All Seminars

Title: Patching Brauer Groups
Seminar: Algebra
Speaker: Feng Chen of Emory University
Contact: Feng Chen (Emory), fchen@emory.edu
Date: 2009-03-31 at 4:00PM
Venue: MSC W303
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Abstract:
Title: Bidirectional Wave Propagation in the Human Arterial Tree
Seminar: Numerical Analysis and Scientific Computing
Speaker: Radu C. Cascaval of University of Colorado at Colorado Springs
Contact: Alessandro Veneziani, ale@mathcs.emory.edu
Date: 2009-03-27 at 3:00PM
Venue: MSC W303
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Abstract:
We describe a nonlinear model for the propagation of the pressure and flow velocity waves in the peripheral circulation, which is based on a Boussinesq-type system. The key ingredient is the inclusion of dispersive effects (amplitude-dependent speeds of propagation) in addition to the nonlinear effects. We discuss the formation and propagation of the transmitted and reflected waves at bifurcations and terminal ends. The timing of the reflections as well as the different speeds of the reflected waves are particularly relevant in view of the complex geometry of the peripheral circulation. The advantage of this analysis in the time domain, compared with linear impedance models, is that it applies for non-periodic flows and also allows the direct implementation of accurate time-dependent controls, such as those exhibited in the peripheral circulation. We discuss an application of this model on the study of the latencies measured experimentally during rest and dynamical changes in the cardiovascular system.
Title: Killing forms of Lie algebras
Dissertation defense: Algebra
Speaker: Audrey Malagon of Emory University
Contact: Skip Garibaldi, skip@mathcs.emory.edu
Date: 2009-03-25 at 4:00PM
Venue: MSC W201
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Abstract:
One approach to the problem of classifying Lie Algebras is to find invariants. One such invariant is the Killing form. In this talk I will give a formula for computing the Killing form of an isotropic Lie algebra defined over an arbitrary field of characteristic zero, based on the Killing form of a subalgebra containing its anisotropic kernel. I will then explicitly compute the Killing form for several Lie algebras of exceptional type and give a general formula for the Killing form of all inner type Lie algebras of type E6, including the anisotropic ones.
Title: Towards Contextual Text Mining
Seminar: Computer Science
Speaker: Qiaozhu Mei of University of Illinois at Urbana-Champaign
Contact: Eugene Agichtein, eugene@mathcs.emory.edu
Date: 2009-03-24 at 11:00AM
Venue: W302
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Abstract:
Text is generally associated with all kinds of contextual information. Contextual information can be explicit, such as the time and the location where a blog article is written, and the author(s) of a biomedical publication, or implicit, such as the positive or negative sentiment that an author had when he/she wrote a product review; there may also be complex context such as the social network of the authors. Many applications require analysis of patterns of topics over different contexts. For instance, analysis of search logs in the context of users can reveal how we can improve the quality of a search engine by optimizing the search results according to particular users, while analysis of text in the context of a social network can facilitate discovery of more meaningful topical communities. Since contextual information affects significantly the choices of topics and words made by authors, in general, it is very important to incorporate it in analyzing and mining text data. In this talk, I will present a new paradigm of text mining, called contextual text mining, where context is treated as a "first-class citizen." I will introduce general ways of modeling and analyzing various kinds of context in text, including simple context, implicit context, and complex context, in the framework of probabilistic language models. I will show the effectiveness of these general contextual text mining techniques with sample applications in web search and social network analysis. Biosketch: Qiaozhu Mei is a Ph.D. candidate of Department of Computer Science at the University of Illinois at Urbana-Champaign. He has broad research interests in text information management, especially text mining and information retrieval with probabilistic models. He has published extensively in these areas, and has received the Best Student Paper Runner-Up Awards of ACM KDD 2006 and ACM KDD 2007. He is also one of the five recipients of the inaugural Yahoo! Ph.D. Student Fellowship.
Title: Representation theory: a brief introduction from the sl(n) perspective
Seminar: Algebra
Speaker: Julie Beier of Mercer University
Contact: Skip Garibaldi, skip@mathcs.emory.edu
Date: 2009-03-24 at 3:00PM
Venue: MSC W303
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Abstract:
Representation theory can be simply defined as the study of the ways a group acts on a vector space. A large piece of this process involves understanding weight spaces, particularly irreducible highest weight spaces. We will explore weight spaces of irreducible representations by looking at $sl(n, \mathbf{C})$, $U_q(sl(n))$ and $U_q(\widehat{sl}(n))$. As the structure of the space becomes more complicated we utilize different combinatorics to understand these irreducible, highest weight spaces.
Title: Signal Processing Approach To Obtain A Direct Multi-grid Solver
Seminar: Numerical Analysis and Scientific Computing
Speaker: Pablo Navarrete of University of Chile, Department of Electrical Engineering
Contact: Jim Nagy, nagy@mathcs.emory.edu
Date: 2009-03-20 at 3:00PM
Venue: W306
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Abstract:
Modifications of the conventional muti-grid algorithm are explored to avoid the use of smoothing iterations. In the full multi-grid algorithm, classical smoothing iterations (e.g. Gauss-Seidel) reduce high-frequency components of the error and a coarse-grid approach reduces the low-frequency components of the error. The problem here is that two methods with different structures are being combined, which introduces additional complexity in the convergence analysis of multi-grid methods. Then, the idea is to avoid the use of smoothing iterations by using different inter-grid configurations. In an analogy with perfect reconstruction filters, a configuration of inter-grid operators is found such that the approximation error is completely cancelled after one iteration of the algorithm. The main assumption for this configuration to work is a particular aliasing pattern in the eigen-vectors of the linear system. Examples and simulations are presented to evaluate the performance of the new algorithm.
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.