The GT seminar typically meets on Fridays at 2:00pm Eastern time in Room 520, Mathematics Department, Columbia University. It will also be live-streamed over Zoom.

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Fall 2022

Date	Time (Eastern)	Speaker	Title
September 16	2pm	Amina Abdurrahman	A global cohomological formula for Reidemeister torsion
September 23	2pm	Jean Pierre Mutanguha	Canonical forms for free group automorphisms
September 30	2pm	Marco Marengon	Relative genus bounds in indefinite 4-manifolds
October 7	n.a.	no speaker	No seminar (Krichever Conference)
October 14	2pm	Marta Magnani
October 21	2pm	Sam Taylor	Endperiodic maps via pseudo-Anosov flows
Octover 28	2pm	Funda Gultepe
November 4	Double Header Pt 1 @ 2pm	Peter Feller
November 4	Double Header Pt 2 @ TBD	John Baldwin
November 11	2pm	Thang Nguyen
November 18	2pm	Jane Wang
November 25	n.a.	no speaker	Happy Thanksgiving!
December 2	2pm	Katie Mann
December 9	2pm	Gary Guth

Abstracts

September 16: Amina Abdurrahman (Stony Brook)

Title: A global cohomological formula for Reidemeister torsion

Abstract: We give a global cohomological formula for Reidemeister torsion of a 3-manifold together with a symplectic local system. This can be considered as the topological analogue of a number-theoretic formula generalizing a result of Deligne in the 70s about local espilon factors. We plan to tell the topological story and touch on some of the related ideas in topology and number theory.

September 23: Jean Pierre Mutanguha (Princeton)

Title: Canonical forms for free group automorphisms

Abstract: The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!

September 30: Marco Marengon (Renyi Institute)

Title: Relative genus bounds in indefinite 4-manifolds

Abstract: Given a closed 4-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X − int(B^4), with boundary a given knot K in the 3-sphere. We give several methods to bound the genus of such surfaces in a fixed homology class. Our techniques include adjunction inequalities from Heegaard Floer homology and the Bauer-Furuta invariants, and the 10/8 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disc) in a 4-manifold and show that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. This is joint work with Ciprian Manolescu and Lisa Piccirillo.

October 21: Sam Taylor (Temple)

Title: Endperiodic maps via pseudo-Anosov flows

Abstract: We show that every atoroidal, endperiodic map of an infinite-type surface is isotopic to a homeomorphism that is naturally the first return map of a pseudo-Anosov suspension flow on a fibered manifold. Morally, these maps are all obtained by “spinning” fibers around a surfaces in the boundary of the fibered cone. The structure associated to these spun pseudo-Anosov maps allows for several applications. These include defining and characterizing stretch factors of endperiodic maps, relating Cantwell—Conlon foliation cones to Thurston’s fibered cones, and defining a convex entropy function on these cones that extends log(stretch factor). This is joint work with Michael Landry and Yair Minsky.

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Previous semesters:

Spring 2021, Fall 2020, Spring 2020, F all 2019 , Spring 2019 , Fall 2018 , Spring 2018 , Fall 2017 , Spring 2017 , Fall 2016 , Spring 2016 , Fall 2015 , Spring 2015 , Fall 2014 , Spring 2014 , Fall 2013 , Spring 2013 , Fall 2012 , Spring 2012, Fall 2011, 2010/11, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006.

Columbia Geometric Topology Seminar

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Fall 2022

Abstracts

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