Geometry/Topology Seminar
Spring 2024
Thursdays 3:30-4:30pm, in
Eckhart 308
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- Thursday March 21 at 3:30-4:30pm in E308
- Fedya Manin, UC Santa Barbara
- The rank of a nilpotent Lie group
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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 n-dimensional
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.
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- Thursday March 28 at 3:30-4:30pm in E308
- Michael Landry, St. Louis University
- Surfaces transverse to pseudo-Anosov flows
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Abstract: A pseudo-Anosov flow on a 3-manifold is a
natural generalization of the suspension flow of a
pseudo-Anosov 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 pseudo-Anosov flow, one might ask "to which
surfaces is the flow transverse?" Alternatively, given a
norm minimizing surface, one might ask "to which
pseudo-Anosov 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.
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- Thursday April 11 at 3:30-4:30pm in E308
- Yvon Verberne, Western Ontario
- Automorphisms of the fine curve graph
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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.
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- Thursday April 18 at 3:30-4:30pm in E308
- Ben Knudsen, Northeastern
- Farber's conjecture and beyond
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Abstract: Topological complexity is a numerical
invariant quantifying the difficulty of motion planning;
applied to configuration spaces, it measures the difficulty
of collision-free 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.
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- Thursday May 2 at 3:30-4:30pm in E308
- Matthew Kahle, Ohio State
- TBA
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Abstract: TBA
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- Thursday May 9 at 3:30-4:30pm in E308
- Jason Manning, Cornell
- TBA
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Abstract: TBA
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- Thursday May 16 at 3:30-4:30pm in E308
- Abdoul Karim Sane, Georgia Tech
- TBA
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Abstract: TBA
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- Thursday May 23 at 3:30-4:30pm in E308
- Inanc Baykur, UMass Amherst
- TBA
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Abstract: TBA
Due to the high number of requests, we are no longer accepting speakers via self-invitations.
For questions, contact