All Seminars

Title: Modern Krylov Subspace Methods (and applications to Parabolic Control Problems)
Seminar: Numerical Analysis and Scientific Computing
Speaker: Daniel B. Szyld of Temple University
Contact: Dr. Michele Benzi, benzi@mathcs.emory.edu
Date: 2012-11-08 at 4:00PM
Venue: MSC W201
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Abstract:
In many circumstances, a known good preconditioner is not easily computable. Instead, an approximation to it is available. This is the case, for example, when the preconditioner has an inverse associated with it, such as in Schur complements (e.g., in saddle point problems), or in the reduced Hessian in some control problems. The application of the preconditioner implies then an iterative solution of a linear system. In these cases, the question is: how accurately to solve the (inner) iteration? In our work on Inexact Krylov methods, we have shown that the inner iterations can be solved progressively less accurately, as the underlying Krylov method (e.g., GMRES) converges to the overall solution. Computable inner stopping criteria were developed to guarantee convergence of the overall method. We discuss these criteria, and illustrate its application to several problems. In particular, we apply these ideas to parabolic control problems, where the reduced Hessian contains two different inverses, and thus two inner iteration criteria are needed. Truncated methods are also discussed.
Title: Minimal Free Resolutions of the toppling ideal of a graph and its initial ideal
Seminar: Algebra and Number Theory Seminar
Speaker: Madhusudan Manjunath of Georgia Tech
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-11-07 at 4:00PM
Venue: W306
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Abstract:
We describe minimal free resolutions of a lattice ideal associated with a graph and its initial ideal. These ideals are closely related to chip firing games and the Riemann-Roch theorem on graphs. Our motivations are twofold: describing information related to the Riemann-Roch theorem in terms of Betti numbers of the lattice ideal and the problem of explicit description of minimal free resolutions. This talk is based on joint work with Frank-Olaf Schreyer and John Wilmes. Analogous results were simultaneously and independently obtained by Fatemeh Mohammadi and Farbod Shokrieh.
Title: Numerical Analysis of Mixed Formulations for Bingham Fluids
Defense: Dissertation
Speaker: Alexis Aposporidis of Emory University
Contact: Alexis Aposporidis, aapospo@emory.edu
Date: 2012-11-06 at 4:00PM
Venue: W304
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Abstract:
Visco-plastic materials have been attracting a great amount of attention among researchers in the study of fluid flow due to their widespread presence in various fields of science. However, the efficient solution of the nonlinear partial differential equations modelling their flow poses many challenges. From a mathematical point of view, the major difficulty associated with solving these equations is the presence of singularities in (a priori unknown) parts of the domain. This "irregularity" often reflects in a slow convergence of numerical solvers. In this presentation we consider an augmented formulation of the Bingham visco-plastic flow which is aimed at circumventing the singularity of the equations. We present a nonlinear solver based on this formulation and compare its performance to other common techniques for solving the Bingham flow, indicating superior convergence properties of the solver based on the augmented formulation. Upon linearization and discretization, a sequence of linear systems is obtained which are in general very large and sparse. For the efficient solution of these linear systems we present a nonlinear geometric multilevel technique which is used to precondition a flexible Krylov subspace method. We conclude by presenting some applications of this work to problems in hemodynamics.
Title: Mining and Using Contextual Information from Large-Scale Web Search Logs
Seminar: Computer Science
Speaker: Paul Bennet of Microsoft
Contact: Eugene Atichtein, eugene@mathcs.emory.edu
Date: 2012-11-05 at 4:00PM
Venue: MSC W303
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Abstract:
Information retrieval has made significant progress in returning relevant results for a single query. However, much search activity is conducted within a much richer context of a current task focus, recent search activities as well as longer-term preferences. For example, our ability to accurately interpret the current query can be informed by knowledge of the web pages a searcher was viewing when initiating the search or recent actions of the searcher such as queries issued, results clicked, and pages viewed. We develop a framework that enables representation of a broad variety of context including the searcher's long-term interests, recent activity, current focus, and other user characteristics. We then demonstrate how that can be used to improve the quality of search results. We describe recent progress on three key challenges in this domain: mining contextual signals from large scale logs; understanding and modeling the combination of short-term and long-term behavior; and learning a more robust model that mitigates the risk of applying the contextual model when a simpler model would suffice.\\ \\ This talk will present joint work with Filip Radlinski, Lidan Wang, Ryen White, Kevyn Collins-Thompson, Wei Chu, Susan Dumais, Peter Bailey, Emine Yilmaz, Fedor Borisyuk, and Xiaoyuan Cui.\\ \\ Bio:\\ \\ Paul Bennett is a Researcher in the Context, Learning and User Experience for Search (CLUES) group at Microsoft Research where he works on using machine learning technology to improve information access and retrieval. His recent research has focused on classification-enhanced and contextual information retrieval, pairwise preferences, human computation, and text classification while his previous work focused primarily on ensemble methods, active learning, and obtaining reliable probability estimates, but also extended to machine translation, recommender systems, and knowledge bases. He completed his dissertation on combining text classifiers using reliability indicators in 2006 at Carnegie Mellon where he was advised by Profs. Jaime Carbonell and John Lafferty.
Title: 3D Floorplanning and Tree Representations
Seminar: Combinatorics
Speaker: Paul Horn of Harvard University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2012-11-02 at 4:00PM
Venue: MSC W303
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Abstract:
A (2D) mosaic floorplan is a partitioning of a square into $n$ rectangles. Schemes which can be used to represent and count these floorplans, under a suitable topological equivalence, have applications in chip design. A 3D mosaic floorplan is a partitioning of a box into $n$ smaller boxes. Modern chip construction techniques, allowing chips with multiple layers, have fueled the desire to understand the number of 3D mosaic floorplans and how to represent them. For the 2D case, the number of unlabeled floorplans with $n$ rectangles, up to topological equivalence, is exponential in $n$. For many classes of 3D floorplans the number of floorplans is also exponential. Notable among these are 'slicing' floorplans, where to obtain an $n$ box floorplan one starts with an $n-1$ box floorplan and divides a box in two. In this talk, we discuss some of the difficulties with more general 3D floorplans, even with only two layers. In particular, if $F_n$ denotes the number of 3D floorplans with two levels, we show that $\log F_n \sim \frac{1}{3}n \log n$, and hence $F_n$ grows superexponentially in $n$. The upper bound comes from a representation scheme using trees, while the lower bound comes from a random construction.
Title: On computations of Shanks and Schmid
Seminar: Algebra and Number Theory
Speaker: Robert Osburn of University College Dublin
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-30 at 4:00PM
Venue: W306
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Abstract:
In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to $x$ which are represented by the quadratic form $X^2+nY^2$, n greater than or equal to 1. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for $n=2$. In this talk, we discuss a proof of the fact that this constant is actually unbounded as one runs through fundamental discriminants with a fixed number of distinct prime divisors. This is joint work with David Brink and Pieter Moree (MPIM).
Title: Exact Minimum Degree Thresholds for Perfect Matchings in Uniform Hypergraphs
Seminar: Combinatorics
Speaker: Yi Zhao of Georgia State University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2012-10-26 at 4:00PM
Venue: MSC W303
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Abstract:
Given positive integers $k$ and $d$ where $k/2 \leq d \leq k-1$, we give a minimum $d$-degree condition that ensures a perfect matching in a $k$-uniform hypergraph. This condition is best possible and extends the work of Pikhurko, Rödl, Ruci\'{n}ski and Szemerédi. Our approach makes use of the absorbing method. This is a joint work with Andrew Treglown.
Title: Ranks of elliptic curves
Seminar: Algebra and Number Theory
Speaker: Karl Rubin of UC Irvine
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-25 at 4:00PM
Venue: MSC W201
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Abstract:
I will discuss some recent conjectures and results on the distribution of Mordell-Weil ranks and Selmer ranks of elliptic curves. After some general background, I will specialize to families of quadratic twists, and describe some recent results in detail.
Title: An approach to nonsolvable base change for GL(2)
Seminar: Algebra and Number Theory
Speaker: Jayce Getz of Duke University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-25 at 5:15PM
Venue: MSC W201
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Abstract:
Motivated by Langlands' beyond endoscopy idea, the speaker will present a conjectural trace identity that is essentially equivalent to base change and descent of automorphic representations of GL(2) along a nonsolvable extension of fields.
Title: The arithmetic of special values
Seminar: Algebra and Number Theory
Speaker: Cristian Popescu of UCSD
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-24 at 3:00PM
Venue: W306
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Abstract:
I will discuss some of my recent joint work with Greither on several classical conjectures on special values of equivariant Artin L-functions.