The Level of a Topological Space

The level of a Z/2Z-space X is defined to be the minimum n such that there is a Z/2Z equivariant map from X to S^n-1 (with the antipodal action). The level of a unital ring is defined to be the minimum n such that -1=e₁²+e₂²+...+e_n² where e_n are elements of the ring. We explore an intimate relationship between the level of a Z/2Z space and the level of commutative R algebras. We also compute the level of even dimensional real projective spaces, spheres, and mention results on the computations of odd dimensional projective spaces.

Equivariant algebraic K-theory

Title: Single Splitter Details

Abstract: Lee defined the winding number w_k in a Gale diagram corresponding to a given simplicial polytope. He showed that w_k equals g_k of the corresponding polytope. We are working on extending Lee's definition of w_k to nonsimplicial polytopes. In this talk, we will discuss our results when the origin in the Gale diagram falls on a single k-splitter, a hyperplane that separates k points from the rest.

Title:  Fluid PDEs with partial or fractional dissipation.

Title:  Boundary integral equations of coupled thermoelastodynamics