All Seminars

Title: The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds
Seminar: Analysis and Differential Geometry
Speaker: Professor Lei Zhang of Univ. of Alabama at Birmingham
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2009-02-17 at 4:00PM
Venue: MSC W301
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Abstract:
Abstract. We study a class of fourth order geometric equations defined on a 4-dimensional compact Riemannian manifold which includes the Q-curvature equation. We obtain sharp estimates on the difference near the blow-up points between a bubbling sequence of solutions and the standard bubble.
Title: Arithmetic of del Pezzo surfaces of degree 1
Colloquium: N16
Speaker: Tony Varilly of The University of California, Berkeley
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2009-02-13 at 4:00PM
Venue: W306
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Abstract:
I will discuss some of the driving questions in the area of Rational points on algebraic varieties (these can be thought of as solutions over fields of number-theoretic interest to systems of homogeneous polynomial equations). I will focus on the case of smooth rational surfaces, and discuss some results concerning the arithmetic of del Pezzo surfaces of degree 1. I will also explain how these results complete a qualitative picture of basic arithmetic phenomena among smooth rational surfaces. Along the way I will go over concepts like weak approximation and the computation of Brauer-Manin obstructions; I will not assume previous knowledge of them.
Title: Negative Correlation Inequalities
Colloquium: N16
Speaker: Mike Neiman of Rutgers University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2009-02-11 at 3:00PM
Venue: MSC W303
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Abstract:
Correlation inequalities are statements about how events in a probability space positively or negatively reinforce each other. After briefly discussing the better-understood theory of positive correlation, I will talk about some negative correlation inequalities and their relationship to celebrated conjectures of J. Mason about log-concavity properties of certain sequences arising from combinatorial objects. Along the way, I'll mention several interesting open problems.
Title: Number Theory and a Lower Bound for Closed Geodesics, Part 2
Seminar: Topology
Speaker: Sean Thomas of
Contact: Emily Hamilton, emh@mathcs.emory.edu
Date: 2009-02-10 at 3:00PM
Venue: MSC E406
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Abstract:
Lehmer's conjecture (1933) states that the Mahler measure of an algebraic number that is not a root of unity is bounded away from 1. The aim of the seminar is to show the conjecture would imply there is a positive lower bound for closed geodesics in compact arithmetic hyperbolic 3-manifolds of finite volume. In the first lecture, I will introduce the necessary background material on arithmetic hyperbolic 3-manifolds. Then, in the second lecture, I will show how Lehmer's conjecture would imply the existence of the aforementioned positive lower bound. Also, I will prove the existence of a positive lower bound for closed geodesics in non-compact arithmetic hyperbolic 3-manifolds of finite volume to fully address the topic.
Title: Number Theory and a Lower Bound for Closed Geodesics
Seminar: Topology
Speaker: Sean Thomas of Emory University
Contact: Sean Thomas, sean.thomas@emory.edu
Date: 2009-02-03 at 3:00PM
Venue: MSC E406
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Abstract:
Lehmer's conjecture (1933) states that the Mahler measure of an algebraic number that is not a root of unity is bounded away from 1. The aim of the seminar is to show the conjecture would imply there is a positive lower bound for closed geodesics in compact arithmetic hyperbolic 3-manifolds of finite volume. In the first lecture, I will introduce the necessary background material on arithmetic hyperbolic 3-manifolds. Then, in the second lecture, I will show how Lehmer's conjecture would imply the existence of the aforementioned positive lower bound. Also, I will prove the existence of a positive lower bound for closed geodesics in non-compact arithmetic hyperbolic 3-manifolds of finite volume to fully address the topic.
Title: Quasiconformal mappings and some extremal problems
Seminar: Analysis and Differential Geometry
Speaker: Professor Zemin Zhou of Renmin University of China
Contact: Shanshuang Yang, syang@mathcs.emory.edu
Date: 2009-02-03 at 4:00PM
Venue: MSC W301
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Abstract:
In this talk we will present some progress on several extremal problems related to quasiconformal mappings and Beltrami coefficients on the unit disk.
Title: A Parameter Decomposition Scheme for Iteratively Regularized Gauss-Newton
Type: AWM Event
Speaker: Dr. Alexandra Smirnova of Georgia State University
Contact: Kinnari Amin, kinnari.amin@emory.edu
Date: 2008-12-08 at 4:00PM
Venue: MSC W301
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Abstract:
A new convergence result for an Iteratively Regularized Gauss Newton (IRGN) algorithm with a Tikhonov regularization term using a seminorm generated by a linear operator will be presented [SRK07]. The convergence theorem uses an a posteriori stopping rule and a modified source condition, without any restriction on the nonlinearity of the operator. The theoretical results are illustrated by simulations for a 2D version of the exponentially ill-posed optical tomography inverse problem for the diffusion and absorption coefficient spatial distributions. The modified Tikhonov regularization performs the mapping of the minimization variables, which are the coefficients of the spline expansions for the diffusion and absorption, to physical space. This incorporates the inherently differing scales of these variables in the minimization, and also suggests relative weighting of the regularization terms with respect to each parameter space. The modified IRGN allows greater flexibility for implementations of iteratively regularized solutions of ill-posed inverse problems in which differing scales in physical space hinder standard IRGN inversions.
Title: Sentry Selection
Seminar: Combinatorics
Speaker: Paul Balister of University of Memphis
Contact: Michal Karonski, michal@mathcs.emory.edu
Date: 2008-12-05 at 4:00PM
Venue: W306
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Abstract:
Suppose we have a collection of sensors in a large region, each of which can detect events within a disk of radius 1. We wish to devise a schedule so that each sensor can sleep for much of the time, while making sure that the whole region is covered by the sensors that are awake. A natural way of doing this is to partition the sensors into k subsets, each subset of sensors covering the whole region. Then in time slot t we activate all the sensors in subset (t mod k). If this is possible we say the sensors are k-partitionable. An obvious necessary condition is that each point in the region is covered by at least k sensors (k-coverage), but this is not in general sufficient. We show that for random deployments of sensors k-coverage usually implies k-partitionability, and identify the most likely obstructions to k-partitionability when this fails. This leads to some natural unsolved problems involving k-partitionability of (deterministic) configurations of disks. This is joint work with B. Bollobas, A. Sarkar, and M. Walters.
Title: Sign Pattern Matrices
Seminar: Numerical Analysis and Scientific Computing
Speaker: Dr. Zhongshan Li of Georgia State University, Dept. of Mathematics & Statistics
Contact: Raya Horesh, rshindm@emory.edu
Date: 2008-12-03 at 3:00PM
Venue: W304
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Abstract:
Title: Invariants of orthogonal involutions
Seminar: Algebra
Speaker: Jean-Pierre Tignol of Universite catholique de Louvain, Belgium
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2008-11-25 at 4:00PM
Venue: MSC W303
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Abstract:
For central simple algebras of even degree with orthogonal involutions, invariants modeled on the discriminant and Clifford algebra of quadratic forms were defined by Jacobson and Tits, and a relative cohomological invariant of degree 3 is defined by using the Rost invariant of Spin groups when the first two invariants vanish. Its properties and computation will be discussed in the particular case where the algebra has degree 8 and index 4, in relation with properties of 8-dimensional quadratic forms in $I^2$. (Joint work with Anne Qu\'eguiner-Mathieu).