All Seminars

Title: Regularity lemmas for (hyper)graphs
Colloquium: N/A
Speaker: Mathias Schacht of Humboldt University Berlin
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2009-03-20 at 3:45PM
Venue: MSC W303
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Abstract:
Szemeredi's regularity lemma is a powerful tool in extramal graph theory, which had have many applications. In this talk we present several variants of Szemeredi's original lemma (due to several researchers including Frieze and Kannan, Alon et al., and Lovasz and Szegedy) and discuss their relation to each other. If time permits we may consider several different looking regularity lemmas for hypergraphs of which some, but not all, turn out to be equivalent.
Title: Numerical Approaches for Large-Scale Ill-Posed Inverse Problems
Dissertation Defense: Numerical Analysis and Scientific Computing
Speaker: Julianne Chung of Emory University
Contact: Julianne Chung, jmchung@emory.edu
Date: 2009-03-19 at 4:00PM
Venue: MSC W303
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Abstract:
Ill-posed inverse problems arise in a variety of scientific applications. Regularization methods exist for computing stable solution approximations, but many of these methods are inadequate or insufficient for solving large-scale problems. This work addresses these limitations by developing advanced numerical methods to solve ill-posed inverse problems and by implementing high-performance parallel code for large-scale applications. Three mathematical models that frequently arise in imaging applications are considered: linear least squares, nonlinear least squares, and nonlinear Poisson maximum likelihood. Hybrid methods are developed for regularization of linear least squares problems, variable projection algorithms are used for nonlinear least squares problems, and reconstruction algorithms are investigated for nonlinear Poisson based models. Furthermore, an efficient parallel implementation based on the Message Passing Interface (MPI) library is described for use on state-of-the-art computer architectures. Numerical experiments illustrate the effectiveness and efficiency of the proposed methods on problems from image reconstruction, super-resolution imaging, cryo-electron microscopy reconstruction, and digital tomosynthesis.
Title: Rational points on varieties
Colloquium: N16
Speaker: Patrick Corn of St. Mary's College of Maryland
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2009-03-16 at 3:00PM
Venue: W306
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Abstract:
Solving Diophantine equations is a central question of number theory. In this talk we focus on several quite explicit examples of Diophantine equations having no nontrivial solutions, and explore various explanations of this phenomenon. In particular, we present some computational evidence that the Brauer-Manin obstruction is the only one for certain Del Pezzo surfaces, as well as an application of the Brauer-Manin obstruction to descent on genus-2 curves. (No prior knowledge of the definitions of the above terms will be assumed!)
Title: Minimal surfaces with an elastic boundary
Colloquium: N/A
Speaker: Professor Gilbert Weinstein of
Contact: Prof. Oliker, oliker@mathcs.emory.edu
Date: 2009-03-06 at 3:00PM
Venue: MSC W303
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Abstract:
I will describe a variational model combining energies in two different dimensions: surface tension, and 1-d elastic energy at the boundary. The model is motivated by findings in molecular dynamics simulations of HDL particle.
Title: Shaping your research so it can transition to practice: a view from data integration research
Seminar: Computer Science
Speaker: Arnon (Arnie) Rosenthal of MITRE
Contact: Li Xiong, lxiong@mathcs.emory.edu
Date: 2009-02-27 at 3:00PM
Venue: MSC W301
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Abstract:
Data integration technology aims to transform data from the providers’ form to a form consumers can use, and also to merge data from multiple providers. Relevant theory and algorithms appeared as early as the 1980s, but until very recently the transition to products was highly disappointing After an introduction to the challenges of data integration, we examine research areas whose results were difficult to transfer. From these, we identify two generic tactics for formulating good research problems whose theoretical results will also be exploitable by product planners and by development teams. First, if you have a theoretical results that applies to constrained, simplified problems, extend it to be /somewhat /useful on systems that violate the constraint. Second, work “downstream” first – tackle the last challenge that blocks creating runnable code with large user bases – otherwise your results may stay on the shelf for decades (e.g., schema matching circa 1985-2008). Finally, we will examine how well research has aligned with needs (i.e., areas desperately needing models and technique to clarify them. While there has been some terrific (and terrifically useful) recent research on data integration (e.g., {IBM, Microsoft, Google} Research), we will describe our pain points – terrifically important challenges for tractable research problems have not yet been formulated (let alone solved).
Title: Sage -- Creating a Viable Free Open Source Alternative to Magma, Maple, Mathematica, and Matlab
Colloquium: N16
Speaker: William Stein of University of Washington
Contact: David Borthwick, davidb@mathcs.emory.edu
Date: 2009-02-27 at 4:00PM
Venue: MSC W201
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Abstract:
Do you currently run Magma, Maple, Mathematica, or Matlab? In this talk, I will take an in-depth look at Sage, which is a free open source mathematics software project that I started in 2005. Sage can be used to study general and advanced, pure and applied mathematics. This includes a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra and much more. It combines various software packages and seamlessly integrates their functionality into a common experience. It is well suited for education, studying and research.
Title: GL(n) Representations - Yeah Schur.
Seminar: Algebra
Speaker: Georgia Benkart of University of Wisconsin
Contact: Audrey Malagon, amalago@emory.edu
Date: 2009-02-26 at 4:00PM
Venue: MSC W303
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Abstract:
By exploiting the commuting actions of the general linear and symmetric groups, Schur was able to prove combinatorial results about such things as symmetric functions and invariants. These methods work in a variety of settings and reveal beautiful connections with diagram algebras and walks on Dynkin diagrams.
Title: Turan theorem: generalizations and applications
Colloquium: Combinatorics
Speaker: Benjamin Sudakov of UCLA
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2009-02-25 at 3:00PM
Venue: MSC W303
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Abstract:
In typical extremal problem one wants to determine maximum cardinality of discrete structure with certain prescribed properties. Probably the earliest such result was obtain 100 years ago by Mantel who computed the maximum number of edges in a triangle free graph on n vertices. This was generalized by Turan for all complete graphs and became a starting point of Extremal Graph Theory. In this talk we survey several classical problems and results in this area and present some interesting applications of Extremal Graph Theory to other areas of mathematics. We also describe a recent surprising generalization of Turan's theorem which was motivated by question in Computational Complexity.
Title: Travels to a Hyperbolic Space Starting from an sl(2) Base
Colloquium: Algebra
Speaker: Georgia Benkart of University of Wisconsin
Contact: Audrey Malagon, amalago@emory.edu
Date: 2009-02-25 at 4:00PM
Venue: MSC W201
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Abstract:
By choosing a suitable basis of the Lie algebra sl(2) of 2 x 2 matrices of trace 0, connections with the modular group, the braid group on 3 strands, Tits buildings, and hyperbolic space become readily apparent. This talk will be a trip through these topics.
Title: On the complexity of factoring polynomials over finite fields
Colloquium: N16
Speaker: Kiran Kedlaya of
Contact: Aaron Abrams, abrams@mathcs.emory.edu
Date: 2009-02-24 at 4:00PM
Venue: MSC W201
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Abstract:
Abstract: While factoring large polynomials over finite fields is (apparently) far easier than factoring large integers, it is still an open problem to give an algorithm that does it ``as fast as possible'' (roughly speaking, in time proportional to the length of the input data). We will explain a recent improvement in the complexity of factoring polynomials over finite fields, based on an asymptotically optimal solution of a related problem (the modular composition problem). Joint work with Chris Umans (Caltech).