Date/Time : 16 Oct 2024 16:30
Venue : S17 #05-11 (SR5)
Speaker : Gu Yejun, Institute of High Performance Computing

Innovations in automated material design demand models that predict both mechanical properties and inherent uncertainties. Traditional deterministic models, reliant on fitting parameters subject to experimental conditions, fall short in addressing these needs. This study introduces a parameter-free statistical methodology tailored for alloy prediction and design. Centered on a data-driven mixed density neural network, our approach uses existing experimental data from traditional alloys to develop a new constitutive rule for the evolution of dislocation density. This methodology allows for predicting the uncertainty in the resulting stress-strain curves and quantifies the relevant microstructures that must be measured experimentally for more of a deterministic prediction. Further, we delve into the origins of uncertainty, identifying and narrowing the gap between experiments and simulations. Our findings highlight potential solutions for bridging experimental-simulation discrepancies and offer a reliable yet efficient path to developing new alloys.

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Date/Time : 16 Oct 2024 14:00
Venue : S17 #05-11 (SR5)
Speaker : Havva Yoldas, Delft University of Technology

After a short introduction on kinetic equations and classical L^2/H^1 hypocoercivity techniques due to Dolbeault, Mouhot, Schmeiser AMS 2015, I will talk about Harris-type theorems that is an alternative method for obtaining quantitative convergence rates. I will discuss some applications of these theorems summarising some recent results obtained jointly with Jo Evans (Warwick) on the run and tumble equations that is a kinetic-transport equation modelling the bacterial movement under the effect of a chemoattractant.

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Date/Time : 09 Oct 2024 14:00
Venue : S17 #04-05 (SR2)
Speaker : Ho Boon Suan, National University of Singapore

When traversing a graph, each subsequent node is typically chosen from the set of unvisited nodes adjacent to the already visited ones. In this talk, I will explore how to count the number of possible traversals, particularly in graphs with a lot of symmetry. We will see how these counting problems lead to interesting hypergeometric identities and how computational methods can help in establishing such identities. The talk is intended for a general mathematical audience.

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Date/Time : 09 Oct 2024 17:00
Venue : S17 #04-04 (SR3)
Speaker : Athipat Thamrongthanyalak, Chulalongkorn University

In this talk, we study a converse of the Banach fixed point theorem and its connection to tameness in expansions of a real closed field. Let R be a definably complete expansion of a real closed field.

We say that R has the BFPP (short for, Banach fixed point property) when, for every locally closed definable set E, if every contraction on E has a fixed point, then E is closed. In this talk, we prove that if R has an o-minimal open core, then R has the BFPP; and if R has the BFPP, then R has a locally o-minimal open core.

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Date/Time : 09 Oct 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Pierre Alquier, ESSEC

The PAC-Bayesian theory provides tools to understand the accuracy of Bayes-inspired algorithms that learn probability distributions on parameters. This theory was initially developed by McAllester about 20 years ago, and applied successfully to various machine learning algorithms in various problems. Recently, it led to tight generalization bounds for deep neural networks, a task that could not be achieved by standard “worst-case” generalization bounds such as Vapnik-Chervonenkis bounds. In this talk, I will provide a brief introduction to PAC-Bayes bounds, and explain the core ideas of the theory. I will also provide an overview of the recent research directions. In particular, I will highlight the application of PAC-Bayes bounds to derive minimax-optimal rates of convergence in classification and in regression, and the connection to mutual-information bounds.

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Date/Time : 09 Oct 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Enrique ARTAL BARTOLO, Universidad de Zaragoza

In this talk we discuss how algebraic (or arithmetic) and geometric properties of plane curves affect the topology. There are some classical results starting from Zariski where the position of some singular points with respect to curves of some fixed degree has surprising consequences on the topology of these curves. We discuss the state of art of the subject, leading to cases where for curves defined over a number field, the action of the Galois group has also influence on the topology. We will present recent discoveries on the subject, specially with my collaborators and from the Hiro Tokunaga’s team, and also open problems.

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Date/Time : 03 Oct 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Dihua Jiang, University of Minnesota

I will discuss relations between non-abelian Fourier transforms and the Langlands conjecture on automorphic L-functions and associated local factors in the framework of Braverman-Kazhdan-Ngo.

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Date/Time : 03 Oct 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Meng Fai Lim, Central China Normal University

In this talk, we begin reviewing the non-commutative Iwasawa theory as developed by Coates, Fukaya, Kato, Sujatha and Venjakob which is concerned with attaching suitable characteristic elements to modules of arithmetic interest (for instance, Selmer groups). By their construction, these characteristic elements are realized as element in an appropriate localized K_1 group. We then introduce a notion of “taking modulo p” of these characteristic elements and discuss some of its properties. This is an ongoing work with Chao Qin.

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Date/Time : 02 Oct 2024 14:00
Venue : via Zoom
Speaker : Jing Yu, Fudan University

Join Zoom Meeting
https://nus-sg.zoom.us/j/81046462775?pwd=aDhaYnhQOTgybzdYS21yajlQdnBmZz09

Meeting ID: 810 4646 2775
Passcode: 23571113

In 1995, Levin and Linial, London, and Rabinovich conjectured that every connected graph $G$ of polynomial growth admits an injective homomorphism to the $n$-dimensional grid graph for some $n$. Moreover, they conjected that if every ball of radius $r$ in $G$ contains at most $O(r^\rho)$ vertices, then one can take $n = O(\rho)$. Krauthgamer and Lee confirmed the first part of this conjecture and refuted the second in 2007. By constructing some finite expander graphs, they showed best possible upper bound on $n$ is $O(\rho \log \rho)$.

Prompted by these results, Papasoglu asked whether a graph $G$ of polynomial growth admits a coarse embedding into a grid graph. We give an affirmative answer to this question. Moreover, it turns out that the dimension of the grid graph only needs to be linear in the asymptotic growth rate of $G$, which confirms the original Levin–Linial–London–Rabinovich conjecture “on the large scale.”

Besides, we find an alternative proof of the result of Papasoglu that graphs of polynomial growth rate $\rho < \infty$ have asymptotic dimension at most $\rho$.

Furthermore, our proof works in the Borel setting and shows that Borel graphs of polynomial growth rate $\rho < \infty$ have Borel asymptotic dimension at most $\rho$.

(This is joint work with Anton Bernshteyn.)

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