Colloquium talks in 2012

Spring 2012

Friday, February 3 at 2:30 pm in the conference room
Margaret Bayer, University of Kansas
Polyhedra from a Combinatorial Viewpoint
"A convex polytope is the convex hull of a finite set of points in Euclidean space. A polytope of dimension d has faces of dimensions 0 through d-1. Ordered by inclusion, they form the face lattice of the polytope. This talk concerns the study of face lattices of convex d-dimensional polytopes. The combinatorial study of polytopes is important in the analysis of algorithms for linear programming and computational geometry. It also has remarkable connections with commutative algebra and algebraic geometry. The talk will be a survey of key results, current themes, and open problems."
Friday, March 16 at 2:00 pm in Fretwell 207
Koya Shimokawa, Saitama University, Japan
Tangle analysis of site-specific recombination
"Knot theory is applied to studies of site-specific recombination of DNA. In this talk I will discuss our recent results on characterization of topological mechanism of Xer recombination. "
Friday, April 13 at 1:30 pm in the conference room
Margaret Readdy, University of Kentucky
Euler flag enumeration of Whitney stratified spaces
" The flag vector contains all the face incidence data of a polytope, and in the poset setting, the chain enumerative data. It is a classical result due to Bayer and Klapper that for face lattices of polytopes, and more generally, Eulerian graded posets, the flag vector can be written as a cd-index, a non-commutative polynomial which removes the generalized Dehn-Sommerville relations, that is, all the linear redundancies among the flag vector entries discovered by Bayer and Billera. This result holds for regular CW complexes. We relax the regularity condition to show the cd-index exists for non-regular CW complexes by extending the notion of a graded poset to that of a quasi-graded poset. This is a poset endowed with an order-preserving rank function and a weighted zeta function. This allows us to generalize the classical notion of Eulerian, and obtain a cd-index in the quasi-graded poset arena. Generally speaking, for an arbitrary quasi-graded poset the weighted zeta function is not unique. However, for a manifold having a Whitney stratification, selecting the weighted zeta function of an interval using the Euler characteristic gives the extended notion of Eulerianess geometric meaning. This is joint work with Richard Ehrenborg (University of Kentucky) and Mark Goresky (Institute for Advanced Study). "

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