All Seminars
| Title: Harmonic Maass forms and periods |
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| Seminar: Algebra |
| Speaker: Jan Hendrik Bruinier of Technische Universität Darmstadt |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2010-12-02 at 1:00PM |
| Venue: MSC E406 |
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| Abstract: The Fourier coefficients of automorphic forms often encode important arithmetic information, such as for instance representation numbers of quadratic forms, divisor sums, and numbers of points on elliptic curves over finite fields. In our talk we consider the coeficients of harmonic Maass forms of weight 1/2. We show that their coefficients are given by the periods of certain algebraic differentials on modular curves. As an example we consider rational elliptic curves. |
| Title: Questions on Serre's open image theorem |
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| Seminar: Algebra |
| Speaker: David Zywina of University of Pennsylvania |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2010-12-02 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: Elliptic curves (smooth curves of genus 1 with a fixed point) are fundamental objects in number theory and one fruitful way to study them is through their Galois representations. These representations arise by considering the natural Galois action on the torsion points of the curve. For a non-CM elliptic curve defined over a number field, a famous theorem of Serre says that the Galois action on the torsion points is "almost as large as possible". After some review and motivation, we will state a precise version of Serre's theorem. This will lead us to a series of natural questions; for example, how large/small can this action be, and what are the possible actions? We will explain some recent results that give partial answers and, time permitting, give some speculation on what one might hope to be true. |
| Title: Iterative linear solvers for PDE-constrained Optimization problems |
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| Colloquium: Numerical Analysis and Scientific Computing |
| Speaker: Andrew J. Wathen of Oxford University |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2010-12-02 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: The numerical approximation of Partial Differential Equation (PDE) problems leads typically to large dimensional linear or linearised systems of equations. For problems where such PDEs provide only a constraint on an Optimization problem (so-called PDE-constrained Optimization problems), the systems are many times larger in dimension. We will discuss the solution of such problems by preconditioned iterative techniques in particular where the PDEs in question are the steady Stokes equations describing incompressible fluid flow and some very recent work on the time-dependent diffusion equation. |
| Title: Tropical and Berkovich analytic curves |
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| Seminar: Algebra and Number Theory |
| Speaker: Matt Baker of Georgia Institute of Technology |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2010-11-30 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: We will discuss the relationship between a Berkovich analytic curve over a complete and algebraically closed non-Archimedean field and its tropicalizations, paying special attention to the natural metric structure on both sides. This is joint work with Sam Payne and Joe Rabinoff. |
| Title: Latex for Dummies |
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| Type: General interest, Math and CS |
| Speaker: Hernando Bermudez of Emory University |
| Contact: Veronica Bustamante, vmejia@emory.edu |
| Date: 2010-11-22 at 4:15PM |
| Venue: MSC W201 |
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| Abstract: A beginner/intermediate level seminar on the basics of latex for mathematics document and article writing. Graduate and undergraduates are especially welcomed! |
| Title: From Kinsey to Anonymization: Approaches to Preserving the Privacy of Survey Participants |
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| Seminar: Computer Science |
| Speaker: Raquel Hill of Indiana University |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2010-11-19 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: Preserving the privacy of medical related data becomes even more challenging when the data is obtained from longitudinal studies that were designed to create unique profiles of individual participants. These studies may create participant profiles where each corresponding record is so unique that traditional anonymization techniques cannot be used to generalize and de-identify the record. Therefore sharing of this data with external parties becomes a lengthy process of negotiating specific use agreements. In some cases, sharing of the data among researchers within the organization that owns the data also risks privacy. Even when traditional identifiers are removed, the uniqueness of these records makes re-identification probable for anyone who has access to the complete record. During this talk, I will present a case study of a Kinsey dataset and discuss the challenges of protecting high dimensional data.\\ \\ Bio: Raquel Hill is an Assistant Professor of Computer Science in the School of Informatics and Computing. Her primary research interests are in the areas of trust and security for distributed and pervasive computing environment and privacy of medical related data. Dr. Hill’s research is funded by the National Science Foundation and the Center for Applied CyberSecurity Research (CACR). She holds B.S. and M.S. degrees in Computer Science from Georgia Tech and a Ph.D. in Computer Science from Harvard University. |
| Title: Fractional perfect matchings in hypergraphs |
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| Seminar: Combinatorics |
| Speaker: Andrzej Rucinski of Adam Mickiewicz University, Poznan, Poland and Emory University, Atlanta |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2010-11-19 at 4:00PM |
| Venue: W306 |
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| Abstract: A perfect matching in a k-uniform hypergraph H=(V,E) on n vertices is a set of n/k disjoint edges of H, while a fractional perfect matching in H is a function w assigning to each edge of H a real number from [0,1] in such a way that for each vertex v the sum of the weights of the edges containing v equals 1. Given n>3 and 2< k< n, let m be the smallest integer such that whenever the minimum vertex degree in H is at least m then H contains a perfect matching, and let m* be defined analogously with respect to fractional perfect matchings. Clearly, m* does not exceed m. We prove that for large n, m and m* are asymptotically equal, and suggest an approach to determine m*, and consequently m, utilizing the Farkas Lemma. This is a joint work with Vojta Rodl. |
| Title: Filling invariants at infinity |
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| Seminar: Topology |
| Speaker: Pallavi Dani of Louisiana State University |
| Contact: Aaron Abrams, abrams@mathcs.emory.edu |
| Date: 2010-11-17 at 2:00PM |
| Venue: MSC E408 |
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| Abstract: The $k$-dimensional isoperimetric function of a space captures the difficulty of filling $k$-spheres with $(k+1)$-balls in the space. Once one understands the isoperimetric functions of a space, it is interesting to study how they change when an obstruction is introduced. In this spirit, Brady and Farb introduced the notion of ``filling invariants at infinity'', by considering the volume required to fill spheres in Hadamard manifolds, provided both the sphere and the filling are far from a fixed basepoint. I will talk about a group theoretic version of this concept, and describe joint work with Aaron Abrams, Noel Brady, Moon Duchin and Robert Young on the case of right-angled Artin groups. |
| Title: Projective modules over an affine algebra |
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| Seminar: Algebra and number theory |
| Speaker: Ravi A. Rao of Tata Institute of Fundamental Research |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2010-11-16 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: The study of finitely generated projective modules along the lines indicated by J-P.~Serre and H.~Bass is outlined; its continuation by the three step Eisenbud-Evans program is then described. The development of the first part of the EE-program by Mohan Kumar, Pavaman Murthy, Madhav Nori's Euler classes vision and Bhatwadekar-Sridharan's completion of it, the functorial French approach of Barge-Morel, and Morel's later ideas are touched. The thesis of Andrei Suslin which touches on the second part of the EE program, his conjecture at his Helsinki talk in 1978, and Jean Fasel's breakthrough work on threefolds, and recent developments of the work of Fasel-Rao-Swan in higher dimension are surveyed. |
| Title: Commensurability classes of hyperbolic knot complements |
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| Seminar: Topology |
| Speaker: Neil Hoffman of University of Texas |
| Contact: Aaron Abrams, abrams@mathcs.emory.edu |
| Date: 2010-11-10 at 2:00PM |
| Venue: MSC E408 |
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| Abstract: Two manifolds are commensurable if they share a common finite sheeted cover. In 2008, Reid and Walsh conjectured that there are at most 3 hyperbolic knot complements in a given commensurability class. Recently, Boileau, Boyer, Cebanu, and Walsh have shown that the conjecture holds in the case where the knot complements do not admit hidden symmetries. After introducing the necessary ideas, we will talk about the case where we assume hidden symmetries exist. |