Abstract: Cubic fourfolds have been classically studied up to birational equivalence, with an eye towards rationality problems. We will discuss two other notions of equivalence: Fourier-Mukai equivalence, and `hyperkahler equivalence'. We'll discuss how these equivalences are conjecturely related. We will give new examples of pairs of cubic fourfolds satisfying all three equivalences. In particular, our examples will be pairs of birational cubic fourfolds, with birational Fano varieties of lines, a previously unknown phenomenon. This is joint work with Corey Brooke and Sarah Frei.
Cubic fourfolds with birational Fano varieties of lines Sponsored by the Meyer Fund
Thu, Nov. 6 2:30pm (MATH 3…
Functional Analysis
James Woodcock (CU Boulder)
X
Minimal homeomorphisms of topological spaces provide a source of simple C*-algebras whose structure and K-theory can be understood through dynamical systems. I will present results on the existence of minimal homeomorphisms of flat manifolds with positive first Betti number. When the flat manifold has a spin^c structure we will show that the resulting cross product satisfies Poincare Duality for C*-algebras. Finally, I will describe ongoing work toward constructing explicit KK-cycle representatives in the presence of minimal flows, in analogy with the classical case of irrational rotation algebras.
Cubic fourfolds with birational Fano varieties of lines