Seminar Schedule
March 3 -7, 2008
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, March 3, 2008
VIGRE – Algebraic Geometry
2:15pm, Room 222
Topology
2:30-3:30, Room 303
Speaker: Elisenda Grigsby (Columbia)
Title of talk: Grid diagrams and Legendrian Links in Lens Spaces
Abstract: The data of a knot in $S3$ can be encoded combinatorially via a {\it grid diagram}. First seen in work of Brunn from the 1890's and further developed by many others, grid diagrams have enjoyed an abundance of recent attention, due primarily to their connection to combinatorial Heegaard Floer homology and contact geometry.
In joint work with Ken Baker and Matt Hedden, I extended the notion of grid diagrams to include a description for all links in lens spaces, culminating in a combinatorial method to compute the knot Floer homology of a lens space knot.
In this talk, I will discuss joint work in progress with Ken Baker which clarifies the connection between lens space grid diagrams and lens space contact geometry. In particular, a grid diagram for a lens space link corresponds naturally to a Legendrian representative of the link with respect to the universally tight contact structure. Our hope is that this connection can be exploited to address the {\it Berge conjecture}, which claims to catalog all knots in lens spaces that admit $S3$ surgeries.
3:45-4:45
Speaker: Tao Li (Boston College)
Title of talk: Heegaard splittings of amalgamated 3-manifolds and distance in the curve complex.
Abstract: We show that if two 3-manifolds with connected boundary are glued together using a map of high complexity, then the low-genus Heegaard splittings of the resulting closed 3-manifold are standard in a certain sense. The complexity of the gluing map is defined using curve complex and the boundary curves of certain properly embedded surfaces in the two 3-manifolds.
Algebra
2:30pm, Room 410
No Meeting this week
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Academic Professional Candidate
3:30pm, Room 304
Candidate: Palanivel Manoharan, Penn State University
During this interview, the candidate will give a model precalculus "lesson", in place of a colloquium talk. There will be opportunities for both Tenure-track faculty and Instructors to meet and socialize with the candidates, and to give input into the selection process.
TUESDAY, March 4, 2008
VIGRE - Graduate Student Seminar
2:00pm, Room 304
Speaker: Brandon Samples, University of Georgia
Title of talk: Report of Vigre Reasearch Group on Algebraic Graph Theory
Abstract: A graph on n vertices has a matrix associated to it called the Laplacian matrix of a graph G, which we can call L(G). We considered the torsion subgroup of the group Z^n/Im(L(G)), which has interesting properties such as its order represents the number of spanning trees of the graph. I will discuss my exploration into a particular category of graphs called the Paley Graphs. Last year, the graph theory group completely understood the general structure of the group associated to the Paley graph, so I modified the question for powers of primes (particularly p2 and p3). I will give a general discussion about some basic computer computations involving matrices I did with Maple, and discuss what we had conjectured the structure of the group was by the close of the semester.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
Mathematical Physics
3:30pm, Room 303
Speaker: Justin Manning and Robert Varley, University of Georgia
Title of talk: Differentiability of the pressure function in ergodic theory
Academic Professional Candidate
3:30pm, Room 304
Candidate: Eddie Fuller, West Virginia University
During this interview, the candidate will give a model precalculus "lesson", in place of a colloquium talk. There will be opportunities for both Tenure-track faculty and Instructors to meet and socialize with the candidates, and to give input into the selection process.
WEDNESDAY, March 5, 2008
Algebraic Geometry
2:30pm, Room 410
Speaker: Dan Abramovich, Brown University
Title of talk: Tame stacks and reduction of coverings
Abstract: This is joint work with Martin Olsson and Angelo Vistoli, in which we describe a class of algebraic stacks, called tame stacks, which for many purposes is a good replacement for Deligne-Mumford stacks in finite and mixed characteristics. This is based on a classification of finite flat linearly reductive group schemes, which should be of independent interest if indeed it is not yet known (a fact that seems correct yet hard to believe).
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Number Theory
3:30pm, Room 304
Speaker: TBA
Title of talk: TBA
THURSDAY, March 6, 2008
VIGRE – Tropical Geometry
2:00pm, Room 304
VIGRE – Circle Packing
2:00pm, Room 326
VIGRE – Number Theory
3:30pm, Room 303
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
Colloquium
3:30pm, Room 304
Speaker: Marty Golubitsky, University of Houston
Title: Symmetry breaking and synchrony breaking
Abstract: A coupled cell system is a network of interacting dynamical systems. Coupled cell models assume that the output from each cell is important and that signals from two or more cells can be compared so that patterns of synchrony can emerge. We ask: Which part of the qualitative dynamics observed in coupled cells is the product of network architecture and which part depends on the specific equations?
In our theory, local network symmetries replace symmetry as a way of organizing network dynamics, and synchrony breaking replaces symmetry breaking as a basic way in which transitions to complicated dynamics occur. Background on symmetry breakingand some of the more interesting examples will be presented.
FRIDAY, March 7, 2008
VIGRE-Algebra
2:30pm, Room 322
Applied Math
2:30pm, Room 302
No meeting this week
Geometry
2:30pm, Room 410
Speaker: Mohammad Ghomi, Georgia Tech
Title of talk: Topology of Riemannian submanifolds with prescribed boundary
Abstract: In this talk we show that a closed submanifold of codimension 2 in Euclidean space bounds at most finitely many topological types of complete hypersurfaces with nonnegative curvature. This settles a question of Guan and Spruck related to a problem of Yau. Further we discuss analogous results for arbitrary Riemannian submanifolds. On the other hand, we show that these finiteness theorems may not hold if the codimension is too high or the boundary is not sufficiently regular. The proofs employ, among other methods, the Gromov-Perelman theory of Alexandrov spaces with curvature bounded below, and a relative version of Nash's isometric embedding theorem. These results include joint works with Stephanie Alexander, Robert Greene, and Jeremy Wong.