Seminars and Colloquia Schedule

Effective equidistribution of horocycle maps

Series
CDSNS Colloquium
Time
Monday, November 16, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
James Tanis – College de France
We prove results concerning the equidistribution of some "sparse" subsets of orbits of horocycle flows on $SL(2, R)$ mod lattice. As a consequence of our analysis, we recover the best known rate of growth of Fourier coefficients of cusp forms for arbitrary noncompact lattices of $SL(2, R)$, up to a logarithmic factor. This talk addresses joint work with Livio Flaminio, Giovanni Forni and Pankaj Vishe.

Trisecting Smooth 4-manifolds with Boundary

Series
Geometry Topology Seminar
Time
Monday, November 16, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nick Castro – University of Georgia
A trisection of a smooth, oriented, compact 4-manifold X is a decomposition into three diffeomorphic 4-dimensional 1-handlebodies with certain nice intersections properties. This is a very natural 4-dimensional analog of Heegaard splittings of 3-manifolds. In this talk I will define trisections of closed 4-manifolds, but will quickly move to the case of 4-manifolds with connected boundary. I will discuss how these "relative trisections" interact with open book decompositions on the bounding 3-manifold. Finally, I will discuss a gluing theorem which allows us to glue together relative trisections to induce a trisection on a closed 4-manifold.

Stochastic models of collective motion

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 16, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gil Ariel – Bar-Ilan University
Collective movement is one of the most prevailing observations in nature. Yet, despite considerable progress, many of the theoretical principles underlying the emergence of large scale synchronization among moving individuals are still poorly understood. For example, a key question in the study of animal motion is how the details of locomotion, interaction between individuals and the environment contribute to the macroscopic dynamics of the hoard, flock or swarm. The talk will present some of the prevailing models for swarming and collective motion with emphasis on stochastic descriptions. The goal is to identify some generic characteristics regarding the build-up and maintenance of collective order in swarms. In particular, whether order and disorder correspond to different phases, requiring external environmental changes to induce a transition, or rather meta-stable states of the dynamics, suggesting that the emergence of order is kinetic. Different aspects of the phenomenon will be presented, from experiments with locusts to our own attempts towards a statistical physics of collective motion.

Secants of the Veronese and the Determinant

Series
Algebra Seminar
Time
Monday, November 16, 2015 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Cameron Farnsworth – Texas A&M –
Let det_n be the homogeneous polynomial obtained by taking the determinant of an n x n matrix of indeterminates. In this presentation linear maps called Young flattenings will be defined and will be used to show new lower bounds on the symmetric border rank of det_n.

Topological full groups

Series
Colloquia
Time
Tuesday, November 17, 2015 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Volodymyr Nekrashevych – Department of Mathematics, Texas A&M –

This talk should interest people in Algebra, Dynamical Systems and Mathematical Physics in addition to Geometry and Topology. Volodia Nekrashevych will visit Atlanta from Sunday November 15th evening until Tuesday November 17th afternoon. He will be available for private talks on Monday November 14th after noon or on Tueasday morning before 10AM. Contact him directly by email or contact <a href="mailto:jeanbel@math.gatech.edu">jeanbel@math.gatech.edu</a> to schedule a meeting or to have a dinner with him.

Topological full groups are naturally associated with semigroups of local homeomorphisms: iterations of a single homeomorphism, holonomy groupoids of laminations, groupoids of local isomorphisms of quasiperiodic sets (for example Penrose tilings), etc. Some of these groups have interesting properties from the point of view of group theory. For instance, they provide first examples of amenable infinite simple finitely generated groups (by a result of K. Juschenko and N. Monod) and first examples of simple amenable groups of Burnside type. The full group of the Penrose tiling is another interesting example from the point of view of amenability.

Random graph processes with dependencies

Series
Job Candidate Talk
Time
Tuesday, November 17, 2015 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lutz Warnke – University of Cambridge
Random graphs are the basic mathematical models for large-scale disordered networks in many different fields (e.g., physics, biology, sociology). Their systematic study was pioneered by Erdoes and Renyi around 1960, and one key feature of many classical models is that the edges appear independently. While this makes them amenable to a rigorous analysis, it is desirable (both mathematically and in terms of applications) to understand more complicated situations. In this talk I will discuss some of my work on so-called Achlioptas processes, which (i) are evolving random graph models with dependencies between the edges and (ii) give rise to more interesting percolation phase transition phenomena than the classical Erdoes-Renyi model.

Uniqueness and Finsler type optimal transport metric for nonlinear wave equations

Series
PDE Seminar
Time
Tuesday, November 17, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Geng Chen – School of Mathematics, Georgia Tech
In this talk, we will discuss a sequence of recent progresses on the global well-posedness of energy conservative Holder continuous weak solutions for a class of nonlinear variational wave equations and the Camassa-Holm equation, etc. A typical feature of solutions in these equations is the formation of cusp singularity and peaked soliton waves (peakons), even when initial data are smooth. The lack of Lipschitz continuity of solutions gives the major difficulty in studying the well-posedness and behaviors of solutions. Several collaboration works with Alberto Bressan will be discussed, including the uniqueness by characteristic method, Lipschitz continuous dependence on a Finsler type optimal transport metric and a generic regularity result using Thom's transversality theorem.

Almost-reducibility for fibered holomorphic dynamics

Series
Dynamical Systems Working Seminar
Time
Tuesday, November 17, 2015 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mikel Viana – Georgia Tech (Math)
In previous talks, we discussed an algorithm (Nash-Moser iteration) to compute invariant whiskered tori for fibered holomorphic maps. Several geometric and number-theoretic conditions are necessary to carry out each step of the iteration. Recently, there has been interest in studying what happens if some of the conditions are removed. In particular, the second Melnikov condition we found can be hard to verify in higher dimensional problems. In this talk, we will use a method due to Eliasson, Moser and Poschel to obtain quasi-periodic solutions which, however, lose an important geometric property relative to the solutions previously constructed.

How Geometry plays a role in Industry

Series
Research Horizons Seminar
Time
Wednesday, November 18, 2015 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dr. Jesse Johnson – Google Company

Food and Drinks will be provided before the seminar.

In this talk, we will discuss: (1) How geometry plays a role in machine learning/data science? (2) What it's like being a mathematician at a software company.

Fourier restriction to degenerate manifolds

Series
Analysis Seminar
Time
Wednesday, November 18, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Betsy Stovall – UW-Madison
We will discuss the problem of restricting the Fourier transform to manifolds for which the curvature vanishes on some nonempty set. We will give background and discuss the problem in general terms, and then outline a proof of an essentially optimal (albeit conditional) result for a special class of hypersurfaces.

Random matrix, concentration and almost sure convergence of the distribution of eigenvalues

Series
Regular Seminars
Time
Wednesday, November 18, 2015 - 17:00 for 1 hour (actually 50 minutes)
Location
Skies 169
Speaker
Inoel Popescu – Georgia Tech
We will summarize what we did so far in this sequence of seminars, among other things, the convergence of eigenvalues of Wigner random matrices and also GUE in expectation. This time we will explore concentration inequalities and use these to go from the convergence in expectation to convergence almost surely.

Thin Position for Knots and Topological Data Analysis

Series
School of Mathematics Colloquium
Time
Thursday, November 19, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jesse Johnson – Google
Topological data analysis is the study of Machine Learning/Data Mining problems using techniques from geometry and topology. In this talk, I will discuss how the scale of modern data analysis has made the geometric/topological perspective particularly relevant for these subjects. I'll then introduce an approach to the clustering problem inspired by a tool from knot theory called thin position.

Convergence of the extremal eigenvalues of empirical covariance matrices with dependence

Series
Stochastics Seminar
Time
Thursday, November 19, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Konstantin Tikhomirov – University of Alberta
Consider a sample of a centered random vector with unit covariance matrix. We show that under certain regularity assumptions, and up to a natural scaling, the smallest and the largest eigenvalues of the empirical covariance matrix converge, when the dimension and the sample size both tend to infinity, to the left and right edges of the Marchenko-Pastur distribution. The assumptions are related to tails of norms of orthogonal projections. They cover isotropic log-concave random vectors as well as random vectors with i.i.d. coordinates with almost optimal moment conditions. The method is a refinement of the rank one update approach used by Srivastava and Vershynin to produce non-asymptotic quantitative estimates. In other words we provide a new proof of the Bai and Yin theorem using basic tools from probability theory and linear algebra, together with a new extension of this theorem to random matrices with dependent entries. Based on joint work with Djalil Chafai.

Mixed norm Leibnitz rules via multilinear operator valued multipliers

Series
Analysis Seminar
Time
Thursday, November 19, 2015 - 16:35 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Francesco Di Plinio – Brown University –
[Special time and location] The content of this talk is joint work with Yumeng Ou. We describe a novel framework for the he analysis of multilinear singular integrals acting on Banach-valued functions.Our main result is a Coifman-Meyer type theorem for operator-valued multilinear multipliers acting on suitable tuples of UMD spaces, including, in particular, noncommutative Lp spaces. A concrete case of our result is a multilinear generalization of Weis' operator-valued Hormander-Mihlin linear multiplier theorem.Furthermore, we derive from our main result a wide range of mixed Lp-norm estimates for multi-parameter multilinear multiplier operators, as well as for the more singular tensor products of a one-parameter Coifman-Meyer multiplier with a bilinear Hilbert transform. These respectively extend the results of Muscalu et. al. and of Silva to the mixed norm case and provide new mixed norm fractional Leibnitz rules.

Bootstrap confidence sets under model misspecification

Series
Job Candidate Talk
Time
Friday, November 20, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mayya Zhilova – Weierstrass Institute
Bootstrap is one of the most powerful and common tools in statistical inference. In this talk a multiplier bootstrap procedure is considered for construction of likelihood-based confidence sets. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension p: the bootstrap approximation works if p^3/n is small, where n is a sample size. The main result about bootstrap validity continues to apply even if the underlying parametric model is misspecified under a so-called small modelling bias condition. In the case when the true model deviates significantly from the considered parametric family, the bootstrap procedure is still applicable but it becomes conservative: the size of the constructed confidence sets is increased by the modelling bias. The approach is also extended to the problem of simultaneous confidence estimation. A simultaneous multiplier bootstrap procedure is justified for the case of exponentially large number of models. Numerical experiments for misspecified regression models nicely confirm our theoretical results.

A Market for Scheduling, with Applications to Cloud Computing

Series
ACO Student Seminar
Time
Friday, November 20, 2015 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sadra Yazdanbod – Georgia Tech
We present a market for allocating and scheduling resources to agents who have specified budgets and need to complete specific tasks. Two important aspects required in this market are: (1) agents need specific amounts of each resource to complete their tasks, and (2) agents would like to complete their tasks as soon as possible. In incorporating these aspects, we arrive at a model that deviates substantially from market models studied so far in economics and theoretical computer science. Indeed, all known techniques developed to compute equilibria in markets in the last decade and half seem not to apply here.We give a polynomial time algorithm for computing an equilibrium using a new technique that is somewhat reminiscent of the ''ironing" procedure used in the characterization of optimal auctions by Myerson. This is inspite of the fact that the set of equilibrium prices could be non-convex; in fact it could have ''holes''. Our market model is motivated by the cloud computing marketplace. Even though this market is already huge and is projected to grow at a massive rate, it is currently run in an ad hoc manner.Joint work with: Nikhil Devanur, Jugal Garg, Ruta Mehta, Vijay V. Vazirani

Concentration of Stationary Measures

Series
CDSNS Colloquium
Time
Friday, November 20, 2015 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yingfei Yi – University of Alberta &amp;amp; Georgia Tech
The talk concerns limit behaviors of stationary measures of diffusion processes generated from white-noise perturbed systems of ordinary differential equations. By relaxing the notion of Lyapunov functions associated with the stationary Fokker-Planck equations, new existence and non-existence results of stationary measures will be presented. As noises vanish, concentration and limit behaviors of stationary measures will be described with particular attentions paying to the special role played by multiplicative noises. Connections to problems such as stochastic stability, stochastic bifurcations, and thermodynamics limits will also be discussed.

Counting Single Cut-or-Join Scenarios

Series
Combinatorics Seminar
Time
Friday, November 20, 2015 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Heather Smith – Georgia Tech –
Represent a genome with an edge-labelled, directed graph having maximum total degree two. We explore a number of questions regarding genome rearrangement, a common mode of molecular evolution. In the single cut-or-join model for genome rearrangement, a genome can mutate in one of two ways at any given time: a cut divides a degree two vertex into two degree one vertices while a join merges two degree one vertices into one degree two vertex. Fix a set of genomes, each having the same set of edge labels. The number of ways for one genome to mutate into another can be computed in polynomial time. The number of medians can also be computed in polynomial time. While single cut-or-join is, computationally, the simplest mathematical model for genome rearrangement, determining the number of most parsimonious median scenarios remains #P-complete. We will discuss these and other complexity results that arose from an abstraction of this problem. [This is joint work with Istvan Miklos.]