All Seminars
| Title: Domination in 3-edge-colored complete graphs |
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| Seminar: Combinatorics |
| Speaker: Daniel Kral of The University of Warwick |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-04-19 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Erdos, Faudree, Gould, Gyarfas, Rousseau and Schelp proved that for every complete graph of order $n$ with edges colored with three colors, there exist a set $X$ of 22 vertices and a color $c$ such that the number of vertices in $X$ or joined to a vertex of $X$ by an edge of color $c$ is at least $2n/3$. They also conjectured that the bound of 22 can be lowered to 3. We improve the bound to 4. The talk is based on joint work with Chun-Hung Liu, Jean-Sebastien Sereni, Peter Whalen and Zelealem Yilma. |
| Title: Differential Approximations of the Radiative Transport Equation |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Qiwei Sheng of The University of Iowa |
| Contact: Hao Gao, haog@mathcs.emory.edu |
| Date: 2013-04-18 at 2:00PM |
| Venue: MSC E408 |
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| Abstract: Abstract: The radiative transport equation (RTE) arises in a variety range of applications in sciences and engineering. It is challenging to solve RTE numerically due to its integro-differential form and high dimension. For highly forward-peaked media, it is even more difficult to solve RTE since accurate numerical solutions require a high resolution of the direction variable, leading to prohibitively large amount of computations. For this reason, various approximations of RTE have been proposed in the literature. This talk is devoted to the introduction and analysis of a family of differential approximations of the RTE. |
| Title: Image Deblurring with Krylov Subspace Methods |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Per Christian Hansen of Technical University of Denmark |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2013-04-17 at 12:50PM |
| Venue: W306 |
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| Abstract: Image deblurring, i.e., reconstruction of a sharper image from a blurred and noisy one, involves the solution of a large and very ill-conditioned system of linear equations, and regularization is needed in order to compute a stable solution. Krylov subspace methods are often ideally suited for this task: their iterative nature is a natural way to handle such large-scale problems, and the underlying Krylov subspace provides a convenient mechanism to regularized the problem by projecting it onto a low-dimensional "signal subspace" adapted to the particular problem. In this talk we consider the three Krylov subspace methods CGLS, MINRES, and GMRES. We describe their regularizing properties, and we discuss some computational aspects such as preconditioning and stopping criteria. |
| Title: Uniform Hypergraphs Containing no Grids |
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| Seminar: Combinatorics |
| Speaker: Miklos Ruszinko of Hungarian Academy of Science and Memphis University |
| Contact: Andrzej Rucinski, andrzej@mathcs.emory.edu |
| Date: 2013-04-15 at 3:00PM |
| Venue: MSC W303 |
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| Abstract: A hypergraph is called an $r\times r$ {\em grid} if it is isomorphic to a pattern of $r$ horizontal and $r$ vertical lines, i.e., a family of sets $\{A_1, \dots ,A_r, B_1,\dots ,B_r\}$ such that $A_i\cap A_j=B_i\cap B_j=\emptyset$ for $1\le i |
| Title: Subcubic triangle-free graphs have fractional chromatic number at most 14/5 |
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| Seminar: Combinatorics |
| Speaker: Zdenek Dvorak of The Georgia Institute of Technology |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-04-12 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Every subcubic triangle-free graph on n vertices contains an independent set of size at least $5n/14$ (Staton'79). We strengthen this result by showing that all such graphs have fractional chromatic number at most 14/5, thus confirming a conjecture by Heckman and Thomas.\\ \\ This is joint work with J.-S. Sereni and J. Volec. |
| Title: Gradient Descent Methods for Large-Scale Linear Inverse Problems |
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| Defense: Honors thesis |
| Speaker: Chen (Cool) Cheng of Emory University |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2013-04-11 at 4:00PM |
| Venue: W306 |
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| Abstract: Iterative gradient descent methods are frequently used for ill-posed inverse problems because they are suitable for large models and they are cheap to work with. In this thesis, we explore three different types of gradient descent methods: the Landweber method, method of steepest descent, and the Barzilai-Borwein method. Specifically, we also compare the efficiency of these methods to the conjugate gradient method. The thesis begins with an introduction to the history and application of the gradient descent methods and to the methods tested, and follows with convergence analysis and numerical experience on real images. Ways to accelerate and smooth the BB method are also included. |
| Title: Mahler measures of hypergeometric families of Calabi-Yau varieties |
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| Seminar: Algebra |
| Speaker: Detchat Samart of Texas A\&M |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-04-10 at 3:00PM |
| Venue: W306 |
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| Abstract: The (logarithmic) Mahler measure of an $n$-variable Laurent polynomial $P$ is defined by $m(P)=\int_0^1\cdots \int_0^1 \log |P(e^{2\pi i \theta_1},\ldots,e^{2\pi i \theta_n})|\,d\theta_1\cdots d\theta_n.$ In some certain cases, Mahler measures are known to be related to special values of $L$-functions. We will present some new results relating the Mahler measures of polynomials whose zero loci define elliptic curves, $K3$ surfaces, and Calabi-Yau threefold of hypergeometric type to $L$-values of elliptic modular forms. A part of the talk is joint work with Matt Papanikolas and Mat Rogers. |
| Title: Automatic Transcription of Polyphonic Musical Signals with Linear Matching Pursuit |
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| Defense: Masters Thesis |
| Speaker: Andrew McLeod of Emory University |
| Contact: Andrew McLeod, apmcleo@emory.edu |
| Date: 2013-04-08 at 3:05PM |
| Venue: W304 |
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| Abstract: The Harmonic Matching Pursuit (HMP) algorithm has ordered promising results in the au- tomatic transcription of audio signals. It works by decomposing the given signal into a set of harmonic atoms, and then grouping those atoms into individual notes. HMP has shown very promising results, but more research has been needed for one case: when multiple notes with rational frequency relation are played simultaneously. This situation is called the overlapping partial problem, and it is very common in music, occurring in intervals such as major thirds, perfect fourths, and perfect fifths. A few solutions have been proposed to handle this over- lapping partial problem by performing post-processing on the output of HMP (notably HMP with Spectral Smoothness (HMP SS)). In this paper, I propose an algorithm called Linear Matching Pursuit (LMP) to solve the overlapping partial problem of automatic note detection, which uses new heuristics to solve the problem with no post-processing required. LMP's run- time is independent of the number of notes present in a given audio signal, unlike HMP. My experiments show that LMP offers an improvement upon the accuracy of the HMP algorithm, though not to the extent of HMP SS, and is very robust in runtime with respect to polyphony. |
| Title: Topics in analytic number theory |
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| Defense: Dissertation |
| Speaker: Robert Lemke Oliver of Emory University |
| Contact: Robert Lemke Oliver, rlemkeo@emory.edu |
| Date: 2013-04-04 at 2:30PM |
| Venue: MSC E408 |
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| Abstract: In this thesis, the author proves results using the circle method, sieve theory and the distribution of primes, character sums, modular forms and Maass forms, and the Granville-Soundararajan theory of pretentiousness. In particular, he proves theorems about partitions and $q$-series, almost-prime values of polynomials, Gauss sums, modular forms, quadratic forms, and multiplicative functions exhibiting extreme cancellation. This includes a proof of the Alder-Andrews conjecture, generalizations of theorems of Iwaniec and Ono and Soundararajan, and answers to questions of Zagier and Serre, as well as questions of the author in the Granville-Soundararajan theory of pretentiousness.\\ \\ The talk will focus on three topics: Gauss sums over finite fields, eta-quotients and theta functions, and the pretentious view of analytic number theory. |
| Title: Homogeneous spaces over function fields of dimension two |
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| Seminar: Algebra and Number Theory |
| Speaker: Yi Zhu of University of Utah |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2013-04-03 at 3:00PM |
| Venue: W306 |
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| Abstract: Let $K$ be either a global function field or a function field of an algebraic surface. Johan de Jong formulated the following principle: a ``rationally simply connected'' $K$-variety admits a rational point if and only if the elementary obstruction vanishes. In this talk, I will discuss how this principle works for projective homogeneous spaces. In particular, it leads to a classification-free result towards the quasi-split case of Serre's Conjecture II over $K$. |