Geometry/Topology Seminar
Spring 2024
Thursdays 3:304:30pm, in
Eckhart 308

 Thursday March 21 at 3:304:30pm in E308
 Fedya Manin, UC Santa Barbara
 The rank of a nilpotent Lie group

Abstract: In the world of symmetric spaces and
nonpositive curvature, the rank of a space X is, roughly
speaking, the largest dimension n such that ndimensional
Euclidean subspaces are abundant in X. In the case of
nilpotent groups, one can define an analogous notion,
although the detailed definitions and intuitions are quite
different. The question then becomes: how can one determine
this rank from the algebraic structure of the group? I will
give a crash course introduction to Carnot geometry before
explaining what is known about the answer. Joint work with
Robert Young.

 Thursday March 28 at 3:304:30pm in E308
 Michael Landry, St. Louis University
 Surfaces transverse to pseudoAnosov flows

Abstract: A pseudoAnosov flow on a 3manifold is a
natural generalization of the suspension flow of a
pseudoAnosov surface diffeomorphism. If a properly embedded
surface is transverse to such a flow, then it is Thurston
norm minimizing in its homology class; this is due to
Mosher. Given a pseudoAnosov flow, one might ask "to which
surfaces is the flow transverse?" Alternatively, given a
norm minimizing surface, one might ask "to which
pseudoAnosov flows is the surface transverse?" I will give
some of the history of these questions and state a few new
results, motivated by larger questions about the Thurston
norm. Some of this is joint work with Chi Cheuk Tsang and
some is joint with Yair Minsky and Sam Taylor.

 Thursday April 11 at 3:304:30pm in E308
 Yvon Verberne, Western Ontario
 Automorphisms of the fine curve graph

Abstract: The fine curve graph of a surface was
introduced by Bowden, Hensel and Webb. It is defined as the
simplicial complex where vertices are essential simple
closed curves in the surface and the edges are pairs of
disjoint curves. We show that the group of automorphisms of
the fine curve graph is isomorphic to the group of
homeomorphisms of the surface, which shows that the fine
curve graph is a combinatorial tool for studying the group
of homeomorphisms of a surface. This work is joint with
Adele Long, Dan Margalit, Anna Pham, and Claudia Yao.

 Thursday April 18 at 3:304:30pm in E308
 Ben Knudsen, Northeastern
 Farber's conjecture and beyond

Abstract: Topological complexity is a numerical
invariant quantifying the difficulty of motion planning;
applied to configuration spaces, it measures the difficulty
of collisionfree motion planning. In many situations of
practical interest, the environment is reasonably modeled as
a graph, and the topological complexity of configuration
spaces of graphs has received significant attention for this
reason. This talk will discuss a proof of a conjecture of
Farber, which asserts that this invariant is as large as
possible in the stable range, and of an analogue of this
result in the setting of unordered configuration spaces.

 Thursday May 2 at 3:304:30pm in E308
 Matthew Kahle, Ohio State
 Configuration spaces of particles: homological solid, liquid, and gas

Abstract: We will discuss configuration spaces of
particles with positive thickness in a metric space. These
spaces generalize configuration spaces of points, and also
arise naturally as energy landscapes or phase spaces in
statistical physics. We will survey recent progress in
understanding the topology of these spaces, and suggest some
open problems and future directions.

 Thursday May 9 at 3:304:30pm in E308
 Jason Manning, Cornell
 A topological perspective on cubings

Abstract: The Sageev construction is a powerful
technique for building actions of groups on CAT(0) cube
complexes from codimension one subgroups. This has been
particularly useful in the study of hyperbolic and
relatively hyperbolic groups thanks to celebrated work of
Agol and Wise. We explain in the hyperbolic case how the
construction can be seen from the action on the boundary at
infinity. Relatively little about this action is used, which
suggests there may be cube complexes lurking in other
actions of groups on topological spaces. This is work in
progress, and the talk may include some wild speculation
about mapping class groups. This is joint work with Matthew
Haulmark.

 Thursday May 16 at 3:304:30pm in E308
 Abdoul Karim Sane, Georgia Tech
 Connected components of surgery graphs.

Abstract: A unicellular graph is the isotopy class
of a graph embedded on whose complement is a disk. We
defined an operation called surgery which turns a
unicellular graph into another one. This endows the set of
unicellular graphs with a graph: the vertices are
unicellular graphs and the edges are given by surgeries. In
this talk, we will discuss connectedness of surgery graphs
and their relation with mapping class group and its subgroup
(one of which is the liftable mapping class group).

 Thursday May 23 at 3:304:30pm in E308
 Inanc Baykur, UMass Amherst
 A dichotomy in dimension four

Abstract: Does every fourmanifold admit either no
smooth structure or infinitely many of them? I'll report on
recent work, joint with A. Stipsicz and Z. Szabó, addressing
this question for oriented fourmanifolds with finite cyclic
fundamental groups. A bonus discussion may feature fake
projective planes in the context of yet another dichotomy.
Due to the high number of requests, we are no longer accepting speakers via selfinvitations.
For questions, contact