Seminars and Colloquia by Series

Systems Biology of Epidemiology: From Genes to Environment

Series
Mathematical Biology Seminar
Time
Wednesday, March 5, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Juan Gutierrez – UGA –
The traditional epidemiological approach to characterize transmission of infectious disease consists of compartmentalizing hosts into susceptible, exposed, infected, recovered (SEIR), and vectors into susceptible, exposed and infected (SEI), and variations of this paradigm (e.g. SIR, SIR/SI, etc.). Compartmentalized models are based on a series of simplifying assumptions and have been successfully used to study a broad range of disease transmission dynamics. These paradigm is challenged when the within-host dynamics of disease is taken into account with aspects such as: (i) Simultaneous Infection: An infection can include the simultaneous presence of several distinct pathogen genomes, from the same or multiple species, thus an individual might belong to multiple compartments simultaneously. This precludes the traditional calculation of the basic reproductive number. (ii) Antigenic diversity and variation: Antigenic diversity, defined as antigenic differences between pathogens in a population, and antigenic variation, defined as the ability of a pathogen to change antigens presented to the immune system during an infection, are central to the pathogen's ability to 1) infect previously exposed hosts, and 2) maintain a long-term infection in the face of the host immune response. Immune evasion facilitated by this variability is a critical factor in the dynamics of pathogen growth, and therefore, transmission.This talk explores an alternate mechanistic formulation of epidemiological dynamics based upon studying the influence of within-host dynamics in environmental transmission. A basic propagation number is calculated that could guide public health policy.

GLOBAL SMOOTH SOLUTIONS IN R^3 TO SHORT WAVE-LONG WAVE INTERACTIONS SYSTEMS FOR VISCOUS COMPRESSIBLE FLUIDS

Series
PDE Seminar
Time
Tuesday, March 4, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hermano Frid – IMPA, Brazil
The short wave-long wave interactions for viscous compressibleheat conductive fluids is modeled, following Dias & Frid (2011), by a Benney-type system coupling Navier-Stokes equations with a nonlinear Schrodingerequation along particle paths. We study the global existence of smooth solutions to the Cauchy problem in R^3 when the initial data are small smooth perturbations of an equilibrium state. This is a joint work with Ronghua Panand Weizhe Zhang.

Algebraic Geometry and Computer Vision

Series
Algebra Seminar
Time
Monday, March 3, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Luke Oeding – Auburn University
In Computer Vision and multi-view geometry one considers several cameras in general position as a collection of projection maps. One would like to understand how to reconstruct the 3-dimensional image from the 2-dimensional projections. [Hartley-Zisserman] (and others such as Alzati-Tortora and Papadopoulo-Faugeras) described several natural multi-linear (or tensorial) constraints which record certain relations between the cameras such as the epipolar, trifocal, and quadrifocal tensors. (Don't worry, the story stops at quadrifocal tensors!) A greater understanding of these tensors is needed for Computer Vision, and Algebraic Geometry and Representation Theory provide some answers.I will describe a uniform construction of the epipolar, trifocal and quadrifocal tensors via equivariant projections of a Grassmannian. Then I will use the beautiful Algebraic Geometry and Representation Theory, which naturally arrises in the construction, to recover some known information (such as symmetry and dimensions) and some new information (such as defining equations). Part of this work is joint with Chris Aholt (Microsoft).

Non-looseness of non-loose knots

Series
Geometry Topology Seminar
Time
Monday, March 3, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ken Baker – University of Miami
A contact structure on a 3-manifold is called overtwisted ifthere is a certain kind of embedded disk called an overtwisted disk; it istight if no such disk exists. A Legendrian knot in an overtwisted contact3-manifold is loose if its complement is overtwisted and non-loose if itscomplement is tight. We define and compare two geometric invariants, depthand tension, that measure how far from loose is a non-loose knot. This isjoint work with Sinem Onaran.

A multiscale computation for highly oscillatory dynamical systems using two approaches

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 3, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Seong Jun Kim – GT Math
In this talk, the two approaches for computing the long time behavior of highly oscillatory dynamical systems will be introduced. Firstly, a generalization of the backward-forward HMM (BF HMM) will be discussed. It is intended to deal with the multiple time scale (>2) behavior of certain nonlinear systems where the non-linearity is introduced as a perturbation to a primarily linear problem. Focusing on the Fermi-Pasta-Ulam problem, I propose a three-scale version of the BF HMM. Secondly, I will consider a multiscale method using a signal processingidea. The dynamics on the slow time scale can be approximated by an averaged system gained by fltering out the fast oscillations. An Adaptive Local Iterative Filtering (ALIF) algorithm is used to do such averaging with respect to fast oscillations.

Component games on the Erdos--Renyi random graph

Series
Combinatorics Seminar
Time
Friday, February 28, 2014 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rani Hod – Georgia Tech
We discuss the Maker-Breaker component game, played on the edge set of a sparse random graph. Given a graph G and positive integers s and b, the s-component (1:b) game is defined as follows. In every round Maker claims one free edge of G and Breaker claims b free edges. Maker wins this game if her graph contains a connected component of size at least s; otherwise, Breaker wins the game. For the Erdos-Renyi graph G(n,p), we show that the maximum component size achievable by Maker undergoes a phase transition around p = lambda_{b+2}/n, where lambda_k is the threshold for the appearance of a non-empty k-core in G(n,p) To this end, we analyze the stabilization time of the k-core process in G(n,p). Joint work with Michael Krivelevich, Tobias Mueller, Alon Naor, and Nicholas Wormald.

Asymptotics of spectral projectors of sample covariance

Series
Stochastics Seminar
Time
Thursday, February 27, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Vladimir Koltchinskii – Gatech
Several new results on asymptotic normality and other asymptotic properties of sample covariance operators for Gaussian observations in a high-dimensional setting will be discussed. Such asymptotics are of importance in various problems of high-dimensional statistics (in particular, related to principal component analysis). The proofs of these results rely on Gaussian concentration inequality. This is a joint work with Karim Lounici.

Packing disjoint A-paths with specified endpoints

Series
Graph Theory Seminar
Time
Thursday, February 27, 2014 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Paul Wollan – University of Rome "La Sapienza"
Consider a graph G and a specified subset A of vertices. An A-path is a path with both ends in A and no internal vertex in A. Gallai showed that there exists a min-max formula for the maximum number of pairwise disjoint A-paths. More recent work has extended this result, considering disjoint A-paths which satisfy various additional properties. We consider the following model. We are given a list of {(s_i, t_i): 0< i < k} of pairs of vertices in A, consider the question of whether there exist many pairwise disjoint A-paths P_1,..., P_t such that for all j, the ends of P_j are equal to s_i and t_i for some value i. This generalizes the disjoint paths problem and is NP-hard if k is not fixed. Thus, we cannot hope for an exact min-max theorem. We further restrict the question, and ask if there either exist t pairwise disjoint such A-paths or alternatively, a bounded set of f(t) vertices intersecting all such paths. In general, there exist examples where no such function f(t) exists; we present an exact characterization of when such a function exists. This is joint work with Daniel Marx.

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