Brandeis Topology Seminar, Spring 2025

Organizers: Carolyn Abbott (carolynabbott@brandeis.edu), Dani Álvarez-Gavela (dgavela@brandeis.edu) Kiyoshi Igusa (igusa@brandeis.edu), Thomas Ng (thomasng@brandeis.edu), Danny Ruberman (ruberman@brandeis.edu)

January 16: No seminar

January 23: Kasia Jankiewicz (UCSC / IAS).

Title: Graph braid groups and their topological complexity

Abstract: Graph braid groups are the fundamental groups of configuration spaces of particles in a graph. They can be expressed as the fundamental groups of special cube complexes. In the introductory part, I will discuss those groups, some of their properties, and their associated cube complexes. In the second part, I will talk about my joint work with Kevin Schreve, where we study a question of whether certain sets of elements in a graph braid group generate a right-angled Artin group, and use it to compute the topological complexity of graph braid groups with sufficiently many particles.

January 30: No seminar (colloquium)

February 6: Chenyang Wu (Brandeis)

Title: Bounded Geodesics on Locally Symmetric Spaces

Abstract: For a general noncompact complete Riemannian manifold, it is of particular interest to know whether there exists a bounded geodesics on it or not. In 1980s, S. G. Dani proved that for a Riemannian manifold M of constant curvature and finite Riemannian volume, the set of bounded geodesics on M has the same Hausdorff dimension as the unit tangent bundle of M. In a recent paper we generalize Dani's result to any locally symmetric space with finite volume. Moreover, for a special locally symmetric space SO_3(Z)\SL_3(R)/SL_3(Z), we can prove a winning property (stronger than full Hausdorff dimension) of the aforementioned set. This is a joint work with Lifan Guan.

February 13: Nima Hoda (Tufts)

Title: Strong shortcuts and generating sets

Abstract: A group is strongly shortcut if it has a Cayley graph in which circles cannot embed at arbitrarily large scales with arbitrarily good bilipschitz constants. This can be shown to be a special case of the Gromov mesh condition implying simply connected asymptotic cones and polynomial Dehn function. Most classes of nonpositively curved groups are strongly shortcut, including CAT(0) groups, Helly groups, systolic groups and hierarchically hyperbolic groups. I will discuss various results on strongly shortcut groups, including recent joint work with Timothy Riley in which we showed that the strong shortcut property is not invariant under change of generating sets.

February 20: No seminar

February 27: Khánh Lê (Rice)

March 6: Ian Biringer (Boston College)

March 13: Jonathan Zung (MIT)

March 20: Miriam Kuzbary (Amherst College)

March 27: Lea Kenigsberg (UC Davis)

April 3: Tam Cheetham-West (Yale)

April 10: Rachel Skipper (Utah)

April 17: No seminar

April 24: Brandis Whitfield (Temple)

May 1: Michelle Chu (U Minnesota)