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Max Dehn Seminar

on Geometry, Topology, Dynamics, and Groups

Fall 2025 and Spring 2026
LCB 323
Wednesdays at 3:00 pm

Date Speaker Title click for abstract (if available)
FALL SEMESTER
September 3 Yotam Svoray
University of Utah
In this talk we discuss completely syndetic (CS) sets in discrete groups - subsets that for every n admit finitely many left translates that jointly cover every n-tuple of group elements. While for finitely-generated groups, the non-virtually nilpotent ones admit a partition into two CS sets, we show that virtually abelian groups do not. We also characterize CS subsets of the integers, and as a result characterize subsets of integers whose closure in the Stone-Cech compacitifcation of Z contains the smallest two sided ideal. Finally, we show that CS sets can have an arbitrarily small density.

This talk is based upon arXiv:2506.18784, a joint work with Guy Salomon and Ariel Yadin.

September 17 Carsten Peterson
Institut de Mathématiques de Jussieu - Paris Rive Gauche

A hyperbolic surface is called geometrically finite if it can be decomposed into a compact core together with finitely many cusps and funnels. The resolvent of the Laplacian on such spaces can be meromorphically continued to the entire complex plane. The poles of this meromorphic family of operators are called resonances and they contain a lot of information about the surface (for example about the long term behavior of solutions to the wave equation). We study such questions in the setting of "geometrically finite" regular graphs, which in particular requires us to make sense of what funnels and cusps mean in this setting. This is based on joint work with Christian Arends, Bartosz Trojan, and Tobias Weich.

October 1 Katia Shchetka
University of Michigan

In dynamics, the speed of mixing depends on the chaos of the map and the regularity of the observables. Notably, two classical linear models—the Bernoulli doubling map and the CAT map—exhibit double exponential mixing for analytic observables. Are linear maps the only ones with this property? In dimension one, we provide a full classification for maps from the space of finite Blaschke products acting on the circle (as well as for free semigroup actions generated by a finite collection of such maps). In higher dimensions, we identify a necessary condition for double exponential mixing and present several families of examples and non-examples. Key ideas of the proof involve the Koopman precomposition operator on spaces of hyperfunctions (elements of the dual space of analytic functions), which turns out to be non-self-adjoint, compact, and quasinilpotent, with spectrum reduced to zero.

The talk is accessible to all; no background knowledge is required.

October 8 No seminar, Fall Break
October 15 Camilo Arosemena Serrato
Rice University

This talk concerns the geometric classification of smooth, locally free, codimension-one actions of higher-rank simple Lie groups G on closed manifolds. Under a natural ergodic assumption, we prove a rigidity theorem giving a sharp dichotomy. Every such action is either: -Equivariantly diffeomorphic to the suspension of an action of a parabolic subgroup of G. -Finitely and equivariantly covered by the standard action on G / \Gamma \times S^1, where \Gamma \leq G is a uniform lattice. This classification is a smooth version of the classic measure-theoretic results of Nevo and Zimmer.

October 22 Leslie Mavrakis
University of Utah

A family F of compact n-manifolds is locally combinatorially defined (LCD) if there is a finite number of triangulated n-balls such that every manifold in F has a triangulation that locally looks like one of these n-balls. In joint work with Daryl Cooper and Priyam Patel, we show that LCD is equivalent to the existence of a compact branched n-manifold W, such that F is precisely those manifolds that immerse into W. In this way, W can be thought of as a universal branched manifold for F. In current and future work, we use this equivalence to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD. In this talk, I will present the main ideas of the proof of the equivalence and if time permits, construct branched 3-manifolds for a few of the geometries.

October 29 Jeremy West
University of Oklahoma

For a finite type surface S, PMap(S) is generated by Dehn twists (which are infinite order). When S is a closed surface of genus at least 3, Map(S) is generated by torsion elements. When S is an infinite type surface, it is a result of Patel-Vlamis that PMap(S) is topologically generated by Dehn twists, along with handle shifts when there are at least 2 ends accumulated by genus. In a recent paper, Bestvina-Fanoni-Tao defined a generalization of periodic mapping classes for infinite type surfaces, the so-called (extra) tame mapping classes. I show that for a large class of infinite type surfaces, PMap(S) is topologically generated by extra tames, and discuss why I expect this result to extend to all infinite type surfaces. I also demonstrate that extra tames topologically generate Map(S) in some cases, and discuss why one should expect this result to fail for some surfaces.

November 5 Miri Son
Rice University

TBD

November 12 George Shaji
University of Utah

TBD

November 26 No seminar, Thanksgiving
December 3 Yun Yang
Virginia Tech

TBD


Archive of past talks         

You may also be interested in the RTG Seminar
Max Dehn Seminar is organized by Mladen Bestvina, Eli Bashwinger, Ken Bromberg, Jon Chaika,
Priyam Patel, Noy Soffer Aranov, Rachel Skipper, Domingo Toledo, Kurt Vinhage and Kevin Wortman.


This web page is maintained by Rachel Skipper.