The GT seminar typically meets on Fridays at 2:00pm Eastern time in Room 407, Mathematics Department, Columbia University. It will also be live-streamed over Zoom.

Spring 2023

Date	Time (Eastern)	Speaker	Title
January 20	2pm Eastern	Nathan Sagman	Hitchin representations and minimal surfaces
January 27	2pm Eastern	Ethan Dlugie	The Burau Representation and Shapes of Polyhedra
February 3	2pm Eastern	Rebekah Palmer	Totally geodesic surfaces in knot complements
February 10	2pm Eastern	Lorenzo Ruffoni
February 17	2pm Eastern	Ty Ghaswala
February 24	2pm Eastern	Tam Cheetham-West
March 3	2pm Eastern	Marissa Loving
March 10	2pm Eastern	Dan Margalit
March 17	2pm Eastern	No Seminar	Spring break
March 24	2pm Eastern	Beibei Liu
March 31	2pm Eastern	No Seminar	Simons Collaboration Meeting in NYC
April 7	2pm Eastern	Noelle Sawyer
April 14	2pm Eastern	potentially taken!	potentially taken!
April 21	2pm Eastern	Oyku Yurttas
April 28	2pm Eastern	Giuseppe Martone

Abstracts

Nathaniel Sagman

Date: January 20

Title: Hitchin representations and minimal surfaces

Abstract:

Labourie proved that every Hitchin representation into PSL(n,R) gives rise to an equivariant minimal surface in the corresponding symmetric space. He conjectured that uniqueness holds as well (this was known for n=2,3) and explained that if true, then the Hitchin component admits a mapping class group equivariant parametrization as a holomorphic vector bundle over Teichmüller space. After giving the relevant background, we will explain that Labourie’s conjecture fails for n at least 4, and point to some future questions

Ethan Dlugie

Date: January 27

Title: The Burau Representation and Shapes of Polyhedra

Abstract:

The Burau representation of braid groups has been around for almost a century. Still we don't know the full answer to whether this representation is faithful. The only remaining case is for the $n=4$ braid group, and faithfulness here has intimate connections to the question of whether the Jones polynomial detects the unknot. By specializing the $t$ parameter in this representation to certain roots of unity, an interesting connection appears with the moduli space of flat cone metrics on spheres explored by Thurston. Leveraging this connection, I will explain how one can place strong restrictions on the kernel of the $n=4$ Burau representation.

Rebekah Palmer

Date: February 3

Title: Totally geodesic surfaces in knot complements

Abstract:

Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader-Fisher-Miller-Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case. In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces. On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover. This talk will explore this progress for both the uniqueness and the absence.

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Previous semesters:

Fall 2022, Spring 2022, Fall 2021, 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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Spring 2023

Abstracts

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Previous semesters:

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