Upcoming seminars

Upcoming Seminars
Tue
08/30/2016
(in 2 days)
4:00pm
Seminar: Algebra
Arithmetic Restrictions on Geometric Monodromy
Daniel Litt, Columbia University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
Let $X$ be an algebraic variety over a field $k$. Which representations of $\pi_1(X)$ arise from geometry, e.g. as monodromy representations on the cohomology of a family of varieties over $X$? We study this question by analyzing the action of $Gal(\bar k/k)$ on $\pi_1(X)$, where $k$ is a finite or $p$-adic field. As a sample application of our techniques, we show that if $A$ is a non-constant Abelian variety over $\mathbb{C}(t)$, such that $A[\ell]$ is split for some odd prime $\ell$, then $A$ has at least four points of bad reduction.
Tue
09/06/2016
(in 9 days)
4:00pm
Seminar: Algebra
Positive Polynomials and Varieties of Minimal Degree
Daniel Plaumann, Universitat Konstanz
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of three squares of quadratic forms. We show more generally that every nonnegative quadratic form on a real projective variety $X$ of minimal degree is a sum of dim(X) + 1 squares of linear forms. This provides a new proof for one direction of a recent result due to Blekherman, Smith, and Velasco. We explain the geometry behind this generalization and discuss what is known about the number of equivalence classes of sum-of-squares representations. (Joint work with G. Blekherman, R. Sinn, and C. Vinzant)
Tue
09/13/2016
(in 16 days)
4:00pm
Seminar: Algebra
Hasse principle for multinorm equations
Eva Bayer-Fluckinger, EPFL
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
This is a joint work with Tingyu Lee and Parimala. A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words local norms are global norms. We investigate the norm principle for finite dimensional commutative \'etale algebras over global fields; since such an algebra is a product of separable extensions, this is often called the multinorm principle. Under the assumption that the \'etale algebra contains a cyclic factor, we give a necessary and sufficient condition for the Hasse principle to hold.
Tue
09/20/2016
(in 23 days)
4:00pm
Seminar: Algebra
Generalized Orbifolds in Conformal Field Theory
Marcel Bischoff, Vanderbilt
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
I will introduce the notion of a finite hypergroup. It turns out that certain subfactors (unital inclusions of von Neumann algebras with trivial center) can naturally be seen as such a fixed point. \\ Chiral conformal field theory can be axiomatized as local conformal nets of von Neumann algebras.The orbifold of a conformal net is the fixed point with respect to a finite group of automorphisms. We define a generalized orbifold to be the fixed point of a conformal net under a proper hypergroup action. The fixed point is finite index subnet and it turns out that all finite index subnets are generalized orbifolds. \\ A holomorphic conformal net is a conformal net with trivial representation category. For example, every positive even self-dual lattice gives such a conformal net. The representation category of a generalized orbifold of a holomorphic net is the Drinfeld center of a categorification of the hypergroup. \\ Based on arXiv:1506.02606.
Tue
09/27/2016
(in 30 days)
4:00pm
Seminar: Algebra
Analogs of the Monstrous Denominator Formula for All $X_0(N)$
Ken Ono, Emory
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
Tue
11/01/2016
(in 65 days)
4:00pm
Seminar: Algebra
Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points
Padmavathi Srinivasan, Georgia Institute of Technology
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic curves, the Ogg-Saito formula shows that (the negative of) the Artin conductor equals the minimal discriminant. In the case of genus two curves, equality no longer holds in general, but the two invariants are related by an inequality. We investigate the relation between these two invariants for hyperelliptic curves of arbitrary genus.
Thu
01/12/2017
(in 137 days)
4:00pm
Colloquium: Algebra
Title to be announced
Chelsea Walton, Temple University
Contact: Victoria Powers, vicki@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
TBA