Abstract: In this talk, we will explore few logical foundations for quantum theory. I will briefly introduce logical syntax and semantic, and the important notion of Lindebaum Algebra. After acquiring essential logical equipment, I will discuss Partial Boolean Algebras as an algebraic model to formulate Kochen- Specker theorem in pure logical setting. I will as well mention the toposical foundation for quantum theory and the formulation of Kochen- Specker theorem in this setting. During the talk, some historical and philosophical issues will also be addressed.

Abstract: We will present a theorem due to J. Cohen that the stable homotopy groups of spheres are generated under higher Toda brackets by the classes in Adams filtration one: the Hopf classes as well as the first alpha element (for odd primes).

Abstract: We construct a combinatorial framework for proving cohomological vanishing results on certain classes of spaces, by means of a Mayer-Vietoris-type spectral sequence and certain Cohen-Macaulayness hypotheses. The spaces include complex hyperplane complements, their De Concini-Procesi compactifications, and configuration spaces of points in tori. In particular, we generalize classical vanishing results due to Kohno, Esnault, Schechtman and Vieweg, and recent work of Davis, Januszkiewicz, Leary and Okun.

This is joint work with Alex Suciu and Sergey Yuzvinsky.