Buffalo Geometry and Topology Seminar |
Unless noted, all seminars are Friday at 4pm, in Mathematics 122.
| Date | Speaker | Organization | Title | Abstract |
| January 18th | Experimental Multimedia seminar! (in Room 250) | |||
| January 25th | Adam Sikora (in Room 250) | University at Buffalo | Quantizations of Character Varieties and Knot theory. | |
| February 1st | Doug LaFountain (in Room 250) | University at Buffalo | Barriers to transverse and Legendrian simplicity | We study transverse and Legendrian iterated torus knots in S3 endowed with the standard contact structure. A knot type is said to be transversally (Legendrian) simple if classical invariants can distinguish between the transverse (Legendrian) isotopy classes of that knot. Menasco has identified necessary conditions for when iterated torus knots fail to be transversally simple; Etnyre and Honda have done the same for the Legendrian case. In this talk we identify connections between the technologies used to arrive at these two sets of conditions. We then use these connections to conjecture a partial transverse classification of iterated torus knots. |
| February 8th | Jason Manning | University at Buffalo | Introduction to stable commutator length and some recent results of Calegari | |
| February 15th | Anne Thomas | Cornell University | Existence, covolumes and commensurators of lattices acting on polyhedral complexes | We compare several properties of lattices in semisimple Lie groups and lattices in automorphism groups of polyhedral complexes, such as Davis complexes and right-angled buildings. Questions considered include existence of lattices, their covolumes and (in joint work with A. Barnhill) their commensurators. |
| February 22nd | Seonhee Lim | Cornell University | Volume entropy rigidity for buildings | Volume entropy of a Riemannian manifold is the exponential growth rate of the volumes of balls. Entropy rigidity for rank-1 Riemannian manifolds is known: a theorem of Besson-Courtois-Gallot says that the locally symmetric metrics attain minimal volume entropy among all Riemannian metrics. In this talk, we are interested in entropy rigidity for buildings, especially hyperbolic ones. We will give several characterizations of the volume entropy, analogous to the ones for trees, that will help us to find some lower bound on volume entropy. This is joint work with François Ledrappier. |
| February 29th | Multimedia seminar in room 250 | |||
| March 7th--9th | TOPOLOGY MINICONFERENCE | |||
| March 14th | No Speaker | Spring Break | ||
| March 21st | ||||
| March 28th | Kelly Delp | Buffalo State College | Convex projective structures | |
| April 4th | Terry Bisson | Canisius College | A homotopical algebra of graphs related to zeta series | Quillen's axioms for homotopical algebra generalize some
of the standard notions and constructions from
algebraic topology to other categories. Methods of
homotopy theory in the category of simplicial sets
provided a major motivating example.
It should be possible to illustrate Quillen's ideas, at a simple combinatorial level, in various categories of graphs related to the category of simplicial sets. I will sketch a Quillen model structure on a category of directed graphs, and examine the resulting homotopical algebra. It seems to fit well with traditional concepts of trees, cycles, and coverings in graph theory, and zeta functions and spectra of graphs from algebraic graph theory. Joint work with Aristide Tsemo (preprint on the ArXiv) |
| April 11th | Eduardo Martinez-Pedroza | Oklahoma University | Amalgamation of Quasiconvex Subgroups in Relatively Hyperbolic Groups | The relatively hyperbolic groups, introduced by Gromov, generalize the class of fundamental groups of complete finite volume hyperbolic manifolds. When considering a relatively hyperbolic group as a geometric object, the quasiconvex subgroups are the natural subgroups to consider. In this talk, we will discuss combination theorems for quasiconvex subgroups of relatively hyperbolic groups. |
| April 18th | Greg Schneider | University at Buffalo | A Combinatorial Survey of Knot Floer Homology | Knot Floer homology, developed by Ozsvath and Szabo, is a categorification of the Alexander polynomial of a knot. Their construction was found to have a connection with grid diagrams of knots, which in turn led to a purely combinatorial description of this homology. We will begin with a brief introduction to grid diagrams and the combinatorial construction of knot Floer homology, and then proceed to a survey of some of the recent developments to this theory, focusing primarily on results which can be proven entirely within the context of grid diagrams. |
| April 25th | Robert Tuzun | University at Buffalo / SUNY Brockport | Computational Search for Nontrivial Knots with Unit Jones Polynomial | A famous and still unsolved conjecture in knot theory states that there are no non-trivial knots in S3 with unit Jones polynomial. A computational search for such a knot is underway using a technique similar to one previously used by Yamada. Much of the work in this talk focuses on dealing with the combinatorial explosion in computational effort with the number of crossings. The intricacies of enumerating knots will be discussed in some detail. Reductions in computational effort are accomplished in part by eliminating unnecessary cases: by exploiting algebraic symmetry in expressions for the Kauffman bracket, by not considering connected sums of knots, and by considering knots composed only of "trivializable" algebraic tangles. Other reductions in computational effort, and in some cases of memory usage, may be accomplished by reducing computational effort for each case: by computing Kauffman brackets rather than Jones polynomials, by using simple strategies such as Horner's rule, and by evaluating Kauffman brackets at a specific value of independent variable, thereby enabling the replacement of computations involving Laurent polynomials with much simpler floating point, but still exact, computations. |