Fri, 13 Jun 2025
13:00
L5

The Likelihood Correspondence

Hal Schenck
(Auburn University)
Abstract

An arrangement of hypersurfaces in projective space is strict normal crossing if and only if its Euler discriminant is nonzero. We study the critical loci of all Laurent monomials in the equations of the smooth hypersurfaces. These loci form an irreducible variety in the product of two projective spaces, known in algebraic statistics as the likelihood correspondence and in particle physics as the scattering correspondence. We establish an explicit determinantal representation for the bihomogeneous prime ideal of this variety.

Joint work with T. Kahle, B. Sturmfels, M. Wiesmann

Further mechanistic insights into the trophic design of free-living mites
 Bowman, C Acarologia
Thu, 12 Jun 2025
17:00
L3

Hrushovski constructions in ordered fields

Yilong Zhang
(Universitat Bonn)
Abstract
Hrushovski constructions are a variant of amalgamation methods. They were invented to construct new examples of strongly minimal theories. The method was later adapted to expansions of fields, including colored fields and powered fields. In this talk, I will present my attempt to apply Hrushovski constructions to ordered fields. I will construct an expansion of RCF by a dense multiplicative subgroup (green points). Hrushovski constructions induce a back-and-forth system, enabling us to study the dp-rank and the open core of this structure. I will also introduce my recent progress on powered fields, an expansion of RCF by "power functions" on the unit circle, and my plan to axiomatize expansions of the real field using Hrushovski constructions.
Reducing phenotype-structured partial differential equations models of cancer evolution to systems of ordinary differential equations: a generalised moment dynamics approach
 MAINI, P Villa, C Browning, A Jenner, A Journal of Mathematical Biology

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Fluid Relaxation Approximation of the Busenberg-Travis Cross-Diffusion System.
 Carrillo, J Chen, X Du, B Jüngel, A Communications in mathematical physics volume 406 issue 7 151 (03 Jan 2025)
Counting sumsets and sum-free sets modulo a prime
 Green, B Ruzsa, I Studia Scientiarum Mathematicarum Hungarica volume 41 issue 3 285-293 (09 Sep 2004)
Restriction theory of the Selberg sieve, with applications
 Green, B Tao, T Journal De Theorie Des Nombres De Bordeaux volume 18 issue 1 147-182 (01 Jan 2006)
On arithmetic structures in dense sets of integers
 Green, B Duke Mathematical Journal volume 114 issue 2 215-238 (15 Aug 2002)
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