Upcoming seminars

Upcoming Seminars
(in 2 days)
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.
(in 3 days)
Seminar: Numerical Analysis and Scientific Computing
Approximating spectral densities of large matrices: old and new
Lin Lin, UC Berkeley
Contact: Michele Benzi, benzi@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W306
In physics, it is sometimes desirable to compute the so-called Density Of States (DOS), also known as the spectral density, of a Hermitian matrix A. The spectral density can be viewed as a probability density distribution that measures the likelihood of finding eigenvalues near some point on the real line. The most straightforward way to obtain this density is to compute all eigenvalues. But this approach is generally costly and wasteful, especially for matrices of large dimension. In many cases, the only affordable operation is matrix-vector multiplication. In this talk I will define the problem of estimating the spectral density carefully, and discuss a few known algorithms based on stochastic sampling, in particular, those using the kernel polynomial method and the Lanczos method, for estimating the spectral density. The accuracy of stochastic algorithms converge as $O(1\sqrt{N_v})$, where $N_v$ is the number of stochastic vectors. I will also talk about recent progresses of stochastic estimation of spectral densities with convergence rate much faster than $O(1\sqrt{N_v})$ using a relatively high degree of polynomials and modest choice of $N_v$. (Joint work with Yousef Saad and Chao Yang)
(in 4 days)
Defense: Dissertation
On Chorded Cycles
Megan Cream, Emory University
Contact: Megan Cream, mcream@emory.edu
Venue: Mathematics and Science Center, Room W303
Historically, there have been many results concerning sufficient conditions for implying certain sets of cycles in graphs. My thesis aims to extend many of these well known results to similar results on sets of {\it chorded} (and sometimes even {\it doubly chorded}) cycles. In particular, we consider the minimum degree, $\delta(G)$ and a Ore-type degree sum condition, $\sigma_2(G)$ of a graph $G$, sufficient to guarantee the existence of $k$ vertex disjoint chorded cycles, often containing specified elements of the graph, such as certain vertices or edges. Further, we extend a result on vertex disjoint cycles and chorded cycles to an analogous result on vertex disjoint cycles and {\it doubly} chorded cycles. We define a new graph property called chorded pancyclicity, and investigate a density condition and forbidden subgraphs in claw-free graphs that imply this new property. Specifically, we forbid certain paths and triangles with pendant paths. This is joint work with Dongqin Cheng, Ralph Faudree, Ron Gould, and Kazuhide Hirohata.
(in 11 days)
Seminar: Algebra
Athens-Atlants joint number theory seminar
Dick Gross and Ted Chinburg, Harvard and Penn
Venue: At UGA
(in 12 days)
Seminar: Algebra
Knots and Brauer groups of curves
Ted Chinburg, Penn
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W302
There has been a great deal of research over the last 20 years on invariants of knots on one hand and on Brauer groups of curves on the other. The goal of this talk is to link these two subjects. This is joint work with Alan Reid and Matt Stover.
(in 19 days)
Seminar: Combinatorics
Extending Partial Geometric Representations of Graphs
Jan Kratochvil, Charles University, Prague
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Venue: Mathematics and Science Center, Room W303
Intersection-defined classes of graphs are intensively studied for their applications and interesting properties. Many of them allow polynomial-time algorithms for otherwise computationally hard problems such as independent set, clique or coloring problems. And many of them can be recognized in polynomial time. In fact the polynomial-time algorithms often need a representation to be given or constructed as the initial step. The rather natural question of extending a partial representation has been studied only recently. It falls into the more general paradigm of extending a partial solution of a problem. Sometimes a global solution can be reached by incremental steps from a partial one in polynomial-time, but in many cases an otherwise easy problem may become hard. Examples of such behavior can be found for instance in graph colorings (e.g., deciding if a partial edge-coloring of a cubic bipartite graph can be extended to a full 3-coloring of it is NP-complete, though it is well known that every cubic bipartite graph is 3-edge-colorable and such a coloring can be found in polynomial time). In this talk we survey the known results about the computational complexity of extending partial geometric representations of graphs.