All Seminars

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Title: Some Old and New Results on an Elimination Game
Seminar: Numerical Analysis and Scientific Computing
Speaker: Esmond G. Ng of Lawrence Berkeley National Laboratory
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2014-10-06 at 12:00AM
Venue: W301
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Abstract:
Sparse matrix problems arise at the heart of many large-scale scientific and engineering applications. State-of-the-art algorithms for solving these problems involve not only numerical techniques, but may also require knowledge of data structures, graph theory, algorithm design, complexity analysis, and computer architectures. This is particularly true for factorization-based algorithms, such as those for solving sparse systems of linear equations, in which the nonzero entries of a matrix are eliminated according to certain prescribed rules. However, the order in which the nonzero entries are eliminated can have a dramatic effect on the overall performance of the solution process. This is referred to as the ordering problem, which is often posed as an elimination game on a graph. In this talk, an overview of the elimination game will be presented. In particular, previously known results and some recently work will be described.
Title: Wall crossing in moduli problems and semi-orthogonal decompositions
Seminar: Algebra
Speaker: Matt Ballard of USC
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-30 at 4:00PM
Venue: W306
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Abstract:
We discuss how the derived category of a smooth algebraic stack of finite type changes as one removes certain types of closed substacks. As an application, we show how wall-crossing in moduli of stable sheaves and Bridgeland stable objects yields semi-orthogonal decompositions of relating their derived categories.
Title: Modeling Temporal Dynamics of User Generated Content
Defense: Dissertation
Speaker: Yu Wang of Emory Unviersity
Contact: Yu Wang, yu.wang@emory.edu
Date: 2014-09-29 at 10:15AM
Venue: PAIS 561
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Abstract:
The evolving nature of user generated content (UGC) lays the key characteristics of Web 2.0. The evolution process in UGC offers valuable evidence to explain the content dynamics in the past and predict trends in the future. In this thesis, we design models to analyze content evolution patterns of UGC in three granularities: words, topics and sentiment. More specifically, this thesis investigates content evolution in the following aspects: (1) on word-level dyanmics: analyzing word frequency change in collaboratively generated content and using historical word frequencies to better weigh the words in ranking functions; (2) on topic-level dynamics: learning temporal transition patterns of topics in microblog streams and predict future topics according to historical posts; (3) on sentiment-level dynamics: estimating and understanding different sentiment change patterns of popular political topics across different user groups. We show that the developed models enable new applications in UGC, such as improving content-based ranking, anticipating future popular topics and visualizing and interpreting sentiment dynamics.
Title: Computing free surface flows of viscoplastic fluids
Seminar: Numerical Analysis and Scientific Computing
Speaker: Maxim Olshanskii of University of Houston
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2014-09-26 at 12:00AM
Venue: W301
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Abstract:
Free surfaces flows of yield stress fluids are common in nature and in engineering applications. Viscoplastic models, such as the Herschel-Bulkley model, are often used to describe the complex rheology of such fluids and predict fluids dynamics with reasonable accuracy. The numerical modeling and analysis of the phenomena is a challenging task due to the non-trivial coupling of complex fluid dynamics and free surface evolution.\\ \\ In this talk we discuss an approach for numerical simulation of free surface flows of viscoplastic incompressible fluids. The approach features adaptive Cartesian grids and a splitting technique for numerical time integration. We shall point to several open problems in the mathematical and numerical analysis of equations governing free surface flows of viscoplastic fluids.
Title: An algebraic approach to enumerating field extensions
Seminar: Algebra
Speaker: Frank Thorne of University of South Carolina
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-22 at 4:00PM
Venue: W302
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Abstract:
Building on previous work of Cohen and several of his collaborators, I will discuss the use Kummer theory and class field theory to enumerate field extensions of low degree. We obtain an explicit Dirichlet series representation, in the form of a finite sum of Euler products, for the set of field extensions with Galois group $S_3, A_4, S_4$, or $D_l$ (l an odd prime) with fixed resolvent. This has a variety of interesting consquences, including results on the Shintani zeta function as well as an extension of the Scholz reflection principle, which I will describe. Most of this is joint work with Henri Cohen, and one part is also joint with Simon Rubinstein-Salzedo.
Title: On the Distribution of Moonshine
Seminar: Algebra
Speaker: Michael Griffin of Emory
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-16 at 4:00PM
Venue: W306
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Abstract:
Monstrous moonshine expresses distinguished modular functions in terms of the representation theory of the Monster. The celebrated observations that \[ (*) 1=1, 196884=196883+1, 21493760=1+196883+21296876,\ldots \] illustrate the case of $J(z)=j(z)-744$, where the coefficients are sums of the dimensions of the 194 irreducible representations of the Monster. Such formulas are dictated by the structure of the graded monstrous moonshine modules. Here we use the modularity of the moonshine modules to address the open problem of obtaining exact formulas for the multiplicities of the irreducible components of the moonshine modules. These formulas imply that such multiplicities are asymptotically proportional to dimensions.
Title: A connection between coupled and penalty projection time-stepping schemes with FE spatial discretization for the Navier-Stokes equations
Seminar: Numerical Analysis and Scientific Computing
Speaker: Leo Rebholz of Clemson University
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2014-09-12 at 12:00AM
Venue: W301
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Abstract:
We prove that in finite element settings where the divergence-free subspace of the velocity space has optimal approximation properties, the solution of Chorin-Temam projection methods for Navier-Stokes equations equipped with grad-div stabilization with parameter $\gamma$, converge to the associated coupled method solution with rate $\gamma^{-1}$ as $\gamma\rightarrow \infty$. We prove this first for backward Euler schemes, and then extend the results to BDF2 schemes, and finally to schemes with outflow boundary conditions. Several numerical experiments are given which verify the convergence rate, and show how using projection methods in this setting with large grad-div stabilization parameters improves accuracy.
Title: Shifted convolution L-functions
Seminar: Algebra
Speaker: Ken Ono of Emory
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-09 at 4:00PM
Venue: W306
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Abstract:
Rankin-Selberg convolution L-functions are important functions in number theory. Their properties play a central role in many of deepest works on the Ramanujan-Petersson Conjecture. In a recent paper, Hoffstein and Hulse defined generalizations of these L-functions, the so-called ``shifted-convolution" L-functions. They obtained the meromorphic continuation of the functions in many cases. Here we consider symmetrizations of these L-functions, and we exactly evaluate their special values at diagonal weights for all shifts. This is joint work with Michael Mertens.
Title: Pursuit and Evasion
Colloquium: N/A
Speaker: Imre Leader of University of Cambridge
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2014-09-08 at 4:00PM
Venue: W303
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Abstract:
In Rado's famous "lion and man" problem, a man and a lion are in a circular arena. The lion wants to catch the man, and the man does not want to be caught by the lion. Each can run at the same speed. Who wins? We will start with some background on this kind of "continuous pursuit" problem, including the solution that was eventually given by Besicovitch. We will then move on to some surprising recent developments.
Title: What is the limit of a line bundle on a non normal variety?
Seminar: Algebra
Speaker: Jesse Kass of USC
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-02 at 4:00PM
Venue: W306
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Abstract:
On a nonnormal variety, the limit of a family of line bundles is not always a line bundle. What is the limit? I will present an answer to this question and give some applications. Time permitting, I will discuss connections with Néron models, autoduality, and recent work of R. Hartshorne and C. Polini.