Upcoming seminars

Upcoming Seminars
Tue
10/21/2014
(today)
4:00pm
Seminar: Algebra
Tropical Independence and Algebraic Curves
David Jensen, University of Kentucky
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
Many questions about an algebraic curve concern the ranks of linear maps between linear series on the curve. Recent years have witnessed the development of a new, combinatorial approach to studying such questions via tropical geometry. We will discuss the basics of this theory, and how it can be used to gain new insight into the geometry of general curves. If time permits, we will discuss joint work with Sam Payne in which we use these techniques to provide a new proof of the Gieseker-Petri Theorem.
Thu
10/23/2014
(in 2 days)
4:30pm
Colloquium: Ergodic Theory and Dynamical Systems
Intermittence and Entropy-Equivalent Measures in Brain Function and Behavior
Arnold Mandell, UCSD School of Medicine
Contact: Vaidy Sunderam, vss@emory.edu
Venue: Mathematics and Science Center, Room W201
Mon
10/27/2014
(in 6 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. Joint work with Yoshi Kohayakawa, Sangjune Lee, Vojta Rodl, and Wojciech Samotij.
Mon
10/27/2014
(in 6 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. Joint work with Yoshi Kohayakawa, Sangjune Lee, Vojta Rodl, and Wojciech Samotij.
Tue
10/28/2014
(in 7 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 7 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.
Mon
11/10/2014
(in 20 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 21 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