All Seminars

Title: Characterization of Quasiconformal Mapping and Extremal Length Decomposition and Its Application
Defense: Dissertation
Speaker: Wenfei Zou of Emory University
Contact: Wenfei Zou, wzou3@emory.edu
Date: 2013-11-12 at 4:00PM
Venue: W302
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Abstract:
My defense includes two parts. The first part is about the characterization of Quasiconformal mapping. It is known that Conformal mapping preserves the measure of angle. The Quasiconformal mapping is a natural generalization of the conformal mapping. Some measure of angle named topological angle could be defined to characterize Quasiconformal mappings. I will discuss these results in higher dimensional Euclidean space.\\ \\ The second part is about extremal length decomposition and its application. Quasiextremal distance domains (QED) are a class of domains introduced by Gehring and Martio in connection with Quasiconformal mapping theories. I will discuss a decomposition theorem about the extremal length of a curve family within the finitely connected QED domain. Moreover, I will discuss its application, a result of sharp upper bound for QED constant of finitely connected domain on the complex plane.
Title: SOUTHEAST GEOMETRY SEMINAR (SGS XXIII)
Type: N/A
Speaker: . of .
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2013-11-10 at 8:00AM
Venue: MSC W201
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Abstract:
Title: Thresholds for Random Geometric k-SAT
Seminar: Combinatorics
Speaker: Will Perkins of Georgia Tech
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2013-11-08 at 4:00PM
Venue: W306
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Abstract:
Random $k-SAT$ is a distribution over boolean formulas studied widely in combinatorics, statistical physics, and theoretical computer science for its intriguing behavior at its phase transition. I will present results on the satisfiability threshold in a geometric model of random $k-SAT$: labeled boolean literals are placed uniformly at random in a d-dimensional cube, and for each set of k contained in a ball of radius r, a k-clause is added to the random formula. For all $k$ we show that the satisfiability threshold is sharp, and for $k=2$ we find the location of the threshold as well. I will also discuss connections between this model and the random geometric graph.
Title: Regularization by Krylov Subspace Methods
Seminar: Numerical Analysis and Scientific Computing
Speaker: Silvia Gazzola of University of Padova
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2013-11-01 at 12:00PM
Venue: W302
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Abstract:
Iterative methods have always played a central role in the regularization of large-scale linear discrete ill-posed problems. These kind of problems arise in a variety of scientific and engineering applications: we are particularly interested in the image deblurring and denoising issues. Historically, the first Krylov subspace methods to be extensively used with regularization purposes were the CGLS and the LSQR methods. In the last three decades, many other Krylov subspace methods have been analyzed and employed to solve linear discrete ill-posed problems and, very recently, some modifications of the usually involved Krylov subspaces have been proposed: we cite the smoothing preconditioning, the augmentation, and the range-restricted techniques. In addition to a purely iterative approach to regularization, some hybrid methods have also been derived: hybrid methods merge an iterative and a variational (Tikhonov-like) approach to regularization. The purpose of this talk is to survey some classical iterative regularization methods and to present some original ones, comparing their performance on some meaningful test problems. Particular emphasis will be posed on the hybrid methods and on the strategies to be employed to set the regularization parameters.
Title: Some problems in Anti-Ramsey Theory
Seminar: Combinatorics
Speaker: Sogol Jahanbekam of The University of Colorado, Denver
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2013-11-01 at 4:00PM
Venue: W306
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Abstract:
In this talk we introduce some new lower bounds for the matching number of bipartite graphs and general graphs. We apply these results to Anti-Ramsey numbers of some families of graphs including disjoint spanning disjoint spanning cycles, disjoint perfect matchings, and graphs with bounded diameter.
Title: Progressions with a pseudorandom step
Seminar: Combinatorics
Speaker: Elad Aigner-Horev of Hamburg University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2013-10-28 at 4:00PM
Venue: MSC W301
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Abstract:
An open problem of interest in combinatorial number theory is that of providing a non-ergodic proof to the so called polynomial Szemerédi theorem. So far, the landmark result in this venue is that of Green who considered the emergence of 3-term arithmetic progressions whose gap is a sum of two squares (not both zero) in dense sets of integers. In view of this we consider the following problem. Given two dense subsets A and S of a finite abelian group G, what is the weakest "pseudorandomness assumption" which, once put on S, implies that A contains a 3-term arithmetic progression whose gap is in S? We answer this question for $G = Z_n$ and $G = F_p^n$. To quantify pseudorandomness we use Gowers norms.
Title: Numerical Tilting and Derived Equivalence
Seminar: Algebra
Speaker: Morgan Brown of University of Michigan
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2013-10-23 at 4:00PM
Venue: W306
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Abstract:
The derived category of an algebraic variety is a categorical invariant which is coarser than the category of coherent sheaves. There are many interesting examples in geometry and representation theory of varieties or algebras with different categories of sheaves or modules but equivalent derived categories. For example, if $G$ is a finite subgroup of $SL(3, \mathbb{C})$, Bridgeland, King, and Reid showed there is a derived equivalence between $G$ equivariant sheaves on $\mathbb{C}^3$ and sheaves on a minimal resolution of the quotient. I will show how in many cases one can understand these equivalences by factoring them into simple equivalences called tilts.
Title: CANCELED
Seminar: Algebra
Speaker: Eva Bayer-Fluckiger of EPFL
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2013-10-23 at 5:00PM
Venue: W306
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Abstract:
This is a joint work with Tingyu Lee and Parimala. Let k be a global field of characteristic not 2, let E be an etale k-algebra with involution, and let q be a quadratic space over k. The aim of this talk is to give necessary and sufficient conditions for the orthogonal group O(q) to contain a maximal torus of type E.
Title: Characterization of Quasiconformal mapping, and extremal length decomposition and upper bound of QED constant for finitely connected domains
Seminar: Analysis and Differential Geometry
Speaker: Wenfei Zou of Emory University
Contact: Wenfei Zou, wzou3@emory.edu
Date: 2013-10-22 at 4:00PM
Venue: W302
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Abstract:
The talk includes two parts. For the first part, it is known that Conformal mapping preserves the measure of angle. The Quasiconformal mapping is a natural generalization of the conformal mapping. Some measure of angle named topological angle can be defined to characterize Quasiconformal mappings. I will discuss these results in higher dimension. For the second part, quasiextremal distance domains (QED) are a class of domains introduced by Gehring and Martio in connection with Quasiconformal mapping theories. I will discuss a decomposition theorem about the extremal length of a curve family within the finitely connected QED domain. Moreover, I will discuss the result of sharp upper bound for QED constant of finitely connected domain on the complex plane.
Title: On the arithmetic of surfaces
Seminar: Algebra
Speaker: Yuri Tschinkel of Courant Institute
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2013-10-18 at 10:00AM
Venue: W304
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Abstract:
I will discuss new geometric constructions arising in the study of rational points on algebraic surfaces over global fields (joint with B. Hassett).