Math Postdoc Seminar

Overview

The Math Postdoc Seminar provides the NYUAD postdoc community with an opportunity to discuss their work. It is a bi-weekly event held at New York University Abu Dhabi. Occasionally, we also have the pleasure of hosting special sessions by senior researchers.

The sessions are tailored in one of the following two formats:

Standard Sessions. 

Our standard sessions are built based on a standard research seminar of 45 minutes, preceded by a non-standard introductory mini-session of about 20 to 30 minutes. Here is an overview of the expected outline:

    • 20-minute presentation of a preliminary result and the elements of its proof, which is preferably linked to the remaining part of the session and may serve in other contexts.
    • 10-minute break (discussion).
    • 45-minute talk (including questions and a final discussion).

Mini-Courses. 

An intensive one-day session of two+two-hours of lectures given by senior researchers, covering broad areas of research such as Analysis, Probability and Geometry with applications in PDEs and Mathematical Physics.

 

Academic year 2024-2025

  • January 24, 2025. 9h:30 –12h:00 & 14h:30 – 17h:00, in A4 Building, Room 003.
    • Mini-Course (2+2 hours) by Prof. Fabrice Baudoin
    • Title: Analysis and geometry of Dirichlet forms: An introduction
    • Abstract: We provide an overview of the fundamentals in the theory of Dirichlet forms. Dirichlet forms theory allow us to define Laplacians, PDEs and boundary conditions in very general frameworks which do not require any kind of smooth structures including metric spaces like fractals. In this mini-course, we will cover the following topics:
        1. Contraction semigroups, quadratic forms and generators in Hilbert spaces;
        2. Dirichlet forms;
        3. Examples of Dirichlet spaces: Divergence forms diffusion operators, Riemannian manifolds, Fractals, Metric spaces;
        4. The Gagliardo-Nirenberg interpolation theory in Dirichlet spaces.
    • Course Material is available here.
  • February 7, 2025. 10h:00 – 11h:30, in A4 Building, Room 003.
    • Standard Session by Dr. Billel Guelmame
    • Title: On some regularized nonlinear hyperbolic equations
    • Abstract: The first part of this talk is dedicated to a brief discussion on Young measures. In the second part, we present some non-diffusive, non-dispersive regularizations of the inviscid Burgers equation and the barotropic Euler equations. We prove the existence of solutions and, in the scalar case, we also study the singular limit.
  • February 21, 2025. 10h:00 –12h:00, in A2 Building, Room 003.
    • Standard Session by Dr. Quentin Ehret
    • Title: On Lie Superalgebras in characteristic 2
    • Abstract: First, I will review certain constructions and examples of Lie superalgebras in characteristic 0 and explain why the case of characteristic 2 necessitates a different approach. Then, I will introduce a method of extensions Lie superalgebras in characteristic 2, known as the Lagrangian extension.
  • April 18, 2025. 9h:30 –11h:30, in A2 Building, Room 003.
    • Standard Session by Dr. Hui Zhu
    • Title: Dynamics Decomposition for Schrödinger Propagators with Irregular Potentials on Tori and Observability from Rough Domains
    • Abstract: Exploiting the cluster structure of lattice points on paraboloids, we obtain a decomposition of dynamics for Schrödinger propagators on tori of arbitrary dimensions. Using this decomposition and mathematical induction on the dimension, we establish general sufficient conditions for observability and hence exact controllability of Schrödinger propagators. We conjecture that these conditions entail observability whenever potentials are bounded and domains of observation have positive measures. This is a joint work with Nicolas Burq.
  • April 25, 2025. 10h:00 –12h:00, in A2 Building, Room 003.
    • Standard Session by Dr. Kiran Kumar
    • Title: Local weak convergence and its applications to random matrix theory
    • Abstract: In the sparse regime, many natural graph sequences happen to converge in the local weak sense, a notion first introduced by Benjamini & Schramm and later developed further by Aldous, Lyons & Steele. These local weak limits are often significantly easier to analyze than the original finite graph sequences, while still capturing the asymptotic behavior of key combinatorial and spectral graph parameters. In this talk, I will present a self-contained introduction to this powerful framework, and discuss some of its applications in random matrix theory and random simplicial complexes.
  • May 2, 2025. 10h:00 –12h:00, in A2 Building, Room 007.
    • Standard Session by Dr. Dahmane Dechicha
    • Title: On the spectral problem and the fractional diffusion limit for the kinetic Fokker-Planck equation.
    • Abstract: After a brief introduction to kinetic equations, I will provide motivation and explain the principle of diffusion approximation, which justifies that the solution of a kinetic equation can be approximated by an equilibrium profile with a density satisfying a macroscopic equation.
      I will then focus on the Fokker-Planck equation with heavy-tailed equilibrium handled by a spectral method.

 

Academic year 2025-2026

  • October 24, 2025. 10h:00 –12h:00, in A2 Building, Room 003.
    • Standard Session by Dr. Haocheng YANG
    • Title: Global Well-posedness of a 2D Fluid-structure Interaction Problem without Dissipation
    • Abstract: In this talk, we will analyze the incompressible Euler equation in a time-dependent 2D fluid domain, whose interface evolution is governed by the law of linear elasticity without damping. Our main result asserts that the Cauchy problem is globally well-posed in the energy space for irrotational initial data without any smallness assumption. We also prove the continuity with respect to the initial data and the propagation of regularity. In the absence of parabolic regularization, a key ingredient in our analysis is a novel reduction to a nonlinear Schrödinger type equation, allowing us to apply dispersive estimates. To carry this out, we develop new estimates for the Dirichlet-to-Neumann operator in low-regularity regimes through tools from classical harmonic analysis and paradifferential calculus. This is a joint work with Thomas Alazard and Chengyang Shao.  

       

  • November 7, 2025. 
    • Standard Session by Dr. Raghavendra Tripathi
    • Title: Dynamics on large graphs and their limits
    • Abstract: Large networks have proved to be an effective tool for studying interactions in many situations of interest in biology, machine learning, physics, and so on. In many of these models, one is interested in optimizing some function of the network, which is done by some dynamics. There are at least two distinct themes in this field: the first theme (and more widely studied) involves a large number of interacting agents on a network — often to optimize (shared or individual) some objective. A more recent theme that has emerged — inspired by deep neural networks —  involves optimizing the weights on the edges (and/or vertices) to minimize a given loss function. This is the case, for example, for neural networks, although many other problems ranging from extremal graph theory to finding maximum likelihood estimates for exponential random graph models can be cast in this framework. In general, these problems are extremely difficult, and the minimizers are rarely explicit.
      An important insight that is emerging in this field is that as the size of these networks goes to infinity, these high-dimensional dynamics give rise to PDEs or processes on the space of graphons. These limiting dynamics are often easier to analyze, and they often reveal important insights about the finite (but large-dimensional) dynamics.This whole field is evolving rapidly (while interacting with other fields) and has led to the generalization of some classical ideas, like gradient flows, propagation of chaos, and McKean-Vlasov equation on the space of graphons. In this talk, I hope to provide a broad overview of the various research themes in this field, problems of interest and their applications, and describe some of the tools and techniques that are used. 
  • November 21, 2025. Mini Course by Prof. Patrick Gérard (Details TBA).
  • February, 2026. Mini Course by Dr. Richard Aoun (Details TBA).