Speaker: Dr. Nir Gavish (Technion – Israel Institute of Technology ) - https://ngavish.net.technion.ac.il/ When: Tue, October 13, 2026 - 12:00pm Where: Kirwan Hall 3206
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Abstract: Multi-strain infectious diseases, such as Dengue and Influenza, frequently exhibit complex, recurrent epidemic waves characterized by sharp peaks and deep inter-epidemic troughs. Historically, mathematical modeling has relied on complex, disease-specific mechanisms, such as Antibody-Dependent Enhancement (ADE) or temporary cross-immunity, to recover these dynamics. In this talk, we introduce a foundational and analytically tractable multi-strain epidemic model featuring simple asymmetric cross-immunity.
We first demonstrate how this minimal framework naturally uncovers standard oscillatory phenomena, including local Hopf bifurcations, period-doubling cascades, and regular limit cycles, which are driven by the relative transmission advantage of secondary infections. Building on these local dynamics, we will explore the broader phase-space geometry to better understand the irregular epidemic patterns observed in real-world data. By reframing clinically observed "deep troughs" as dynamic states defined by exceptionally long residence times near saddle points, we will examine the single-strain equilibria as saddle-foci. We will discuss how trajectories interacting with these stable and unstable manifolds might organize into Shilnikov-type (or Bykov) cycles, offering a compelling geometric mechanism for recurrent, multi-peaked epidemic waves and global pandemic orbits.
Speaker: Arjun Krishnan (University of Rochester) - https://shirleyarjun.net/homepage/ When: Wed, October 14, 2026 - 2:00pm Where: Kirwan Hall 1311
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Abstract:Â In directed last-passage percolation on the square lattice with iid exponential weights, the coalescence time of two semi-infinite geodesics with a fixed asymptotic direction has a heavy tail with KPZ exponent 2/3, and hence infinite expectation. We show that three geodesics behave differently. Suppose we are given a stationary, non-crossing family of semi-infinite geodesics such as those arising from Busemann functions. In standard directed first- or last-passage percolation (FPP/LPP) with arbitrary weights, we show that the first time at which some pair among three neighboring geodesics coalesces has finite expectation. In models of directed FPP or LPP with general iid weights in which additional antidiagonal motion is allowed, we consider three geodesics started from colinear points on an antidiagonal line spaced distance k apart. We show that for every k, the first-pair coalescence time again has finite expectation. This confirms a prediction of a heuristic that says that coalescence times of pairs of non-crossing geodesics must be negatively associated.
(joint with Firas Rassoul-Agha and Timo Seppalainen)
Speaker: Jinxin Xue (Tsinghua University) - https://sites.google.com/view/jxue/home When: Thu, October 15, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: Poincare's last geometric theorem asserts that an area
preserving homeomorphism of the annulus twisting two boundaries admits
two fixed points. The Arnold conjecture leading to the Floer theory is
one way of generalizing the theorem.
Another way of generalizing theorem by Birkhoff is to assume the twist
is monotone from one boundary to the other, i.e. the so-called twist
maps. Birkhoff, Morse, Hedlund obtained a complete characterization of
the action minimizing orbits. The theory was revived by Aubry and
Mather in the last 80s.
The motivation of Aubry was the transition from metal to insulator of
a one-dimensional chain called the Frenkel-Kontorova model and his
work left open a conjecture stating that when the ground states are
uniformly hyperbolic, then the graph of the differential of the \alpha
function is purely singularly continuous (called a complete devil
staircase). In this talk, we explain our proof of Aubry's completeness
conjecture.
Related to this, we also explain another model called Hubbard-Wigner
model exhibiting not only the phenomenon of complete devil staircase,
but also admits an elegant analogue with Aubry-Mather theory. This
model is considered as the thin torus limit of the fractional quantum
Hall effects and the devil stair case reflects the fractional Hall
conductance. In the talk, we also explain the passage from
Aubry-Mather theory to the fractional quantum Hall effects.
Speaker:Â Immanuel Ben Porat (UT Austin) When: Thu, October 15, 2026 - 3:30pm Where: MTH3206
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Abstract: The semiclassical limit concerns the rigorous derivation of kinetic or monokinetic PDEs from dispersive equations of Schrödinger type in the regime where the Planck constant tends to zero. A fundamental example is the passage from the Hartree equation to the Vlasov–Poisson equation, where the singularity of the Coulomb interaction requires the development of suitable analytical tools. The presence of an external or self-consistent magnetic field introduces additional difficulties and has motivated growing interest in semiclassical limits for magnetized quantum systems. In this talk, I will review several modern approaches to the semiclassical limit, with particular emphasis on the additional analytical structures and estimates needed to account for magnetic effects.