## Seminars and Colloquia by Series

Monday, September 18, 2017 - 13:55 , Location: Skiles 006 , Michael Landry , Yale , , Organizer: Balazs Strenner
Let M be a closed hyperbolic 3-manifold with a fibered face \sigma of the unit ball of the Thurston norm on H_2(M). If M satisfies a certain condition related to Agol’s veering triangulations, we construct a taut branched surface in M spanning \sigma. This partially answers a 1986 question of Oertel, and extends an earlier partial answer due to Mosher. I will not assume knowledge of the Thurston norm, branched surfaces, or veering triangulations.
Monday, September 18, 2017 - 12:30 , Location: Skiles 006 , Livia Corsi , Georgia Institute of Technology , , Organizer: Livia Corsi
I will consider the isotropic XY quantum chain with a transverse magnetic field acting on a single site and analyze the long time behaviour of the time-dependent state of the system when a periodic perturbation drives the impurity. It has been shown in the early 70’s that, in the thermodynamic limit, the state of such system obeys a linear time-dependent Schrodinger equation with a memory term. I will consider two different regimes, namely when the perturbation has non-zero or zero average, and I will show that if the magnitute of the potential is small enough then for large enough frequencies the state approaches a periodic orbit synchronized with the potential. Moreover I will provide the explicit rate of convergence to the asymptotics. This is a joint work with G. Genovese.
Friday, September 15, 2017 - 15:00 , Location: Skiles 005 , Tom Trotter , Georgia Tech , Organizer: Lutz Warnke
The original concept ofdimension for posets was formulatedby Dushnik and Miller in 1941 and hasbeen studied extensively in the literature.Over the years, a number of variant formsof dimension have been proposed withvarying degrees of interest and application.However, in the recent past, two variantshave received extensive attention.  Theyare Boolean dimension and local dimension.This is the first of two talks on these twoconcepts, with the second talk givenby Heather Smith.  In this talk, wewill introduce the two parameters and providemotivation for their study.  We will alsogive some concrete examples andprove some basic inequalities.This is joint work with a GeorgiaTech team in which my colleaguesare Fidel Barrera-Cruz, Tom Prag,Heather Smith and Libby Taylor.
Friday, September 15, 2017 - 15:00 , Location: Skiles 154 , Jiaqi Yang , Georgia Tech , Organizer: Jiaqi Yang
We will introduce Arnold diffusion in Mather's setting. There are many advances toward proof of this. In particular, we will study an approach based on recent work of Marian-Gidea and Jean-Pierre Marco.
Friday, September 15, 2017 - 13:55 , Location: Skiles 006 , Peter Lambert-Cole , Georgia Institute of Technology , Organizer: Peter Lambert-Cole
In this series of talks, I will introduce basic concepts and results in singularity theory of smooth and holomorphic maps.  In the first talk, I will present a gentle introduction to the elements of singularity theory and give a proof of the well-known Morse Lemma that illustrates key geometric and algebraic principles of singularity theory.
Friday, September 15, 2017 - 13:05 , Location: Skiles 005 , Peng Zhang , Computer Science, Georgia Tech , , Organizer: He Guo
In this talk, we study solvers for geometrically embedded graph structured block linear systems. The general form of such systems, PSD-Graph-Structured Block Matrices (PGSBM), arise in scientific computing, linear elasticity, the inner loop of interior point algorithms for linear programming, and can be viewed as extensions of graph Laplacians into multiple labels at each graph vertex. Linear elasticity problems, more commonly referred to as trusses, describe forces on a geometrically embedded object.We present an asymptotically faster algorithm for solving linear systems in well-shaped 3-D trusses. Our algorithm utilizes the geometric structures to combine nested dissection and support theory, which are both well studied techniques for solving linear systems. We decompose a well-shaped 3-D truss into balanced regions with small boundaries, run Gaussian elimination to eliminate the interior vertices, and then solve the remaining linear system by preconditioning with the boundaries.On the other hand, we prove that the geometric structures are necessary for designing fast solvers. Specifically, solving linear systems in general trusses is as hard as solving general linear systems over the real. Furthermore, we give some other PGSBM linear systems for which fast solvers imply fast solvers for general linear systems.Based on the joint works with Robert Schwieterman and Rasmus Kyng.
Thursday, September 14, 2017 - 15:05 , Location: Skiles 006 , Gerandy Brito , Georgia Institute of Technology , , Organizer: Michael Damron
This talk concerns to spectral gap of random regular graphs. First, we prove that almost all bipartite biregular graphs are almost Ramanujan by providing a tight upper bound for the non trivial eigenvalues of its adjacency operator, proving Alon's Conjecture for this family of graphs. Also, we use a spectral algorithm to recover hidden communities in a random network model we call regular stochastic block model. Our proofs rely on a technique introduced recently by Massoullie, which we developed for random regular graphs.
Thursday, September 14, 2017 - 13:30 , Location: Skiles 005 , Shijie Xie , Math, GT , Organizer: Robin Thomas
Let G be a graph containing 5 different vertices a0, a1, a2, b1 and b2. We say that (G, a0, a1, a2, b1, b2) is feasible if G contains disjoint connected subgraphs G1, G2, such that {a0, a1, a2}⊆V(G1) and {b1, b2}⊆V(G2). In this talk, we will continue our discussion on the operations we use for characterizing feasible (G, a0, a1, a2, b1, b2). If time permits, we will also discuss useful structures for obtaining that characterization, such as frame, ideal frame, and framework. Joint work with Changong Li, Robin Thomas, and Xingxing Yu.
Wednesday, September 13, 2017 - 13:55 , Location: Skiles 005 , Michael Lacey , Georgia Tech , Organizer: Shahaf Nitzan
A sparse bound is a novel method to bound a bilinear form. Such a bound gives effortless weighted inequalities, which are also easy to quantify.  The range of forms which admit a sparse bound is broad.  This short survey of the subject will include the case of spherical averages, which has a remarkably easy proof.
Wednesday, September 13, 2017 - 13:55 , Location: Skiles 006 , Hyun Ki Min , Georgia Tech , Organizer: Jennifer Hom
The Weeks manifold W is a closed orientable hyperbolic 3-manifold with the smallest volume. Understanding contact structures on hyperbolic 3-manifolds is one of problems in contact topology. Stipsicz previously showed that there are 4 non-isotopic tight contact structures on the Weeks manifold. In this talk, we will exhibit 7 non-isotopic tight contact structures on W with non-vanishing Ozsvath-Szabo invariants.