Upcoming Seminars
SPEAKER: Andrew Pendleton
December 11th, 2025
11:30AM – 12:00PM in BSB 116
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https://rutgers.zoom.us/j/97858173592?pwd=j5fuOdhss4lw5bLX6S1wJB9Ipb7hwX.1;
Meeting ID: 978 5817 3592; Password: 452800).
TITLE: Can you hear the aspect ratio of a drum?
ABSTRACT: Eigenvalues of the Dirichlet Laplacian on a rectangular domains can be interpreted physically as the fundamental tone and the overtones produced by an idealized drumhead with the same aspect ratio. The multiplicity of an eigenvalue represents the number of modes with which the drumhead vibrates in the corresponding frequency and therefore affects the timbre of the drum. A recent conjecture proposed a strikingly simple criterion for when rectangular domains admit eigenvalues with an arbitrary multiplicity. We exploit some surprising connections to algebraic number theory and the study of quadratic forms to confirm this classification; thus showing that in some ways, you can really hear the rationality of the square of the aspect ratio of a drum. This is a joint work with Dr. Siqi Fu.
SPEAKER: Jack Heimrath
December 11th, 2025
12:10PM – 1:00PM in BSB 116
TITLE: The Statistics of Gaps Between Primes and Values of Quadratic Forms
ABSTRACT: The aim of this talk is twofold. First, we will introduce Cramér’s probabilistic model of primes and use it to derive a distribution of gaps between primes. Addressing the shortcomings of Cramér’s model we will lead us to rediscover the First Hardy-Littlewood Conjecture, which we will lead to another distribution. A method of moments argument will show that these two distributions are in fact the same. Second, we will show how the approach for primes can be modified to obtain analogous statistics of gaps between values of quadratic forms.
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SPEAKERS: Emiliano Cristiani, Giovanni Franzina, Francesca L. Ignoto
December 3rd, 2025
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https://rutgers.zoom.us/j/97859651562?pwd=T1ImTZwiFz0VMCcBDwiAaAvKS6UtWl.1
TITLE: Analysis of traffic models via numerical computation of balanced and unbalanced Wasserstein distances.
ABSTRACT: Balanced and unbalanced Wasserstein distances allow us to quantitatively compare two mass distributions with equal and different masses, respectively.
In this talk, we first propose some numerical methods for the approximation of the Wasserstein distances and, after that, we explore their usage for studying the sensitivity of differential models for vehicular traffic flow.
The quantification of the models’ sensitivity is obtained by computing the Wasserstein distances between two (numerical) solutions corresponding to different inputs, including different initial and boundary conditions.
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SPEAKER: Xiaoqian Gong
November 20, 2025
Armitage Hall – Room 124 during free period
TITLE: Mathematical Analysis of Traffic Flow Models: Microscopic and Macroscopic Perspectives
ABSTRACT: In this talk, we will present the mathematical properties of some microscopic and macroscopic descriptions of traffic flow models. From the microscopic perspective, we will examine the well-posedness of the “Bando-Follow-the-Leader” (Bando-FtL) Model as well as its time-delayed version. We will also discuss the model’s large time behavior and briefly introduce a Non-local extension of the Bando-FtL framework. On the macroscopic side, we will investigate the well-posedness of a non-local GARZ model and its singular limit. Numerical simulations will also be presented.
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SPEAKER: Xiaohua Hu, Drexel University
November 17th, 2025
BSB – 116 during free period (11:20AM to 12:20PM)
TITLE: Towards Effective Biomedical Natural Language Processing with Large Language Models
ABSTRACT: This talk explores leveraging advancements in NLP to address challenges in developing Product-Specific Guidance (PSG) for generic drug products within the biomedical field. Our work focuses on the opportunity to automate tasks during this process, particularly extracting ADME (Absorption, Distribution, Metabolism, and Excretion) details from RLD drug labeling. It addresses key challenges such as the automation of ADME information extraction from imbalanced datasets, the summarization of complex biomedical documents, and the constraints posed by data privacy in real-world applications. This work contributes practical, scalable solutions to facilitate PSG development and promote the broader use of specialized, resource-efficient NLP models in biomedical research.
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Speaker: Lorenzo Pareschi, Department of Mathematics and Computer Science, University of Ferrara, Italy
October 30th, 2025
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https://rutgers.zoom.us/j/96442897289?pwd=bPsYXaIvu0BuaxSVQxU0VTLnRUSotm.1
Title: Consensus and Particles: New Directions in Optimization
Abstract: Optimization problems in high dimensions are at the core of modern science and engineering. Traditional algorithms, such as gradient-based methods, can be effective, but they often face serious challenges in nonconvex landscapes, in very high-dimensional regimes, or when objectives are nonsmooth or non-differentiable. Consensus-Based Optimization (CBO) is a relatively new approach that draws inspiration from collective behaviour in particle systems: a swarm of agents explores a landscape while exchanging information and gradually forming consensus around promising solutions. What makes CBO attractive is its simplicity, versatility, and the fact that its behaviour can be rigorously analyzed through mean-field models. In this talk I will present two recent developments. First, we introduce a superlinear drift mechanism, inspired by ideas from quantum models, which accelerates the convergence of CBO and improves its ability to concentrate around global minimizers. Second, we propose a swarm dynamic with random jumps, described by a kinetic model, which allows for heavy-tailed random exploration (such as Cauchy noise) and enhances the ability of the swarm to escape local traps. I will also explain how the approach connects back to classical CBO in suitable limits.
This is a joint research with J. Franceschi (Ferrara), M.Herty (Aachen), M. Zanella (Pavia), H. Im (Edinburgh), and G. Borghi (Edinburgh).
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