Upcoming seminars

Upcoming Seminars
Tue
03/10/2015
(in 5 days)
4:00pm
Seminar: Numerical Analysis and Scientific Computing
Algebraic Preconditioning of Symmetric Indefinite Systems
Miroslav Tuma, Academy of Sciences of the Czech Republic
Contact: Michele Benzi, benzi@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W301
Sparse symmetric indefinite linear systems of equations arise in many practical applications. An iterative method is frequently the method of choice to solve such systems but a system transformation called preconditioning is often required for the solver to be effective. In the talk we will deal with development of incomplete factorization algorithms that can be used to compute high quality preconditioners. We will consider both general indefinite systems and saddle-point problems. Our approach is based on the recently adopted limited memory approach (based on the work of Tismenetsky, 1991) that generalizes recent work on incomplete Cholesky factorization preconditioners. A number of new ideas are proposed with the goal of improving the stability, robustness and efficiency of the resulting preconditioner. For general indefinite systems, these include the monitoring of stability as the factorization proceeds and the use of pivot modifications when potential instability is observed. Numerical experiments involving test problems arising from a range of real-world applications are used to demonstrate the effectiveness of our approach and comparisons are made with a state-of-the-art sparse direct solver. The talk will be based on joint work with Jennifer Scott, Rutherford Appleton Laboratory.
Tue
03/17/2015
(in 12 days)
4:00pm
Seminar: Algebra
Mock theta functions and quantum modular forms
Larry Rolen, University of Cologne
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
In this talk, I will describe several related recent results related to mock theta functions, which are functions described by the Indian mathematician Ramanujan shortly before his death in 1920. These functions have very recently been understood in a modern framework thanks to the work of Zwegers and Bruinier-Funke. Here, we will revisit the original writings of Ramanujan and look at his original conception of these functions, which gives rise to a surprising picture connecting important objects such as generating functions in combinatorics and quantum modular forms.
Mon
03/23/2015
(in 18 days)
4:00pm
Seminar: Combinatorics
A new upper bound on the size of diamond-free families
Ryan Martin, Iowa State University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W302
In the Boolean lattice, we say that a family ${\mathcal F}$ has a diamond as a (weak) subposet if there are four distinct subsets A, B, C, D such that $A\subset B\subset D$ and $A\subset C\subset D$. There has been a great deal of recent activity on the size of families in the Boolean lattice with no (weak) copy of a fixed subposet. However, the maximum size of a diamond-free family is still unknown, even asymptotically.\\ \\ Using a method due to Manske and Shen, we have obtained a new upper bound for the size of a diamond-free family in the $n$-dimensional Boolean lattice of $(2.2067+o(1)){n\choose\lfloor n/2\rfloor}$. This improves the previous bound of $2.25$, which was due to the authors and Michael Young.\\ \\ This is joint work with Lucas Kramer, Carroll College
Mon
03/23/2015
(in 18 days)
4:00pm
Seminar: Algebra
Comparison of compactifications of modular curves
Andrew Niles, Holy Cross
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
Modular curves and their compactifications are of fundamental importance in number theory. A key property of modular curves is that they are moduli spaces: their points classify certain geometric objects (elliptic curves equipped with level structure). Similarly, it was shown by Deligne-Rapoport that compactified modular curves may be viewed as moduli spaces for "generalized" elliptic curves equipped with level structure. It was shown by Abramovich-Olsson-Vistoli that modular curves naturally lie inside certain complicated moduli spaces, classifying "twisted stable maps" to certain algebraic stacks. These moduli spaces turn out to be complete, so the closure of a modular curve inside such a moduli space gives a compactification of the modular curve. In this talk I explain how these new compactifications can themselves be viewed as moduli spaces, and I compare them to the "classical" compactified modular curves considered by Deligne-Rapoport.
Tue
03/24/2015
(in 19 days)
4:00pm
Seminar: Algebra
Comparison of compactifications of modular curves
Andrew Niles, Holy Cross
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
Modular curves and their compactifications are of fundamental importance in number theory. A key property of modular curves is that they are moduli spaces: their points classify certain geometric objects (elliptic curves equipped with level structure). Similarly, it was shown by Deligne-Rapoport that compactified modular curves may be viewed as moduli spaces for "generalized" elliptic curves equipped with level structure. It was shown by Abramovich-Olsson-Vistoli that modular curves naturally lie inside certain complicated moduli spaces, classifying "twisted stable maps" to certain algebraic stacks. These moduli spaces turn out to be complete, so the closure of a modular curve inside such a moduli space gives a compactification of the modular curve. In this talk I explain how these new compactifications can themselves be viewed as moduli spaces, and I compare them to the "classical" compactified modular curves considered by Deligne-Rapoport.
Tue
03/31/2015
(in 26 days)
4:00pm
Seminar: Algebra
An Effective Log-Free Zero Density Estimate for Automorphic $L$-functions and the Sato-Tate Conjecture
Jesse Thorner, Emory
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
The classical techniques used to put primes in intervals of the form $[x,2x]$ are insufficient to put primes in intervals of the form $[x,x+x^{1-\delta}]$ for any $\delta>0$, or to find the least prime in an arithmetic progression $a\bmod q$. Such problems are easily answered assuming the Generalized Riemann Hypothesis, but they can be answered unconditionally using very detailed information about the location and density of zeros of Dirichlet $L$-functions in regions of the critical strip. We will discuss effective results on the distribution of general automorphic $L$-functions in the critical strip and use these distribution results to study generalizations of the aforementioned problems in the context of the Sato-Tate Conjecture.
Thu
04/09/2015
(in 35 days)
4:00pm
Seminar: Algebra
Athens-Atlants joint number theory seminar
Dick Gross and Ted Chinburg, Harvard and Penn
Venue: At UGA
Tue
04/14/2015
(in 40 days)
4:00pm
Seminar: Algebra
Title to be announced
Abbey Bourdon, UGA
Contact: David Zurieck-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304
Tue
04/21/2015
(in 47 days)
4:00pm
Seminar: Algebra
Title to be announced
Noah Giansiracusa, UGA
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W304