All Seminars
| Title: Some People Have All The Luck |
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| 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 |
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| 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 |
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| 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 |
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| Defense: Dissertation |
| Speaker: Marie Jameson of Emory University |
| Contact: Marie Jameson, mjames7@emory.edu |
| Date: 2014-03-31 at 11:30AM |
| Venue: MSC 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 |
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| Seminar: Computer Science |
| Speaker: Annie Louis of University of Edinburgh |
| Contact: Vaidy Sunderam, VSS@emory.edu |
| Date: 2014-03-28 at 3:00PM |
| Venue: MSC 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 |
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| 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: Optimal Central Bank Interventions in the presence of Regime Switching |
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| 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. |
| Title: Deep Models for Gene Regulation |
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| Defense: Dissertation |
| Speaker: Olgert Denas of Emory University |
| Contact: Olgert Denas, odenas@emory.edu |
| Date: 2014-03-27 at 4:00PM |
| Venue: W302 |
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| Abstract: The recent increase in the production pace of functional genomics data has created new opportunities in understanding regulation. Advances range from the identification of new regulatory elements, to the prediction of gene expression from genomic and epigenomic features. At the same time, this data-rich environment has raised challenges in retrieving and interpreting information from these data.\\ \\ Based on recent algorithmic developments, deep artificial neural networks (ANN) have been used to build representations of the input that preserve only the information needed to the task at hand. Prediction models based on these representations have achieved excellent results in machine learning competitions. The deep learning paradigm describes methods for building these representations and training the prediction models in a single learning exercise.\\ \\ In this work, we propose ANN as tools for modeling gene regulation and a novel technique for interpreting what the model has learned.\\ \\ We implement software for the design of ANNs and for training practices over functional genomics data. As a proof of concept, use our software to model differential gene expression during cell differentiation. To show the versatility of ANNs, we train a regression model on measurements of protein-DNA interaction to predict gene expression levels.\\ \\ Typically, input feature extraction from a trained ANN is formulated as an optimization problem whose solution is slow to obtain and not unique. We propose a new efficient technique for classification problems that provides guarantees on the class probability of the features and their norm. We use this technique to identify input features used by the trained model in classification and show how these features agree with previous empirical studies.\\ \\ Finally, we propose building representations of functional features from protein-DNA interaction measurements using a deep stack of nonlinear transformations. We train the model on a small portion of the input and compute small dimensional representations for the rest of the genome. We show that these reduced representations are informative and can be used to label parts of the gene, regulatory elements, and quiescent regions.\\ \\ While widely successful, deep ANNs are considered to be hard to use and interpret. We hope that this work will help increase the adoption of such models in the genomics community. |
| Title: A computational model of drug delivery through microcirculation to compare different tumor treatment options |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Paolo Zunino of University of Pittsburgh |
| Contact: TBA |
| Date: 2014-03-27 at 4:00PM |
| Venue: MSC N304 |
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| Abstract: Starting from the fundamental laws of filtration and transport in biological tissues, we develop a mathematical model able to capture the interplay between blood perfusion, fluid exchange with the interstitial volume, mass transport in the capillary bed, through the capillary walls and into the surrounding tissue. These phenomena are accounted at the microscale level, where the capillary bed and the interstitial volume are viewed as two separate regions. The capillary bed is described as a network of vessels carrying blood flow. We complement the model with a state of art numerical solver, based on the finite element method. The numerical scheme is based on the idea to represent the capillary bed as a network of one-dimensional channels that acts as a concentrated source of flow immersed into the interstitial volume, because of the natural leakage of capillaries. As a result, it can be classified as an embedded multiscale method. We apply the model to study drug delivery to tumors. Owing to its general foundations, the model can be adapted to describe and compare various treatment options. In particular, we consider drug delivery from bolus injection and from nanoparticles, which are in turn injected into the blood stream. The computational approach is prone to perform a systematic quantification of the treatment performance, enabling the analysis of interstitial drug concentration levels, drug metabolization rates, cell surviving fractions and the corresponding timecourses. Our study suggests that for the treatment based on bolus injection, the drug dose is not optimally delivered to the tumor interstitial volume. Using nanoparticles as intermediate drug carriers overrides the shortcomings of the previous delivery approach. Being directly derived from the fundamental laws of flow and transport, the model relies on general foundations and it is prone to be extended in different directions. On one hand, we are planning to combine it with a poroelastic description of the interstitial tissue, in order to capture the interplay of mechanical deformations and transport phenomena. On the other hand, the model may be adapted in future to study different types of cancer, provided that suitable metrics are available to quantify the transport properties of a specific tumor mass. |
| Title: Solving geometric variational problems by gluing |
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| 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: MSC 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. |