Logic Seminar - Valentina Disarlo
| Dates: | 7 October 2026 |
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| Times: | 15:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Valentina Disarlo (The University of Manchester)
Title: The model theory of the curve graph
Abstract: The curve graph of a finite-type surface is a countable graph whose vertices are isotopy classes of essential simple closed curves, with adjacency determined by disjointness. Although it arises naturally in low-dimensional topology and geometric group theory, it also provides a remarkably rigid first-order structure. Ivanov's classical theorem identifies the automorphism group of the curve graph with the extended mapping class group, and his subsequent metaconjecture predicts analogous rigidity for a large class of naturally associated complexes made of adjacency relations between topological objects on a surface.
In joint work with Thomas Koberda and Javier de la Nuez González, we present the first study of the curve graph from the point of view of model theory. I will discuss the first-order theory of the curve graph, with particular emphasis on definability and stability phenomena. In particular, we prove that the curve graph is w-stable and has a relative form of quantifier elimination. I will then present a model-theoretic framework for the Ivanov Metaconjecture and for comparing the curve graph with other complexes associated to a surface.
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Frank Adams 1
Alan Turing Building
Manchester
