Seminars and Colloquia by Series

Lagrangian concordance and contact invariants in sutured Floer theories

Series
Geometry Topology Seminar
Time
Monday, March 23, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Baldwin – Boston College
In 2007, Honda, Kazez, and Matic defined an invariant of contact 3-manifolds with convex boundaries using sutured Heegaard Floer homology (SHF). Last year, Steven Sivek and I defined an analogous contact invariant using sutured Monopole Floer homology (SMF). In this talk, I will describe work with Sivek to prove that these two contact invariants are identified by an isomorphism relating the two sutured theories. This has several interesting consequences. First, it gives a proof of invariance for the contact invariant in SHF which does not rely on the relative Giroux correspondence between contact structures and open books (something whose proof has not yet been written down in full). Second, it gives a proof that the combinatorially computable invariants of Legendrian knots in Heegaard Floer homology can obstruct Lagrangian concordance.

Dynamics of the Standard Map under Atypical Forcing

Series
CDSNS Colloquium
Time
Monday, March 23, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Adam Fox – Western New England Univ.
The Standard Map is a discrete time area-preserving dynamical system and is one of the simplest of such systems to exhibit chaotic dynamics. Traditional studies of the Standard Map have employed symmetric forcing functions that do not induce a net flux. Although the dynamics of these maps is rich there are many systems which cannot be modeled with these restrictions. In this talk we will explore the dynamics of the Standard Map when the forcing is asymmetric and induces a positive flux on the system. We will introduce new numerical methods to study these dynamics and give an overview of how transport in the system changes under these new forces.

Implicit interface boundary integral methods

Series
Applied and Computational Mathematics Seminar
Time
Friday, March 13, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 168
Speaker
Richard Tsai – University of Texas at Austin
I will present a new approach for computing boundary integrals that are defined on implicit interfaces, without the need of explicit parameterization. A key component of this approach is a volume integral which is identical to the integral over the interface. I will show results applying this approach to simulate interfaces that evolve according to Mullins-Sekerka dynamics used in certain phase transition problems. I will also discuss our latest results in generalization of this approach to summation of unstructured point clouds and regularization of hyper-singular integrals.

Birational Models of Moduli of Sheaves on Surfaces via the Derived Category

Series
Algebra Seminar
Time
Wednesday, March 11, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Aaron Bertram – University of Utah
Jacobians aren't particularly interesting from the point of view of the minimal model program, and neither are the moduli spaces of vector bundles on curves. But once we pass to vector bundles of higher rank (or torsion-free sheaves) on surfaces, then the birational geometry becomes very interesting. In this talk, I want to describe some recent results that rely on "tilting" the category of coherent sheaves on a surface to produce birational models of moduli that are themselves moduli spaces that come up naturally in the minimal model program.

Maximal Bounds on Cartesian Powers of Finite Graphs

Series
Analysis Seminar
Time
Wednesday, March 11, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jordan Greenblat – UCLA
In the course of their work on the Unique Games Conjecture, Harrow, Kolla, and Schulman proved that the spherical maximal averaging operator on the hypercube satisfies an L^2 bound independent of dimension, published in 2013. Later, Krause extended the bound to all L^p with p > 1 and, together with Kolla, we extended the dimension-free bounds to arbitrary finite cliques. I will discuss the dimension-independence proofs for clique powers/hypercubes, focusing on spectral and operator semigroup theory. Finally, I will demonstrate examples of graphs whose Cartesian powers' maximal bounds behave poorly and present the current state and future directions of the project of identifying analogous asymptotics from a graph's basic structure.

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