Upcoming seminars

Upcoming Seminars
Mon
10/27/2014
(in 2 days)
4:00pm
Seminar: Combinatorics
On the Number of $B_h$ Sets of a Given Size
Domingos Dellamonica, Sao Paulo
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W303
For an integer h bigger or equal to 2, a $B_h$ set is a set of integers with the property that every collection containing h of its elements yield a unique sum (and repetitions are allowed). For $h = 2$, such sets are also called Sidon sets. In this talk we will describe our recent results on estimating $F(n, s, h)$, which we define as the number of $B_h$ sets of cardinality s containing integers from $[n] = {1, 2, ..., n}$. It is not hard to see that for $s > n^(1/h)$, we have $F(n, s, h) = 0$. Indeed, in this case there are more h-sums than possible outcomes for the sums. On the other hand, there are constructions of B-h sets having cardinality $c.n^(1/h)$, (with c depending on h only) hence we shall estimate the behavior of $F(n, s, h)$ for s up to $O( n^(1/h))$. Our counting shows the existence of a surprising threshold function $T(n)$: for values of $s << T(n)$, the B-h sets are abundant while for $s >> T(n)$ the B-h sets become very rare. More precisely, we show that $T(n) ~ n^{(1 + o(1))/(2h - 1)}$ and establish fairly precise estimates of $F(n, s, h)$ for the entire range of s.
Tue
10/28/2014
(in 3 days)
4:00pm
Seminar: Algebra
The genus of a division algebra
Igor Rapinchuk, Harvard
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
In this talk, I will address the following problem. Suppose D and D' are central division algebras over a field K. What can be said about D and D' if they have the same maximal subfields? I will discuss various motivations for this question and recent results. I will also mention some generalizations to arbitrary absolutely almost simple algebraic groups. This is joint work with V. Chernousov and A. Rapinchuk.
Tue
10/28/2014
(in 3 days)
5:00pm
Seminar: Algebra
Embeddings of maximal tori in classical groups and explicit Brauer–Manin obstruction
Eva Bayer, EPFL
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
This is a joint work with Parimala and Ting–Yu Lee. Embeddings of maximal tori into classical groups over global fields of characteristic $\neq$ 2 are the subject matter of several recent papers (for instance by Prasad and Rapinchuk, Fiori, Lee), with special attention to the Hasse principle. The aim of this talk is to describe a complete criterion for the Hasse principle to hold, and to give necessary and sufficient conditions for a classical group to contain a maximal torus of a given type. The embedding problem will be described in terms of embeddings of \'etale algebras with involution into central simple algebras with involution.
Fri
10/31/2014
(in 6 days)
12:00pm
Seminar: Numerical Analysis and Scientific Computing
Regularization by Krylov-Tikhonov methods
Silvia Gazzola, University of Padova
Contact: James Nagy, nagy@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W301
Krylov subspace methods have always played a central role in the iterative regularization of large-scale linear discrete ill-posed problems, which arise in a variety of scientific and engineering applications; we are particularly interested in image deblurring and denoising issues. In addition to a purely iterative approach to regularization, some "hybrid" Krylov-Tikhonov methods have also been derived, which merge an iterative and a variational (Tikhonov-like) approach to regularization. The purpose of this talk is to survey some classical Krylov and Krylov-Tikhonov methods, and to present some original ones, comparing their performance on some meaningful test problems. Particular emphasis will be posed on the strategies to be employed to set the regularization parameters and matrices in the Krylov-Tikhonov framework.
Mon
11/10/2014
(in 16 days)
4:00pm
Seminar: Analysis and Differential Geometry
Mathematical problems in visual sciences
Professor Jacob Rubinstein, Israel Institute of Technology - Technion
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W303
This talk should be of general interest to mathematicians and researchers in visual science and ophthalmology. It will be accessible to graduate students.
Tue
11/11/2014
(in 17 days)
4:00pm
Seminar: Algebra
Title to be announced
John Duncan, Case Western
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306