Archived Events

In a joint project with Rob Schneiderman and Peter Teichner, we have analyzed the structure of the set of links up to "Whitney tower concordance." A crucial aspect of this analysis is a conjecture of Jerry Levine, which relates an algebraically defined Lie ring to a combinatorially defined abelian group of labeled trees modulo the IHX relation. This conjecture is easy to verify after tensoring with a field of characteristic $0$, but the general statement is not so easy.

In this talk I will survey the historical and recent development in the study of multiple harmonic sums, multiple zeta values and some other related values such as multiple zeta star values and their q-analogs, mainly from the number theory point of view. Starting with Euler's decomposition formula for double zeta values I will conclude with a sketch of the Two-one formula conjectured by Ohno and Zudilin when they were here at MPIM in 2007. Most part of the talk will be accessible to the general
audience.

I will discuss a correspondence relating two specific classes of complex algebraic K3 surfaces. The first class consists of K3 surfaces polarized by the rank-sixteen lattice H+E_7+E_7. The second class consists of K3 surfaces obtained as minimal resolutions of double covers of the projective plane branched over a configuration of six lines. The correspondence underlies a geometric two-isogeny of K3 surfaces.