Purdue University Model Theory and Applications Seminar
For the seminar archive, please click here.
Fall Semester 2026
The planned regular time for the seminar is Thursday 10:30am EDT/EST (WL Campus Time), with some talks possibly being held at other times.
This semester, in-person talks at the regular time will take place in SCHM 121.
Please email Margaret E. M. Thomas to be added to the mailing list for talk reminders and other seminar-related notices, and in order to obtain the connection details for any Zoom talk, which will be circulated by email shortly before the talk.
Talks
Thursday September 24 2026, 10:30am
SCHM 121
Jose Miguel Contreras Mantilla (Purdue University)
Title: Looking at Partition Lattices from continuous logic
Abstract: In this talk we will do a quick introduction to continuous logic and show some results from using it to study the “continuous” theory of Finite Partition Lattices. Continuous Logic was developed to use the tools of Model Theory in complete metric spaces, and it has been used to study C*-algebras, Banach Spaces, Probability Spaces, among others. On the other side, Finite Partition Lattices are the structures resulting from taking all the partitions of a finite set and ordering them by “refinement” and have a rich structure that allows a lot of combinatorial arguments. This presentation is based on joint work with Professor Thomas Sinclair.
Thursday October 8 2026, 10:30am
SCHM 121
Yuyan He (University of Notre Dame)
Title: Sum-product estimate in fields via dimension
Abstract: The counting statements of the form "$X$ has cardinality $O(c^n)$" can be seen as resembling the geometric statement "$X$ has dimension at most $n$". Hrushovski formalized this intuition in terms of pseudo-finite dimensions in model theory. Adapting ideas from stable group theory, he proved a qualitative precursor to Breuillard Green and Tao’s characterization of linear algebraic groups. The pseudo-finite dimension fits into the general framework of model theoretic dimension in works by Hrushovski and Wagner. We follow this line of research, and prove that a sum-product estimate holds in fields equipped with a dimension satisfying a natural set of dimension axioms. This is based on joint work with Sergei Starchenko.
Thursday October 15 2026, 10am (note unusual earlier time!)
LILY G458 (note unusual room!)
Spencer Dembner (Stanford University)
Title: Complex curves in o-minimal geometry
Abstract: There has recently been considerable progress relating o-minimality to complex analytic geometry. Yet almost nothing is known about coherent cohomology or the classification of vector bundles, even for curves. In $\mathbb{R}_{\mathrm{an}}$ and similar structures, we show that cohomology of noncompact curves is concentrated entirely at punctures. As an application, we compute the cohomology of the structure sheaf on a punctured Riemann surface, and show that it is governed by a Diophantine approximation question. Finally, we use similar techniques to characterize which definable Riemann surfaces have definable compactifications. The proofs are based on a careful analysis of boundary behavior for definable holomorphic functions.
Followed at 11am by: Panel discussion on AI in model theory.
Thursday October 22 2026, 10:30am
SCHM 121
Hongyu Zhu (University of Wisconsin - Madison)
Title: Comparing Lightface and Boldface Definitions
Abstract: The boldface Borel hierarchy classifies Borel subsets of a Polish space by topological complexity. By requiring the Borel descriptions to be effective, we obtain the corresponding lightface hierarchy. While certain natural subsets have fully effective descriptions, other sets can have vastly different lightface and boldface complexities. This talk will discuss such examples and some implications for computable structure theory.
Thursday November 12 2026, 10:30am
SCHM 121
Mathias Stout (McMaster University)
Title: TBA
Abstract: TBA
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