Upcoming Seminars
Seminar: Continuity Equations in Fibered Wasserstein Spaces – A common framework for meanfield and graphon dynamics
Beniot Bonnet-Weill, Chargé de Recherche CNRS (Junior Researcher)
March 25th, 2025
12:45pm to 1:45pm (Free Period)
Armitage – 124
Abstract: During the past fifteen to twenty years, the the concept of meanfield approximation has become one of the leading paradigms in the mathematical analysis of large multiagent systems. This prominence can be explained by its mathematical versatility, its modelling power, and its general amenability to various families of numerical schemes.
However, meanfield limits are, by essence, confined to operating at the level of homogeneous particle systems, wherein the dynamics of each agent only depends on purely spatial quantities (e.g. its own position and that of the others). In order to provide a macroscopic description of heterogeneous multiagent systems, a more recent trend has consisted in leveraging the concept of graph limit, introduced by Lovasz and Szegedy. These are quite natural and relatively easy to manipulate, albeit a bit rigid as they lead to considering ODEs in Lebesgue spaces, coined graphon dynamics.
In this ongoing work in collaboration with Nastassia Pouradier Duteil (INRIA, Sorbonne Université), we investigate a new class of evolutions taking the form of continuity equations over spaces of Young measures endowed with an adequate “fibered” Wasserstein metric. The main interest in doing so is that the latter combine some of the desirable features of both meanfield and graphon dynamics, while providing an embedding of both in natural limit cases. In this context, I will present the basics of all three models, discuss some of the topological properties of fibered Wasserstein distances, and expose Carathéodory and Cauchy-Lipschitz well-posedness results for the underlying dynamics.
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Seminar: The Cauchy-Riemann Equations on Domains in the Complex Projective Space
Mei-Chi Shaw, University of Notre Dame
April 1st, 2025
11:00AM to 12:00PM
Armitage – 124
Abstract: The Cauchy-Riemann equations play central role in one and several complex variables. The Cauchy-Riemann operator ∂ has been studied extensively on domains in the complex Euclidean space Cⁿ. Much less is known when the ambient manifold is not Cⁿ.
In this talk, we discuss the range of ∂ on domains in the complex projective space CPⁿ. We also study the ∂-Cauchy problem on pseudoconvex domains and use it to prove the Sobolev estimates for ∂ on pseudoconcave domains in CPⁿ. In particular, we show that ∂ does not have closed range in L² for (2,1)-forms on the Hartogs triangle in CP². This is in sharp contrast to ∂ on the Hartogs triangle in C², where L² results have long been established by Hörmander.
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Seminar: Agent-Oriented Programming of Language Models
Dei Wong, National AI Campus and Managing Director of Ann Harbor Algorithms
April 17th, 2025
12:45pm to 1:45pm (Free Period)
Online
Abstract: A large language model is an automaton, and like any automaton, it should be programmed in the language it accepts. When we view prompt engineering as programming through the lens of automata theory, it becomes clear that traditional software engineering practice — rooted in the strict separation of programming languages and natural languages — must be rethought. In this seminar, Dr. Dong will present a conceptual framework of agent-oriented programming based on emails and share intriguing experimental results from Ann Harbor.
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Seminar: The AI’s impact on the Future of Education
Ananda Gunawardena, NJ AI Hub
April 22nd, 2025
12:45PM to 1:45PM (Free Period)
Armitage – 124 followed by open discussion and refreshments at “The Alumni House” Cooper Street
This is a joint event by the Research Office, Provost Office, and Math department.
Abstract: As AI continues to transform education, we need to think about how AI will impact education and future workforce development. This seminar will highlight our work with NJ AI Hub (https://njaihub.org/), a centralized resource for foundational research, innovation economy, education and workforce development. We will also introduce key AI innovations, including Cubits.ai, an AI-driven course platform; CodeBench, a cloud-based coding environment; and SmartSlides, an AI-powered tool for creating dynamic presentations. These technologies aim to make learning more interactive, accessible, and effective. We will explore how AI is reshaping education and how new tools and course reimagining can support instructors and students in the evolving digital landscape.