Seminars and Colloquia Schedule

On some invariants of arrangements

Series
Algebra Seminar
Time
Monday, November 15, 2010 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Uli Walther – Purdue University
I will discuss D-module type invariants on hyperplane arrangements and their relation to the intersection lattice (when known).

Localized planar patterns

Series
CDSNS Colloquium
Time
Monday, November 15, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Björn Sandstede – Brown University
In this talk, I will discuss localized stationary 1D and 2D structures such as hexagon patches, localized radial target patterns, and localized 1D rolls in the Swift-Hohenberg equation and other models. Some of these solutions exhibit snaking: in parameter space, the localized states lie on a vertical sine-shaped bifurcation curve so that the width of the underlying periodic pattern, such as hexagons or rolls, increases as we move up along the bifurcation curve. In particular, snaking implies the coexistence of infinitely many different localized structures. I will give an overview of recent analytical and numerical work in which localized structures and their snaking or non-snaking behavior is investigated.

Semi-infinite cycles in Floer Theory

Series
Geometry Topology Seminar
Time
Monday, November 15, 2010 - 15:45 for 1 hour (actually 50 minutes)
Location
Room 326, Boyd Graduate Studies (UGA)
Speaker
Max Lipyanskiy – Columbia University

This is the first talk in the Emory-Ga Tech-UGA joint seminar. The second talk will begin at 5:00. (NOTE: These talks are on the UGA campus.)

I will survey the program of realizing various versions of Floer homology as a theory of geometric cycles. This involves the description of infinite dimensional manifolds mapping to the relevant configuration spaces. This approach, which goes back to Atiyah's address at the Herman Weyl symposium, is in some ways technically simpler than the traditional construction based on Floer's version of Morse theory. In addition, it opens up the possibility of defining more refined invariants such as bordism andK-theory.

Dilatation vs self-intersection number for point-pushing pseudo-Anosovs

Series
Geometry Topology Seminar
Time
Monday, November 15, 2010 - 17:00 for 1 hour (actually 50 minutes)
Location
Room 326, Boyd Graduate Studies (UGA)
Speaker
Spencer Dowdall – University of Chicago –
This talk is about the dilatations of pseudo-Anosov mapping classes obtained by pushing a marked point around a filling curve. After reviewing this "point-pushing" construction, I will give both upper and lower bounds on the dilatation in terms of the self-intersection number of the filling curve. I'll also give bounds on the least dilatation of any pseudo-Anosov in the point-pushing subgroup and describe the asymptotic dependence on self-intersection number. All of the upper bounds involve analyzing explicit examples using train tracks, and the lower bound is obtained by lifting to the universal cover and studying the images of simple closed curves.

Comparing the effects of rapidly induced and rapidly evolving traits on predator-prey interactions

Series
Mathematical Biology Seminar
Time
Wednesday, November 17, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 168
Speaker
Michael Cortez – School of Biology, Georgia Tech
Interactions between trophic levels are influenced not only by species abundances, but also by the behavioral, life history, morphological traits of the interacting species as well. Adaptive changes in these traits can be heritable or plastic in nature and both yield phenotypic change that occurs as fast as changes in population abundances. I present how fast-slow systems theory can be used to understand the effects rapid adaptation has on community dynamics in predator-prey systems. This analysis emphasizes that heritable and plastic traits have different effects on community dynamics.

Discrete Littlewood-Paley analysis and multiparameter Hardy spaces

Series
Analysis Seminar
Time
Wednesday, November 17, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Guozhen Lu – Wayne State
In this talk, we will discuss the theory of Hardy spacesassociated with a number of different multiparamter structures andboundedness of singular integral operators on such spaces. Thesemultiparameter structures include those arising from the Zygmunddilations, Marcinkiewcz multiplier. Duality and interpolation theoremsare also discussed. These are joint works with Y. Han, E. Sawyer.

Maximum likelihood estimation of a multidimensional log-concave density

Series
Stochastics Seminar
Time
Thursday, November 18, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Richard Samworth – Statistical Laboratory, Cambridge, UK
If $X_1,...,X_n$ are a random sample from a density $f$ in $\mathbb{R}^d$, then with probability one there exists a unique log-concave maximum likelihood estimator $\hat{f}_n$ of $f$. The use of this estimator is attractive because, unlike kernel density estimation, the estimator is fully automatic, with no smoothing parameters to choose. We exhibit an iterative algorithm for computing the estimator and show how the method can be combined with the EM algorithm to fit finite mixtures of log-concave densities. Applications to classification, clustering and functional estimation problems will be discussed, as well as recent theoretical results on the performance of the estimator. The talk will be illustrated with pictures from the R package LogConcDEAD. Co-authors: Yining Chen, Madeleine Cule, Lutz Duembgen (Bern), RobertGramacy (Cambridge), Dominic Schuhmacher (Bern) and Michael Stewart

Riemann-Roch Theory for Directed Graphs

Series
SIAM Student Seminar
Time
Friday, November 19, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Spencer Backman – School of Mathematics, Georgia Tech
The talk will begin with an elementary geometric discussion of Riemann-Roch theory for sub-lattices of the integer lattice orthogonal to some positive vector. A pair of necessary and sufficient conditions for such a lattice to have the Riemann-Roch property will be presented. By studying a certain chip firing game on a directed graph related to the lattice spanned by the rows of its Laplacian I will describe a combinatorial method for checking whether a directed graph has the Riemann-Roch property. The talk will conclude with a presentation of arithmetical graphs, which after the application of a simple transformation, may be viewed as a special class of directed graphs. Examples from this class demonstrate that either, both or neither of the Riemann-Roch conditions may be satisfied for a directed graph. This is joint work with Arash Asadi.

Curve operators and Toeplitz operators in TQFT.

Series
Geometry Topology Seminar
Time
Friday, November 19, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Julien Marche – Paris VII & Ecole Polytechnique
Topological quantum field theory associates to a surface a sequence of vector spaces and to curves on the surface, sequence of operators on that spaces. It is expected that these operators are Toeplitz although there is no general proof. I will state it in some particular cases and give applications to the asymptotics of quantum invariants like quantum 6-j symbols or quantum invariants of Dehn fillings of the figure eight knot. This is work in progress with (independently) L. Charles and T. Paul.