All Seminars
| Title: Superimposed Codes |
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| Colloquium: N/A |
| Speaker: Zoltan Furedi of University of Illinois at Urbana-Champaign and Renyi Institute of Mathematics of the Hungarian Academy of Sciences |
| Contact: Andrzej Rucinski, andrzej@mathcs.emory.edu |
| Date: 2013-02-04 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: There are many instances in Coding Theory when codewords must be restored from partial information, like defected data (error correcting codes), or some superposition of the strings. These lead to superimposed codes, a close relative of group testing problems. There are lots of versions and related problems, like Sidon sets, sum-free sets, union-free families, locally thin families, cover-free codes and families, etc. We discuss two cases {\it cancellative} and {\it union-free} codes. A family of sets $\mathcal F$ (and the corresponding code of 0-1 vectors) is called {\bf union-free} if $A\cup B\neq C\cup D$ and $A,B,C,D\in \mathcal F$ imply $\{ A,B\}=\{ C, D \}$. $\mathcal F$ is called $t$-{\bf cancellative} if for all distict $t+2$ members $A_1, \dots, A_t$ and $B,C\in \mathcal F$ $$A_1\cup\dots \cup A_t\cup B \neq A_1\cup \dots A_t \cup C. $$ Let $c_t(n)$ be the size of the largest $t$-cancellative code on $n$ elements. We significantly improve the previous upper bounds of K\"orner and Sinaimeri, e.g., we show $c_2(n)\leq 2^{0.322n}$ (for $n> n_0$). We introduce a method to deal with such problems, namely we first investigate the constant weight case (i.e., uniform hypergraphs). |
| Title: Faces of Weight Polyhedra and some related algebraic structures |
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| Colloquium: N/A |
| Speaker: Tim Ridenour of Northwestern University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-01-31 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: The set of weights which lie on a face of the weight polyhedron associated to a highest weight module can be used to construct Koszul algebras. I will provide a classification of the set of weights on a face of a weight poylhedron and discuss the construction of the related Koszul algebras. |
| Title: Group presentations: history and recent results |
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| Seminar: Algebra and Number Theory |
| Speaker: William Kantor of University of Oregon |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2013-01-30 at 3:00PM |
| Venue: W306 |
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| Abstract: Group presentations somewhat started with Hamilton. I'll review 19th century history before getting to a recent result: almost all finite simple groups have presentations requiring surprisingly few relations (with Guralnick, Kassabov and Lubotzky). For example, all alternating (and symmetric) groups have presentations using only 3 generators and 7 relations. The proofs are relatively elementary but too long for more than a few small hints. |
| Title: The Geometry of Random (Closed) Space Polygons |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Professor Jason Cantarella of University of Georgia |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2013-01-29 at 4:00PM |
| Venue: W306 |
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| Abstract: Here are some natural questions from statistical physics: What is the expected shape of a ring polymer with $n$ monomers in solution? What is the expected knot type of the polymer? The radius of gyration? Numerical simulations are absolutely required to make progress on these questions, but pose some interesting challenges for geometers. We wish to sample the space of closed $n$-gons in 3-space, which is a nonlinear submanifold of the larger space of open $n$-gons. To sample equilateral polygon space, current algorithms use a Markov process which randomly "folds'' polygons while preserving closure and edgelengths. Such algorithms are expected to converge in O$(n^3)$ time. The main point of this talk is that a much better sampling algorithm is available if we widen our view to the space of $n$-gons in three dimensional space of fixed total length (rather than fixed edgelengths). We describe a natural probability measure on length 2$n$-gon space pushed forward from the standard measure on the Stiefel manifold of 2-frames in complex $n$-space using methods from algebraic geometry. We can directly sample the Stiefel manifold in O(n) time, allowing us to generate closed polygons using the pushforward map. We will give some explicit computations of expected values for geometric properties for such random polygons, discuss their topology, and compare our theorems to numerical experiments using our sampling algorithm. The talk describes joint work with Malcolm Adams (University of Georgia, USA), Tetsuo Deguchi (Ochanomizu University, Japan), and Clay Shonkwiler (University of Georgia, USA). |
| Title: A statistical-numerical approach for data fitting over two-dimensional manifolds |
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| Colloquium: N/A |
| Speaker: Bree Ettinger of |
| Contact: Steve Batterson, sb@mathcs.emory.edu |
| Date: 2013-01-29 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: In this talk, a new approach for fitting data over two-dimensional manifolds will be presented. In particular, a generalized additive model with a suitable regularizing term is proposed. The estimation problem is recast over a planar domain via a conformal map. The conformal map and the resulting planar estimation problem are computed by a finite element approximation. The estimators are linear in the observed data values and classical inferential tools are derived. The application driving this research is the study of hemodynamic forces exerted by blood-flow over the wall of an internal carotid artery affected by an aneurysm. Based on joint work with Simona Perotto and Laura Sangalli (MOX, Department of Mathematics, Politecnico di Milano, Italy) and Tiziano Passerini (Mathematics and Computer Science, Emory University) |
| Title: Adaptive spline approximation: error analysis and construction of the partitions |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Yuliya Babenko of Kennesaw State University, GA |
| Contact: Alessandro Veneziani, ale@mathcs.emory.edu |
| Date: 2013-01-28 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: |
| Title: The pretentious view of analytic number theory |
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| Seminar: Algebra |
| Speaker: Robert Lemke Oliver of Emory University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-01-23 at 3:00PM |
| Venue: W306 |
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| Abstract: Analytic number theory was borne out of the desire to understand the distribution of the primes. In particular, much of modern analytic number theory can trace its origins to Riemann's seminal 1859 memoir, in which he outlines an attack on the prime number theorem by means of the study of the zeros of what we now call the Riemann zeta function. This approach has been fruitful, and has given rise to a lot of beautiful mathematics, but this hides the dirty truth of analytic number theory: what we can prove, and what we believe to be true, are incredibly far apart. What's more, the best known zero-free region is more than fifty years old. In other words, analytic number theory is in dire need of new ideas. The pretentious view of analytic number theory, as put forward by Granville and Soundararajan, is an attempt at doing this; it is analytic number theory without zeros of L-functions and without analytic continuation. As a substitute, Granville and Soundararajan propose a general study of multiplicative functions, with the goal being to obtain deep structure theorems from which arithmetic results arise as corollaries; as such, it can be seen as finally establishing the context for the elementary proof of the prime number theorem developed by Erdos and Selberg. In this talk, we ask about the structure of functions exhibiting more cancellation than they have a right to. We are able to completely classify such functions in a natural setting, and we establish the right context to consider this question pretentiously. Moreover, as pretentiousness is still a young theory, we outline our vision of what the future holds and what we believe to be the major outstanding questions. This talk is a practice job talk, so feedback would be greatly appreciated. |
| Title: Visibility of Torsors of an Abelian Variety |
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| Seminar: Algebra and Number Theory |
| Speaker: Saikat Biswas of Georgia Tech |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-01-16 at 3:00PM |
| Venue: W306 |
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| Abstract: We survey results that uses the theory of visibility developed by Mazur to study torsors (global as well as local) associated to an abelian variety. |
| Title: Topological and Functional Properties of Proteins in Protein-Protein Interaction Networks |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Concettina Guerra of College of Computing, Georgia Institute of Technology, USA |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2012-12-05 at 12:50PM |
| Venue: W306 |
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| Abstract: I will discuss the connection between the topological properties of proteins in Protein-Protein Interaction (PPI) networks and their biological relevance focusing on hubs, i.e. proteins with a large number of interacting partners. In particular, the following questions will be addressed: Do hub proteins tend to be more essential than non-hub proteins? Do they play a central role in modular organization of the protein interaction network? Are they more evolutionarily conserved? Are there structural properties that characterize hub proteins? I will then present recently developed algorithms for identifying groups of highly connected proteins, or complexes, that are evolutionary conserved. Given the networks of two organisms, the algorithms uncover sub-networks of proteins that relate in biological function and topology of interactions. The discovered conserved sub-networks have a general topology and need not to correspond to specific interaction patterns, so that they more closely fit the models of functional complexes proposed in the literature. |
| Title: Crystalline cohomology of the Igusa tower and families of ordinary cuspforms |
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| Seminar: Algebra and Number Theory |
| Speaker: Bryden Cais of University of Arizona |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2012-12-05 at 3:00PM |
| Venue: W306 |
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| Abstract: We explain a relation between the crystalline cohomology of the Igusa tower and the Iwasawa module of ordinary Lambda-adic cusp forms. By studying the de Rham cohomology of Igusa curves in characteristc p, we will use this relation to give a new proof of the existence of ordinary families of cuspforms. |