All Seminars
| Title: Vanishing and identities of conformal blocks divisors. |
|---|
| Seminar: Algebra |
| Speaker: Angela Gibney of UGA |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-03-22 at 4:00PM |
| Venue: W304 |
| Download Flyer |
| Abstract: In this talk I will give a tour of recent results and open problems about vector bundles of conformal blocks on the moduli space of curves. I will discuss how these results fit into the context of some of the open problems about the binational geometry of the moduli space. |
| Title: Torsion subgroups of rational elliptic curves over the compositum of all cubic fields. |
|---|
| Seminar: Algebra |
| Speaker: Drew Sutherland of MIT |
| Contact: David Zureick-Brown, dab@mathcs.emory.edu |
| Date: 2016-03-18 at 4:00PM |
| Venue: MSC W303 |
| Download Flyer |
| Abstract: Let E/Q be an elliptic curve and let Q(3^infty) denote the compositum of all cubic extensions of Q. While the group E(3^infty) is not finitely generated, one can show that its torsion subgroup is finite; this holds more generally for any Galois extension of Q that contains only finitely many roots of unity. I will describe joint work with Daniels, Lozano-Robledo, and Najman, in which we obtain a complete classification of the 20 torsion subgroups that can and do occur, along with an explicit description of the elliptic curves E/Q that realize each possibility (up to twists). This is achieved by determining the rational points on a corresponding set of modular curves and relies on several recent results related to the mod-n Galois representations attached to elliptic curves over Q. |
| Title: Gerbes, twisted sheaves and their relation to the Brauer group(s) of schemes |
|---|
| Seminar: Algebra |
| Speaker: Max Lieblich of University of Washington |
| Contact: Raman Parimala, parimala@mathcs.emory.edu |
| Date: 2016-03-17 at 1:00PM |
| Venue: MSC E406 |
| Download Flyer |
| Abstract: |
| Title: Gerbes, twisted sheaves and their relation to the Brauer group(s) of schemes |
|---|
| Seminar: Algebra |
| Speaker: Max Lieblich of University of Washington |
| Contact: Raman Parimala, parimala@mathcs.emory.edu |
| Date: 2016-03-16 at 1:00PM |
| Venue: MSC E408 |
| Download Flyer |
| Abstract: |
| Title: Integral points on groupic varieties (work of Yang Cao and Fei Xu) |
|---|
| Seminar: Algebra |
| Speaker: J.L. Colliot-Thelene of CNRS et Universite Paris-Sud |
| Contact: David Zureick-Brown, dab@mathcs.emory.edu |
| Date: 2016-03-15 at 4:00PM |
| Venue: W304 |
| Download Flyer |
| Abstract: Summary : Let G be a connected linear algebraic group over a field k. By definition, a groupic G-variety X over k is a smooth (left) G-variety with a dense open set isomorphic to G with its (left) action on itself. Let X be a groupic G-variety over a number field. Under a suitable noncompactness hypothesis for the simple factors of the semisimple part of G at the archimedean places, Cao and Xu show that the Brauer-Manin obstruction is the only obstruction to strong approximation for X off the archimedean places. The proof builds upon the case X=G (handled in earlier papers by Xu and the speaker, Harari, Demarche). The toric case (G is a torus) was already handled in a previous paper by Cao and Xu. For X projective, the statement is a weak approximation result and the theorem has been known for a long time (Sansuc).. The proof of the strong approximation result for an arbitrary groupic G-variety X involves novel arguments, both geometric and arithmetic. |
| Title: Genus one curves in Severi-Brauer Varieties. |
|---|
| Seminar: Algebra |
| Speaker: David Saltman of IDA |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-03-15 at 5:00PM |
| Venue: W304 |
| Download Flyer |
| Abstract: Let A/F be a division algebra of degree 3, and X its Severi-Brauer variety which is a form of the projective plane. The linear system of cubic curves is defined on X, and so we can let C \subset X be one such. If C is a nonsingular such curve, then C is a genus one curve with Jacobian E, an elliptic curve. The question we address is the one asked by Asher Auel, namely, which E arise. We give an answer that depends on the structure of A. |
| Title: Some Ramsey-type Theorems |
|---|
| Defense: Dissertation |
| Speaker: Troy Retter of Emory University |
| Contact: Troy Retter, tretter@emory.edu |
| Date: 2016-03-02 at 11:30AM |
| Venue: MSC E408 |
| Download Flyer |
| Abstract: See downloadable flyer. |
| Title: Beyond the moduli of marked rational curves |
|---|
| Seminar: Algebra |
| Speaker: Patricio Gallardo of UGA |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-03-01 at 4:00PM |
| Venue: W304 |
| Download Flyer |
| Abstract: We describe several generalizations of the moduli space of marked rational curves, their combinatorial structure and construction methods. In particular, we report joint work with Noah Giansiracusa in which we revisit the smooth configuration space compactifying n distinct points in affine space up to translation and homothety. I will also report joint work with Kenny Ascher in understanding a good locus inside the moduli space of weighted line arrangements constructed by V. Alexeev. |
| Title: Matrix Completion and Free Resolutions |
|---|
| Seminar: Algebra |
| Speaker: Rainer Sinn of Georgia Tech |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-02-23 at 4:00PM |
| Venue: W304 |
| Download Flyer |
| Abstract: I will discuss a matrix completion problem arising in combinatorial statistics and explain how we can use results in algebraic geometry to understand it better. The object linking the two different areas is the cone of sums of squares and its properties as a convex cone. |
| Title: A Mathematician's Guide to Working with Engineers |
|---|
| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Steven Hamilton of Oak Ridge National Laboratory |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2016-02-19 at 1:00PM |
| Venue: W306 |
| Download Flyer |
| Abstract: Problems in computational science often require interdisciplinary collaboration. Differences in the vocabulary, skills, and expectations of different fields can make these collaboration efforts extremely challenging. In this talk, I will discuss strategies for working on interdisciplinary teams that can contribute to the success (or failure) of a project. In particular, I will discuss some common pitfalls that I have seen mathematicians fall into when working with engineers and domain scientists. |