UF Mathematics Colloquium
The canonical time and room for the UF Mathematics Colloquium is 3:00-3:50pm (8th period) in the Atrium (Little Hall 339), but nonstandard days and rooms may occur.
Schedule for Fall 2026
Title: Systemic Risk: Mathematical Models of Cascades and Complex Contagion
Abstract: We study mathematical models of cascading losses and contagion in large stochastic systems. The main questions are how local interactions, threshold effects, and heterogeneity shape the emergence and size of large cascades, and how these effects can be characterized in large-system limits. I will discuss limit theorems for cascade size and fluctuations, the role of network structure in resilience and phase transitions, and dynamic threshold models in which losses and capital levels evolve over time. These models connect naturally with branching processes, percolation, and ruin theory, and lead to questions of intervention and control. The motivating applications come from systemic risk in financial and economic systems, but the mathematical framework applies more broadly to interacting systems and complex contagion on random graphs
Title: Compact Equilibria in the Liquid Drop Model
Abstract: This work addresses the liquid drop model, introduced by Gamow in 1930 and Bohr–Wheeler in 1939, to describe the structure of atomic nuclei in nuclear physics. The problem involves finding a surface in three-dimensional space that is critical for a specific energy functional, balancing surface tension and nonlocal repulsion, subject to a volume constraint. Spherical solutions always exist and minimize the energy for sufficiently small volumes. However, for larger volumes, constructing non-minimizing critical points becomes more challenging. In this study, we present a new class of large-volume solutions, resembling “pearl collars” arranged along an axis in the shape of a large circle, with geometry close to Delaunay’s unduloids—surfaces of constant mean curvature. We also construct non-minimizing solutions with small mass that resemble two nearly identical spheres connected by a narrow neck.
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Title: On the circumcentered-reflection method
Abstract: The talk will discuss several variants of the circumcentered-reflection method (CRM) for the convex feasibility problem (CFP): finding a point in the intersection of closed convex sets. CRM was developed as an acceleration tool for classical projection-based algorithms. For affine sets, it provides an effective way to track a common point and often exhibits very fast behavior, including finite termination in many cases. For general convex sets, global convergence results obtained are obtained via Pierra’s product-space reformulation, together with convergence guarantees once the iterates enter a region of “centralized points,” where pure circumcenter steps have useful structural properties. Linear convergence is obtained under an error-bound condition and superlinear convergence holds in favorable geometric settings, such as a nonempty interior of the intersection with locally differentiable boundaries. Finally, a practical finite-convergence approach is discussed that replaces exact projections onto the sets with projections onto separating halfspaces, using positive exogenous perturbation parameters.
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Hotels are hard Saturday nights on the weekends of home football games (Sep 5, Sep 12, Sep 26, Oct 10, Nov 7, Nov 21), but okay Sunday nights.
Schedule for Spring 2027
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Gatornationals (March 11-14) will make hotels difficult over the period March 8-16, or so. Florida Relays may make hotels difficult over early April (dates TBD).
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