All Seminars
| Title: Pathologies of the Brauer-Manin obstruction |
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| Seminar: Algebra |
| Speaker: Jean-Louis Colliot Thelene of Paris-Sud |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-10-09 at 4:00PM |
| Venue: W306 |
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| Abstract: In 1970, Manin used the Brauer group of varieties to account for most known counterexamples to the Hasse principle over number field. In 1999, A. Skorobogatov produced the first unconditional examples of varieties without rational point not accounted for by the Brauer-Manin obtruction. Simpler examples were produced by B. Poonen in 2010. We present even simpler examples. This is joint work with A. P\'al and A. Skorobogatov. |
| Title: Expander families and variation of Galois representations |
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| Seminar: Algebra |
| Speaker: Chris Hall of University of Wyoming |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-10-02 at 4:00PM |
| Venue: W306 |
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| Abstract: Given a pair of curves U,V over the complex numbers, one can associate to a finite unramified map $V \to U$ a finite Cayley-Schreier graph. In this talk we consider families of maps $V_i \to U$ indexed by a parameter i such that the family of associated graphs is an expander family. As we will explain, the expander hypothesis has remarkable geometric implications, e.g. the set of $V_i$ such that the gonality of $V_i$ is less than your favorite positive number N is finite. We will also explain some of the arithmetic implications, e.g. for all but finitely many $V_i$, there are only many points on $V_i$ defined over some extension of K of degree at most N. As one an application, we can derive results on the variation of Galois representations in a one-parameter family of abelian varieties defined over a number field. |
| Title: Rational and quadratic preperiodic points for quadratic polynomials |
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| Seminar: Algebra |
| Speaker: Xander Faber of Joining IDA/CCS |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-09-25 at 4:00PM |
| Venue: W306 |
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| Abstract: Let f be a quadratic polynomial with coefficients in a number field K. The action of f on the affine line induces a dynamical system. Many researchers have speculated on and provided evidence for uniform bounds on the number of K-rational points with finite orbit under this action: such points are called preperiodic. I will survey what is expected and what is known, and then I will describe some new contributions by myself and my collaborators John Doyle and David Krumm when K=Q or when K is a quadratic number field. |
| Title: A Space-Time Finite Element Method for PDEs posed on Eveolving Surfaces |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Maxim A. Olshanskii of University of Houston |
| Contact: James Munch, jmunch@emory.edu |
| Date: 2013-09-23 at 4:00PM |
| Venue: W304 |
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| Abstract: |
| Title: A problem of Erdos and Sós on 3-graphs |
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| Seminar: Combinatorics |
| Speaker: Jan Volec of University of Warwick |
| Contact: Vojtech Rodl, rodl@mathcs.emory.edu |
| Date: 2013-09-23 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: We show that for every epsilon > 0 there exist delta > 04 and natural number n_0 such that every 3-uniform hypergraph on n >= n_0 vertices with the property that every k-vertex subset, where k is at least delta*n, induces at least (1/4 + epsilon)*(k choose 3) edges, contains K4- as a subgraph, where K4- is the 3-uniform hypergraph on 4 vertices with 3 edges. This question was originally raised by Erdos and Sos. The constant 1/4 is the best possible. |
| Title: The Weierstrass mock modular form and modular elliptic curves |
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| Seminar: Algebra |
| Speaker: Ken Ono of Emory |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-09-11 at 4:00PM |
| Venue: W306 |
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| Abstract: No abstract. |
| Title: On a Conjecture of Thomassen |
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| Seminar: Combinatorics |
| Speaker: Domingos Dellamonica of Emory University and the University of Sao Paulo |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-09-06 at 4:00PM |
| Venue: W306 |
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| Abstract: About thirty years ago, Thomassen announced the following conjecture in graph theory: for all positive integers k, g there exists some D such that any graph with average degree at least D must contain a subgraph which has average degree at least k AND at the same time does not contain any cycle of length g or smaller. The conjecture is still open but it is known to be true with some additional constraints on the graph or when g < 6. This seminar will present joint work with Daniel Martin, Vaclav Koubek, and Vojta Rodl. |
| Title: A determining condition of Hilbert modular forms |
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| Seminar: Algebra |
| Speaker: Yuuki Takai of Keio University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-09-05 at 4:00PM |
| Venue: W306 |
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| Abstract: The elliptic holomorphic modular forms of weight $k$ and level $\Gamma_1(N)$ are determined by the first $(k/12)[\Gamma_1(1): \Gamma_1(N)]$ Fourier coefficients. The mod $\ell$ analogue of the fact is called Sturm's theorem. In this talk, I will give a generalization of the first fact and Sturm's theorem for Hilbert modular forms. To prove them, I use geometric properties of some compacitifications of Hilbert modular varieties. |
| Title: Mathematical Models and Numerical Methods for Wavefront Reconstruction |
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| Defense: Dissertation |
| Speaker: Qing Chu of Emory University |
| Contact: Qing Chu, chu@emory.edu |
| Date: 2013-08-27 at 11:00AM |
| Venue: MSC W301 |
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| Abstract: Obtaining high resolution images of space objects from ground based telescopes is challenging, and often requires computational post processing methods to remove blur caused by atmospheric turbulence. In order for an image deblurring (deconvolution) algorithm to be effective, it is important to have a good approximation of the blurring operator. In space imaging, the blurring operator is defined in terms of the wavefront of light, and how it is distorted as it propagates through the atmosphere.\\ \\ In this thesis we consider new mathematical models and algorithms to reconstruct the wavefront, which requires solving a large scale ill-posed inverse problem. We show that by exploiting and fusing information from multiple measurements, we are able to obtain better reconstructed wavefronts than existing methods. In addition, we present results of a parallel implementation utilizing the Trilinos project. |
| Title: Maass forms and quantum modular forms |
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| Defense: Dissertation |
| Speaker: Larry Rolen of Emory University |
| Contact: Larry Rolen, lrolen@emory.edu |
| Date: 2013-06-26 at 1:00PM |
| Venue: W304 |
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| Abstract: This thesis describes several new results in the theory of harmonic Maass forms and related objects. Maass forms have recently led to a flood of applications throughout number theory and combinatorics, especially following their development by the work of Bruinier and Funke and the interpretation of Ramanujan's mock theta functions in this framework by Zwegers. Here, we will prove results on integrality of singular moduli and we will revisit Ramanujan's original definition of a mock theat function. Furthermore, we will construct a new example of a quantum modular form using ``strange'' series and sums of tails formulas. |