All Seminars

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Title: Linear Preserver Problems and Cohomological Invariants
Defense: Dissertation
Speaker: Hernando Bermudez of Emory University
Contact: Hernando Bermudez, hbermud@emory.edu
Date: 2014-04-02 at 4:00PM
Venue: W306
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Abstract:
Let G be a simple linear algebraic group over a field F. In this work we prove several results about G and it's representations.. In particular we determine the stabilizer of a polynomial f on an irreducible representation V of G for several interesting pairs (V,f). We also prove that in most cases if f is a polynomial whose stabilizer has identity component G then there is a correspondence between similarity classes of twisted forms of f and twisted forms of G. In a different direction we determine the group of normalized degree 3 cohomological invariants for most G which are neither simply connected nor adjoint.
Title: Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels
Seminar: N/A
Speaker: Annalisa Quaini of University of Houston
Contact: TBA
Date: 2014-04-02 at 4:00PM
Venue: W302
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Abstract:
We discuss the validation of an open source framework for the solution of problems arising in hemodynamics. The framework is assessed through experimental data for fluid flow in an idealized medical device with rigid boundaries and a numerical benchmark for flow in compliant vessels. The core of the framework is an open source parallel finite element library that features several algorithms for fluid and fluid-structure interaction problems. A detailed account of the methods is provided.
Title: Some People Have All The Luck
Type: N/A
Speaker: Skip Garibaldi / Lawrence Mower of Emory and UCLA / Palm Beach Post
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-04-02 at 6:00PM
Venue: MSC E208
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Abstract:
Winning a prize of at least $600 in the lottery is a remarkable thing — for a typical scratcher ticket the odds are worse than 1-in-1200 and 1-in-9000 is a more typical figure. Some people have won several of these large prizes, and clearly they are very lucky or they buy a ton of lottery tickets. When we investigated records of all claimed lottery prizes, we discovered that some people had won hundreds of these prizes! Such people seem to be not just lucky, but suspiciously lucky. We will explain what we thought they might have been up to, what mathematics says about it, and what further investigations revealed. This talk is about joint work with Philip B. Stark. Skip Garibaldi is associate director of UCLA's Institute for Pure and Applied Mathematics and a professor in Emory University's Department of Mathematics & Computer Science. His previous work on the lottery received the Lester R. Ford Award and is the subject of a chapter in the popular book “Brain Trust". Millions of people have seen him talk about math on 20/20, CNN, and Fox & Friends, and he is featured in a museum exhibit about mathematics currently on display at Exploration Place in Wichita. Lawrence Mower is an investigative reporter with The Palm Beach Post. He joined The Post in 2013, after working for the Las Vegas Review-Journal, where his yearlong investigation into Las Vegas police shootings sparked a Department of Justice investigation and led to reforms in policy and oversight. The five-part series was awarded by the National Headliner Awards, Investigative Reporters and Editors, and the ACLU of Nevada, and in 2012 he was named Nevada's Outstanding Journalist by the Nevada Press Association. He is a 2006 graduate of the University of Nevada, Las Vegas.
Title: 3F2-hypergeometric functions and supersingular elliptic curves
Undergraduate Honors Thesis Defense: Algebra
Speaker: Sarah Pitman of Emory University
Contact: Ken Ono, ono@mathcs.emory.edu
Date: 2014-04-01 at 2:30PM
Venue: W304
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Abstract:
Here we explore elliptic curves, specifically supersingular elliptic curves, and their relationship to hypergeometric functions. We begin with some background on elliptic curves, supersingularity, hypergeometric functions, and then use work of El-Guindy, Ono, Kaneko, Zagier, and Monks to extend results. In recent work, Monks described the supersingular locus of families of elliptic curves in terms of 2F1-hypergeometric functions. We “lift" his work to the level of 3F2-hypergeometric functions by means of classical transformation laws and a theorem of Clausen.
Title: Number Theory of Moonshine
Seminar: Algebra
Speaker: Sarah Trebat-Leder of Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-04-01 at 4:00PM
Venue: W302
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Abstract:
The classical theory of monstrous moonshine describes the unexpected connection between the representation theory of the monster group $M$, the largest of the simple sporadic groups, and certain modular functions, called Hauptmodln. For example, the $n$th Fourier coefficient of Klein's $j(\tau)$ function is the dimension of the grade $n$ part of a special infinite dimensional representation $V$ of the monster group. Similar phenomena have been shown to hold for the Matthieu group $M_{24}$, but instead of modular functions, mock modular forms must be used. This has been conjecturally generalized even further, to umbral moonshine, which associates to each of 23 Niemeier lattices a finite group, infinite dimensional representation, and mock modular form. We use generalized Borcherds products to relate monstrous moonshine and umbral moonshine. Namely, we show that twisted traces of classical moonshine functions are equal to coefficients of umbral mock modular forms. We also show that certain umbral coefficients have $p$-adic properties.
Title: Combinatorial Objects at the Interface of $q$-series and Modular Forms
Defense: Dissertation
Speaker: Marie Jameson of Emory University
Contact: Marie Jameson, mjames7@emory.edu
Date: 2014-03-31 at 11:30AM
Venue: E406
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Abstract:
In this work, the author proves various results related to $q$-series and modular forms by employing a broad range of tools from analytic number theory, combinatorics, the theory of modular forms, and algebraic number theory. More specifically, the circle method, the connection between modular forms and elliptic curves, continued fractions, period polynomials, and several other tools from the theory of modular forms are used here. These allow the author to prove a number of results related to $q$-series and partition functions, modular forms, period polynomials, and certain quadratic polynomials of a fixed discriminant. This includes a proof of the Alder-Andrews conjecture on certain restricted partition functions, and a resolution of a speculation of Don Zagier regarding the Eichler integrals of a distinguished class of modular forms.
Title: Supporting Information Access through Text Quality Prediction and Automatic Summarization
Seminar: Computer Science
Speaker: Annie Louis of University of Edinburgh
Contact: Vaidy Sunderam, VSS@emory.edu
Date: 2014-03-28 at 3:00PM
Venue: W303
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Abstract:
When users look for information on the world wide web, not only do they seek relevant documents, but also desire information that is of high quality, and is organized, and summarized in an easy to digest format. In this talk, I will overview my work in two areas aiming to create richer search and browsing experiences for users. First, I will describe work on automatically assessing the writing quality of documents. Well-written documents are obviously more valuable to users. While spelling and grammar errors are detected easily by current systems, there are numerous other aspects of writing quality for which computational methods do not exist. I will outline some models I have built to predict coherent, concise and popular writing style. Second I will describe some ongoing work to automatically uncover the structure of and summarize conversations from web discussion forums. Often forums are organized as threads with posts appearing in a simple chronological order. I will describe two models which add more structure to these conversations: one which groups forum participants based on the content and reply patterns of their conversations, and a second model to identify easy and difficult instructions suggested in computer troubleshooting forums.
Title: Multilevel Monte Carlo simulations with algebraically constructed coarse spaces
Seminar: Numerical Analysis and Scientific Computing
Speaker: U. Villa, P. Vassilevski of Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory (LLNL)
Contact: Veneziani,
Date: 2014-03-28 at 4:00PM
Venue: W306
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Abstract:
We consider the numerical simulation of multiscale multiphysics phenomena with uncertain input data in a Multilevel Monte Carlo (MLMC) framework. Multilevel Monte Carlo techniques typically rely on the existence of hierarchies of computational meshes obtained by successive refinement. We apply MLMC to unstructured meshes by using specialized element-based agglomeration techniques that allow us to construct hierarchies of coarse spaces that possess stability and approximation properties for wide classes of PDEs. An application to subsurface flow simulation in mixed finite element setting illustrates our approach. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344
Title: Solving geometric variational problems by gluing
Colloquium: Analysis and Differential Geometry
Speaker: Professor Matthew J. Gursky of University of Notre Dame
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2014-03-27 at 4:00PM
Venue: W301
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Abstract:
In this talk I will describe give a schematic overview of a technique for constructing new solutions of geometric variational problems from known ones, called "gluing." I will focus on two examples which share a key feature, namely, conformal invariance. I will begin with an outline of the work of D. Joyce, who used gluing techniques to construct metrics of constant scalar curvature. Then, I will then describe some recent work with J. Viaclovsky, in which we create new examples of four-manifolds which are critical points of L^2-curvature functionals.
Title: Optimal Central Bank Interventions in the presence of Regime Switching
Seminar: General Colloquium
Speaker: Luz Rocio Sotomayor of Georgia State University
Contact: Steve Batterson, sb@mathcs.emory.edu
Date: 2014-03-27 at 4:00PM
Venue: W306
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Abstract:
In a foreign exchange market that is affected by the conditions of the monetary fundamentals (unemployment, interest rate, inflation rate, trade deficit and GDP, among others), we model the foreign exchange rate as a process with parameters modulated by an observable continuous-time Markov chain. Under this setup, we consider the problem of the domestic Central Bank that has to choose the optimal intervention strategy that minimizes the total intervention cost of keeping the exchange rate as close as possible to a given target rate. We solve the problem by using techniques of stochastic impulse control with regime switching.