Upcoming seminars

 Upcoming Seminars Tue03/10/2015(in 6 days)4:00pm Seminar: Numerical Analysis and Scientific ComputingAlgebraic Preconditioning of Symmetric Indefinite SystemsMiroslav Tuma, Academy of Sciences of the Czech RepublicContact: Michele Benzi, benzi@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 41.4 kB)Hide abstractSparse 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. Tue03/17/2015(in 13 days)4:00pm Seminar: AlgebraMock theta functions and quantum modular formsLarry Rolen, University of CologneContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 37.8 kB)Hide abstractIn 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. Mon03/23/2015(in 19 days)4:00pm Seminar: CombinatoricsA new upper bound on the size of diamond-free familiesRyan Martin, Iowa State UniversityContact: Dwight Duffus, dwight@mathcs.emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 55.1 kB)Hide abstractIn 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 Mon03/23/2015(in 19 days)4:00pm Seminar: AlgebraComparison of compactifications of modular curvesAndrew Niles, Holy CrossContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 38.4 kB)Hide abstractModular 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. Tue03/24/2015(in 20 days)4:00pm Seminar: AlgebraComparison of compactifications of modular curvesAndrew Niles, Holy CrossContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 38.7 kB)Hide abstractModular 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. Tue03/31/2015(in 27 days)4:00pm Seminar: AlgebraAn Effective Log-Free Zero Density Estimate for Automorphic $L$-functions and the Sato-Tate ConjectureJesse Thorner, EmoryContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 53.9 kB)Hide abstractThe 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. Thu04/09/2015(in 36 days)4:00pm Seminar: AlgebraAthens-Atlants joint number theory seminarDick Gross and Ted Chinburg, Harvard and PennVenue: At UGADownload printable flyer (PDF, 22.3 kB) Tue04/14/2015(in 41 days)4:00pm Seminar: AlgebraTitle to be announcedAbbey Bourdon, UGAContact: David Zurieck-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 19.2 kB) Tue04/21/2015(in 48 days)4:00pm Seminar: AlgebraTitle to be announcedNoah Giansiracusa, UGAContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 19 kB)