All Seminars

Title: On division algebras having the same maximal subfields
Seminar: Algebra and number theory
Speaker: Andrei Rapinchuk of University of Virginia
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2011-02-08 at 3:00PM
Venue: W306
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Abstract:
The talk will be built around the following question: let $D_1$ and $D_2$ be two central quaternion division algebras over the same field $K$; when does the fact that $D_1$ and $D_2$ have the same maximal subfields imply that $D_1$ and $D_2$ are actually isomorphic over $K$? I will discuss the motivation for this question that comes from the joint work with G.~Prasad on length-commensurable locally symmetric spaces, and will then talk about some available results. One of the results (joint with I.~Rapinchuk) states that if the answer to the above question is positive over a field $K$ (of characteristic not 2) then it is also positive over any finitely generated purely transcendental extension of $K$. I will also discuss some generalizations to algebras of degree $> 2$.
Title: Ricci solitons and warped product Einstein metrics.
Seminar: Analysis and Differential Geometry
Speaker: William Wylie of University of Pennsylvania
Contact: David Borthwick, davidb@mathcs.emory.edu
Date: 2011-02-08 at 4:00PM
Venue: MSC W301
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Abstract:
One of the fundamental questions in geometry is, given a space what is the "best" geometry we can put on it? In the context of Riemannian geometry, the Ricci flow is a tool that has produced a number of exciting recent breakthroughs in understanding this basic question. Ricci solitons appear prominently in some of these developments as singularity models for the flow and as natural new candidates for optimal geometries. On the other hand, gradient Ricci solitons also have a natural interpretation in terms of Riemannian manifolds with measure. In this talk we will explore this second perspective and discuss some recent classification results that have arisen from this viewpoint.. A natural connection between gradient Ricci solitons and warped product Einstein metrics also arises and we will discuss some recent developments in understanding this connection.
Title: Computational models and challenges in tokamak fusion reactors
Seminar: Numerical Analysis and Scientific Computing
Speaker: Alfredo Portone of Analysis and Codes Group Fusion for Energy
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2011-02-04 at 4:00PM
Venue: MSC W201
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Abstract:
The aim of this presentation is twofold. Firstly the key concepts about magnetic fusion with tokamaks are introduced by focusing the attention on the key dimensioning parameters as well as on the basic operational principles of a tokamak reactor.  In the second part of the talk the main models used in tokamak plasmas simulation and in the most challenging engineering problems are presented. With respect to tokamak plasmas the MHD approximations and models are introduced (e.g. single fluid MHD, ideal MHD, etc.). The attention is then focused to the key problem of magnetic equilibrium and stability computation. As far as the engineering applications are concerned, three areas of interested are discussed, namely (1) the computation of transient electromagnetics in the metallic structures surrounding the plasma, (2) the stability problem of low-temperature superconductors and (3) the main features in 14 MeV neutron shielding.
Title: The fractional version of Hedetniemi's Product Conjecture - Part 2
Seminar: Combinatorics
Speaker: Dwight Duffus of Emory University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2011-02-04 at 4:00PM
Venue: W306
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Abstract:
Recently Xuding Zhu has verified the fractional version of Hedetniemi's conjecture that the chromatic number of the product of two n-chromatic graphs is n-chromatic. This settles a conjecture of Burr, Erdos and Lovasz on chromatic Ramsey numbers. In this second talk, we will see how the second conjecture follows and outline the proof of Zhu's result.
Title: Mini-Apps for Modern Architectures
Seminar: Scientific Computing
Speaker: Benjamin Bergen of Los Alamos National Laboratory 
Contact: James Nagy, nagy@compute.mathcs.emory.edu
Date: 2011-02-02 at 12:50PM
Venue: W306
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Abstract:
A mini-app is a simulation code that captures the fundamental complexity of some aspect of a full-scale solver.  For classified applications, this is advantageous because the mini-app may be shared with vendors or academics, while the original code may not.  In this presentation, we describe such a mini-app that is designed to capture the cardinal aspects of an Adaptive Mesh Refinement (AMR) framework for multi-physics problems in astrophysics and weapons science.  The approach introduced here can be classified as block-structured AMR with the addition of a novel data decomposition technique that helps address many of the issues that arise when considering the challenges of exascale computing, e.g., fault tolerance, data migration--for load balancing--and adaptability to accelerated architectures.  The work discussed in this presentation will be in the context of a multi-physics solver for radiation hydrodynamics simulations to help us better understand Inertial Confinement Fusion (ICF) experiments underway at the National Ignition Facility (ICF) at Lawrence Livermore National Laboratory.
Title: Moments of zeta and L-functions
Seminar: Athens-Atlanta Number Theory
Speaker: K. Soundararajan of Stanford University
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2011-02-01 at 4:00PM
Venue: MSC W201
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Abstract:
An important theme in number theory is to understand the values taken by the Riemann zeta-function and related L-functions. While much progress has been made, many of the basic questions remain unanswered. I will discuss what is known about this question, explaining in particular the work of Selberg, random matrix theory and the moment conjectures of Keating and Snaith, and recent progress towards estimating the moments of zeta and L-functions.
Title: Complex dynamics and adelic potential theory
Seminar: Athens-Atlanta Number Theory
Speaker: Matthew Baker of Georgia Institute of Technology
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2011-02-01 at 5:00PM
Venue: MSC W201
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Abstract:
I will discuss the following theorem: for any fixed complex numbers a and b, the set of complex numbers c for which both a and b both have finite orbit under iteration of the map $z -->z^2 + c$ is infinite if and only if $a^2 = b^2$. I will explain the motivation for this result and give an outline of the proof. The main arithmetic ingredient in the proof is an adelic equidistribution theorem for preperiodic points over product formula fields, with non-archimedean Berkovich spaces playing an essential role. This is joint work with Laura DeMarco, relying on earlier joint work with Robert Rumely.
Title: A shape-based method for determining protein binding sites in a genome
Colloquium: Topology
Speaker: Valerie Hower of University of California, Berkeley
Contact: Susan Guppy, sguppy@emory.edu
Date: 2011-01-31 at 4:30PM
Venue: MSC W201
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Abstract:
We present a new algorithm for the identification of bound regions from ChIP-Seq experiments. ChIP-Seq is a relatively new assay for measuring the interactions of proteins with DNA. The binding sites for a given protein in a genome are "peaks" in the data, which is given by an integer-valued height function defined on the genome. Our method for identifying statistically significant peaks is inspired by the notion of persistence in topological data analysis and provides a non-parametric approach that is robust to noise in experiments. Specifically, our method reduces the peak calling problem to the study of tree-based statistics derived from the data. The software T-PIC (Tree shape Peak Identification for ChIP-Seq) is available at http://math.berkeley.edu/~vhower/tpic.html and provides a fast and accurate solution for ChIP-Seq peak finding.
Title: Superfast and stable direct solutions of Toeplitz systems
Seminar: Numerical Analysis and Scientific Computing
Speaker: Jianlin Xia of Department of Mathematics, Purdue University
Contact: Jim Nagy, nagy@mathcs.emory.edu
Date: 2011-01-28 at 12:50PM
Venue: W306
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Abstract:
Toeplitz matrices arise in many applications such as signal and image processing, time series analysis, solution methods for PDEs, and regularization of inverse problems. In this talk, we will discuss some ideas of structured solutions of Toeplitz linear systems. These ideas can also be used to solve some other structured systems. With the displacement structure, our methods quickly solve a Cauchy-like system converted from the Toeplitz system, based on a fact that the Cauchy-like matrix is rank structured. Semiseparable structured factorizations are used to develop different versions of superfast (roughly O(n) cost) and stable Toeplitz solvers. These versions include: direct semiseparable matrix approximation, randomized sampling together with fast Toeplitz matrix-vector products, and multi-layer structured approximation. In particular, the last version uses two layers of structured representations to achieve high efficiency: an outer layer hierarchically semiseparable (HSS) structure, and an inner Cauchy-like structure for each dense HSS generator. Fast strong rank revealing LU factorizations are used in a hierarchical scheme for the structured approximation. We test the methods on various highly ill-conditioned examples to show both the efficiency and the stability. This is joint work with Ming Gu at UC Berkeley and Yuanzhe Xi at Purdue University.
Title: Information Discovery on Vertical Domains
Seminar: Computer Science
Speaker: Vagelis Hristidis of Florida International University
Contact: Eugene Agichtein, eugene@mathcs.emory.edu
Date: 2011-01-28 at 3:00PM
Venue: MSC W301
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Abstract:
As the amount of available data increases, the problem of information discovery, often referred to as finding the needle in the haystack problem, becomes more pressing. The most successful search applications today are the general purpose Web search engines and the well-structured database querying (e.g., SQL). Directly applying these two search models to specific domains is ineffective since they ignore the domain semantics -meaning of object associations- and the needs of the domain users -a biologist wants to see different results from a physician for the same query on PubMed. We present challenges and techniques to achieve effective information discovery on vertical domains by modeling the domain semantics and its users, and exploiting the knowledge of domain experts. Our focal domains are products marketplace, biological data, clinical data, bibliographic data, blogs and patents. This project is being funded by NSF.\\ \\Bio:\\ Vagelis Hristidis is an Associate Professor at the School of Computing and Information Sciences at Florida International University, in Miami. He received his PhD in Computer Science from the University of California, San Diego, in 2004. He has received funding from the National Science Foundation, the Department of Homeland Security, Google, IBM and the Kauffman Entrepreneurship Center, including the NSF CAREER Award. He has also received the FIU SCIS Excellence in Research Award twice, the FIU University Faculty Award, and the FIU University Service Award. His main research addresses the problem of bridging the gap between databases and information retrieval, with particular interest in the interdisciplinary directions of Healthcare and Disaster Management. His work has received more than 2,100 citations according to Google Scholar. He also recently edited and co-authored a book on “Information Discovery on Electronic Health Records”. For more information, please visit http://www.cis.fiu.edu/~vagelis/.