seminars:topsem

Geometry and Topology Seminar

We meet Thursdays at 2:50–3:50 pm in WH-100E followed by refreshments served from 4:00–4:25 pm in WH-102. This semester's organizer is Jonathan Williams.

Some seminar speakers will also give a colloquium talk at 4:30 pm on the same day as the seminar talk. This seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.

The seminar has an announcement mailing list open to all. There is also a Google calendar with the seminar schedule (also in iCal).

Previous semesters

Summer 2017

• July 17
Speaker: Collin Bleak (University of St. Andrews)
Title: On Finite generation for groups of homeomorphisms of Cantor spaces

Abstract: Given a Cantor space $c$, we define a broad class of subgroups of the group of homeomorphisms of $c$ so that, if a given group $G$ is a subgroup of a finitely generated subgroup $H$ of $Homeo(c)$, and is in our class, then we can immediately conclude that $G$ is two-generated. The argument has connections with Higman and Epstein's general arguments toward simplicity for groups of homeomorphisms, and is general enough to immediately prove two-generation, e.g., for many relatives of the Thompson groups, and many other groups as well. Joint with James Hyde.

Fall 2017

• August 24

Organizational meeting

• August 31 (Joint with combinatorics)
Speaker: Olakunle Abawonse (Binghamton University)
Title: Topological Tverberg Theorem (prime power case)

Abstract: We will solve some discrete geometry problems using methods of equivariant topology. This talk is based on the paper “Beyond The Borsuk-Ulam Theorem – The Topological Tverberg Story” by Blagojevic and Ziegler. Topological techniques ranging from the Borsuk-Ulam theorem to spectral sequences will be used in solving these problems.

• September 7
Speaker: Casey Donoven (Binghamton University)
Title: Topology of Fractals

Abstract: Invariant factors are quotients of Cantor space that generalize the topology of certain fractals. They provide insight into the topology of self-similar sets and Julia sets and are interesting in their own right. Under certain conditions, invariant factors are inverse limits of finite topological spaces realizable as finite graphs. In this talk, I will present basic definitions and results pertaining to invariant factors and motivate them through poorly-drawn examples of self-similar fractals.

• September 14
Speaker: Jun Zhang (Tel Aviv University)
Title: Applications of persistent homology in symplectic and Riemannian geometry

Abstract: In this talk, I will start from a brief introduction of persistent homology and its related formulations from the perspective of symplectic geometry, especially in various forms of Floer theory. Then I will quickly demonstrate via several examples how persistent homology is used in symplectic geometry, for instance in solving some (Hamiltonian) dynamical problems. Finally, I will focus on a recent work (joint with V. Stojisavljevic) on an application in Riemannian geometry - quantitatively comparing Riemannian metrics, which is based on a newly developed concept called symplectic Banach-Mazur distance.

• September 21 (no seminar - Rosh Hashahah)
• September 28
Speaker: Oleg Lazarev (Columbia University)
Title: Contact manifolds with flexible fillings

Abstract: In this talk, I will show that all flexible Weinstein fillings of a given contact manifold have isomorphic integral cohomology. As an application, in dimension at least 5 any almost contact class that has an almost Weinstein filling has infinitely many exotic contact structures. Using similar methods, I will also construct an infinite family of almost symplectomorphic Weinstein domains whose contact boundaries are not contactomorphic. These results are proven by studying Reeb chords of loose Legendrians and positive symplectic homology.

• October 5
Speaker: Michael Cohen (North Dakota State University)
Title: Polishability of some groups of interval and circle diffeomorphisms

Abstract: Consider a group $G$ consisting of all $C^k$ diffeomorphisms of the circle whose derivatives satisfy a regularity condition arising from classical real analysis: a Lipschitz/Hoelder condition; absolute continuity; or bounded total variation. Is it possible to assign a separable complete metric topology to $G$, in such a way that the group operations become continuous? If so, $G$ is called Polishable. I'll discuss this Polishability problem in the cases mentioned above, where the answer turns out to vary dramatically depending on the choice of analytic condition. In particular, I'll exhibit an infinite class of what appear to be new Polish topological groups.

• October 12
Speaker: Robert Kropholler (Tufts University)
Title: TBA

Abstract: TBA

• October 19
Speaker: Ramón Vera (Institute of Mathematics, National Autonomous University of Mexico)
Title: Poisson Structures of near-symplectic Manifolds

Abstract: TBA

• October 26
Speaker: Adam Saltz (University of Georgia)
Title: TBA

Abstract: TBA

• November 2
Speaker: Eugenia Sapir (Binghamton University)
Title: TBA

Abstract: TBA

• November 9
Speaker: Cary Malkiewich (Binghamton University)
Title: TBA

Abstract: TBA

• November 16
Speaker: Mark Sapir (Vanderbilt University)
Title: TBA

Abstract: TBA

• November 23 (no seminar - Thanksgiving)
• November 30
Speaker: TBA (institution)
Title: TBA

Abstract: TBA

• December 7
Speaker: TBA (institution)
Title: TBA

Abstract: TBA