Math Colloquium - Fall 2026
Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall I, unless noted otherwise.
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September 4
Roy Goodman, NJIT
Host: Amir Sagiv
Massive vortices in quantum fluids: Hamiltonian Mechanics, Averaging, Normal Forms, and Slow Manifolds
The point vortex model is a classical ODE system that describes the interaction of idealized localized vortices in a planar, inviscid fluid. It has found significant application in quantum fluids such as liquid helium and Bose-Einstein condensates. In several physical systems, vortices are better modeled as having mass, in sharp contrast to classical point vortices, which are massless. We study a model of massive point vortices proposed by Richaud. Its inertial terms constitute a singular perturbation and have profound consequences for the dynamics. Fast oscillations superimposed on the vortices' slower motion are immediately apparent, but careful mathematical analysis may reveal more. Mathematically, the vortex motion satisfies a system of Hamiltonian differential equations, and the inertial terms introduce a singular perturbation. We apply methods from Hamiltonian mechanics, most notably Lie transform perturbation theory, to derive a normal-form approximation, construct a slow manifold, and reveal the behavior of solutions.
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September 11
Yuri Antipov, Louisiana State University
Host: Daniel Massatt
Carleman problem for a strip and crack propagation in a power-law graded material
The steady-state subsonic and transonic models of an interfacial crack moving along the interface between two power-law graded half-planes under conditions of plane strain are considered. The problems are governed by the Navier equations with variable coefficients. The solution method consists of two steps. First, the Navier equations are transformed into a Carleman problem wit two shifts of two meromorphic functions in a strip that is recast as a system of singular integral equations with a fixed singularity solved numerically. At the second stage, on satisfying the boundary conditions, a vector Riemann-Hilbert (RH) problem of two functions with a piece-wise constant matrix coefficient is derived. Its entries are expressed through the solution of the Carleman problem. An exact solution to the RH problem is determined. Asymptotics of the displacements jumps and the stresses at the crack tip are recovered. A Griffith-type criterion of crack propagation is proposed. An application to the Heun differential equation is also discussed.
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September 18
Naoki Masuda, University of Michigan
Host: James MacLaurin
Anticipating bifurcations in network dynamics: temporal and spatial early warning signals
Complex dynamical systems often undergo sudden major changes, or tipping points, as conditions vary gradually. Examples discussed include mass extinctions of species, deforestation, and aggressive disease progression. Early warning signals (EWSs), often based on "critical slowing down", aim to anticipate such transitions. In fact, many systems of interest are heterogeneous networks arising from interactions among nodes, where constructing reliable EWSs is challenging. I will discuss temporal and spatial approaches to this problem. For temporal EWSs, we present heuristic and mathematically grounded methods (based on linear stochastic differential equation theory) for selecting small sets of sentinel nodes that can anticipate transitions as well as, or better than, monitoring the entire network. Because temporal EWSs demand many observations per node in general, spatial EWSs instead use a single snapshot and compute statistics across nodes, but network heterogeneity can obscure dynamical warning patterns. Therefore, we introduce a preprocessing step called baseline referencing, which compares each node’s state with its own far-from-transition baseline before computing spatial statistics. Numerically, this substantially improves variance-based signals. Finally, we develop theory explaining how equilibrium heterogeneity across nodes, network eigenvectors, and bifurcation type govern the success or failure of spatial EWSs in networks.
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September 25
Hector Baños, California State University - San Bernardino
Host: Kristina Wicke
Title Forthcoming
Abstract forthcoming
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October 9
Fioralba Cakoni, Rutgers University
Host: Thi Phong Nguyen
Title Forthcoming
Abstract forthcoming
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October 16
Youssef Marzouk, Massachusetts Institute of Technology [MIT]
Host: Amir Sagiv
Title Forthcoming
Abstract forthcoming
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October 23
David Nicholls, University of Illinois Chicago
Host: Xinyu Zhao
Title Forthcoming
Abstract forthcoming
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October 30
John Zweck, New York Institute of Technology
Host: Roy Goodman
Title Forthcoming
Abstract forthcoming
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November 6
Michael Goldberg, University of Cincinatti
Host: Amir Sagiv
Title Forthcoming
Abstract forthcoming
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November 13
Chris Rasmussen, San Diego State University
Host: Michelle Cirillo
Title Forthcoming
Abstract forthcoming
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November 20
Anirudh Sridhar, NJIT
Host: Michael Siegel
Title Forthcoming
Abstract forthcoming
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December 2 [Special Time - Wednesday 10AM]
Miguel Onorato, University of Turin
Host: Roy Goodman
Title Forthcoming
Abstract forthcoming
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December 11
Pierre-Emmanuel Jabin, Penn State University
Host: James MacLaurin
Title Forthcoming
Abstract forthcoming
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Last Updated: September 8, 2026