Guest lectures and seminars - Page 152

Andrea Riebler ( Dept. of math., NTNU) gives a seminar in room 107, 1st floor N.H. Abels House at 15:15 December 2nd: Projecting the future burden of cancer: Bayesian APC analysis made simple.

Modular forms are certain complex-analytic functions on the upper-half plane. They can also be interpreted as giving linear-algebraic invariants of elliptic curves, perhaps equipped with some extra structure, and in this way they reveal their algebraic-geometric nature. One of the most fundamental modular forms is the Dedekind eta function. However, it seems that only recently has it been pinned down precisely what extra structure on an elliptic curve is needed to define eta. Namely, Deligne was able to express this extra structure in terms of the 2- and 3-power torsion of the elliptic curve. Deligne's proof, apparently, is computational. In this talk I'll describe a conjectural reinterpretation of Deligne's result, together with some supporting results and a hint at a possible conceptual proof. The reinterpretation is homotopy theoretic, the key being to think of an elliptic curve as giving a class in framed cobordism. This directly connects the number "24" which often appears in the study of eta to the 3rd stable stem in topology. 

Johannes Kleppe, Høgskolen i Buskerud og Vestfold, gives the Seminar in Algebra and Algebraic Geometry:

Abelian varieties XII

I will discuss joint work in progress with David Gepner, computing the ring of endomorphisms of the equivariant motivic sphere spectrum, for a finite group. The result is a combination of the endomorphism ring of the equivariant topological sphere spectrum (which equals the Burnside ring by a result of Segal) and that of the motivic sphere spectrum (which equals the Grothendieck-Witt ring of quadratic forms by a result of Morel). This computation is a corollary of a tom Dieck style splitting for certain equivariant motivic homotopy groups.