Convex hypersurface theory in higher-dimensional contact topology

Speaker: 

Ko Honda

Institution: 

UCLA

Time: 

Tuesday, November 20, 2018 - 4:00pm

Location: 

RH 306

Convex surface theory and bypasses are extremely powerful tools
for analyzing contact 3-manifolds.  In particular they have been
successfully applied to many classification problems.  After reviewing
convex surface theory in dimension three,  we explain how to generalize many
of their properties to higher dimensions.   This is joint work with Yang
Huang.

Hull-Strominger system and Anomaly flow over Riemann surfaces

Speaker: 

Teng Fei

Institution: 

Columbia University

Time: 

Monday, November 19, 2018 - 4:00pm to 5:00pm

Location: 

RH 340P

The Hull-Strominger system is a system of nonlinear PDEs describing the geometry of compactification of heterotic strings with torsion to 4d Minkowski spacetime, which can be regarded as a generalization of Ricci-flat Kähler metrics coupled with Hermitian Yang-Mills equation on non-Kähler Calabi-Yau 3-folds. The Anomaly flow is a parabolic approach to understand the Hull-Strominger system initiated by Phong-Picard-Zhang. We show that in the setting of generalized Calabi-Gray manifolds, the Hull-Strominger system and the Anomaly flow reduce to interesting elliptic and parabolic equations on Riemann surfaces. By solving these equations, we obtain solutions to the Hull-Strominger system on a class of compact non-Kähler Calabi-Yau 3-folds with infinitely many topological types and sets of Hodge numbers. This talk is based on joint work with Zhijie Huang and Sebastien Picard.

Teichmuller curves mod p

Speaker: 

Ronen Mukamel

Institution: 

Rice University

Time: 

Monday, November 26, 2018 - 4:00pm to 5:00pm

Location: 

RH 340P

A Teichmuller curve is a totally geodesic curve in the moduli space of Riemann surfaces. These curves are defined by polynomials with integer coefficients that are irreducible over C.  We will show that these polynomials have surprising factorizations mod p.  This is joint work with Keerthi Madapusi Pera.

Section problems

Speaker: 

Lei Chen

Institution: 

Caltech

Time: 

Monday, December 3, 2018 - 4:00pm to 5:00pm

Host: 

Location: 

RH 340P

In this talk, I will discuss a direction of study in topology: Section problems. There are many variations of the problem: Nielsen realization problems, sections of a surface bundle, sections of a bundle with special property (e.g. nowhere zero vector eld). I will discuss some techniques including homology, Thurston-Nielsen classication and dynamics. Also I will share many open problems. Some of the result are joint work with Nir Gadish, Justin Lanier and Nick Salter.

String topology, Hitchin's integrable system and noncommutative geometry

Speaker: 

Nick Rozenblyum

Institution: 

University of Chicago

Time: 

Monday, April 30, 2018 - 4:00pm to 5:00pm

Host: 

Location: 

RH 340P

A classical result of Goldman states that character variety of an oriented surface is a symplectic algebraic variety, and that the Goldman Lie algebra of free loops on the surface acts by Hamiltonian vector fields on the character variety. I will describe a vast generalization of these results, including to higher dimensional manifolds where the role of the Goldman Lie algebra is played by the Chas-Sullivan string bracket in the string topology of the manifold. These results follow from a general statement in noncommutative geometry. In addition to generalizing Goldman's result to string topology, we obtain a number of other interesting consequences including the universal Hitchin system on a Riemann surface. This is joint work with Chris Brav.

Pages

Subscribe to RSS - Geometry and Topology