Venue : S17 #04-05 (SR2)
Speaker : Alexander Rabinovich, Tel Aviv University

Church’s Problem asks for the construction of a procedure which, given a logical specification S(I,O) between input-strings I and output-strings O, determines whether there exists an operator F that implements the specification in the sense that S(I,F(I)) holds for all inputs I. Buechi and Landweber gave a procedure to solve Church’s problem for MSO specifications and operators computable by finite-state automata. We investigate a generalization of the Church synthesis problem to the continuous time of the non-negative reals. It turns out that in the continuous time there are phenomena which are very different from the canonical discrete time domain of the natural numbers.

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Date/Time : 06 Feb 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Ian Gleason, Universitat Bonn

The local Langlands correspondence, proposed by Langlands as the non-abelian analogue of local class field theory for non-Archimedean local fields, has been established for various reductive groups over the years. However, a construction in full generality was lacking until the recent proposal by Fargues and Scholze, who introduced semi-simplified Langlands parameters for every reductive group. Their construction employs Scholze’s theory of diamonds, a modern approach to p-adic analytic geometry. This talk begins by revisiting historical developments in number theory that led to the formulation of the local Langlands correspondence. Subsequently, we explore the relevance of p-adic analytic geometry to the study of the local Langlands program and the impact these innovative methods have on our comprehension of the local Langlands correspondence.

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Date/Time : 06 Feb 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Dong Bin, Peking University

This presentation delves into the recent advancements in applying artificial intelligence (AI) to mathematical exploration. Initially, we will outline the current state of integrating AI methodologies, including machine learning, deep learning, and neural networks, into mathematical research, thereby fostering enhanced approaches and innovative concepts. Subsequently, we will highlight some preliminary results from ongoing research in this intersecting domain. Concluding the discussion, we will anticipate the future trajectory of research at the intersection of AI and mathematics, focusing on the potential of AI techniques to tackle new challenges and uncover novel problems in mathematical studies.

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Date/Time : 05 Feb 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Xiaoping Wang, The Chinese University of Hong Kong, Shenzhen

Topology optimization, which aims to find the optimal physical structure that maximizes mechanical performance,is vital in engineering design applications in aerospace, mechanical, and civil engineering. We introduce a deep generative model, based on diffusion models, to address the structure optimization problem. Combine with the threshold dynamics method, we present a successful frame for the topology optimization.

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Date/Time : 02 Feb 2024 16:00
Venue : S17 #04-06 (SR1)
Speaker : Dianbo Liu, National University of Singapore

Our team at National university of Singapore utilizes newest discovery from cognitive sciences especially consciousness related knowledge to inspire next generation of machine learning and apply the methods to understand biomedical sciences. In this talk we focus on using method inspired by compositional thoughts in human brain to discover causal relationships within Gene Regulatory Networks (GRNs). Causal discovery in GRNs is a challenging problem for multiple reasons including the existence of cyclic feedback loops and uncertainty that yields diverse possible causal structures. Previous works in this area either ignore cyclic dynamics (assume acyclic structure) or struggle with scalability. We introduce Swift-DynGFN as a novel framework that enhances causal structure learning in GRNs while addressing scalability concerns. Specifically, Swift-DynGFN exploits gene-wise independence to boost parallelization and to lower computational cost. Experiments on real single-cell RNA velocity and synthetic GRN datasets showcase the advancement in learning causal structure in GRNs and scalability in larger systems.

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Date/Time : 01 Feb 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Wang Jialin, National University of Singapore

Fix a finite group G and an algebraically closed field F of characteristic p. For an FG-module M, the complexity of M is the rate of growth of a minimal projective resolution of M which is a cohomological invariant of M. The rank varieties introduced by Carlson are defined for modules for elementary abelian p-groups and can be extended to modules for G by looking at the restriction to elementary abelian subgroups of G. Moreover, the dimension of the rank variety gives the complexity of the module. In this talk, I will discuss some basic properties of rank varieties and complexities and then review some known results on complexities of some simple modules for symmetric groups.

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