Abstracts for Seminar on Algebra, Geometry and Physics

The Bost-Connes system is a C*-dynamical system whose dynamics realize the class field theory of Q.
The analogous construction of a C*-dynamical system for an arbitrary number field K is known, but to
realize again the class field theory of K through the dynamics of this system requires the construction
of a distinguished arithmetic subalgebra. Until recently the construction of such arithmetic subalgebras
was only known for K an imaginary quadratic field. In our talk we will explain how to construct such

The motivic cohomology spectral sequence (MCSS) is an algebraic-geometrical counterpart of the Atiyah--Hirzebruch spectral sequence. For smooth varieties, it has the second term consisting of
motivic cohomology groups and converges to algebraic $K$-groups. The spectral sequence was initially constructed only for fields by Bloch and Lichtenbaum in their unpublished preprint. Further, three different approaches to construction of the spectral sequence for varieties were given by Friedlander -- Suslin,

In this talk I shall give an exposition of fragments from Gauss
where he discovered,
with the help of some work of Jacobi,
a remarkable connection between Napier pentagons on the sphere and Poncelet
pentagons on the plane.

This gives rise to a parametrization of the variety of Napier pentagons
using
the division by 5 of elliptic functions.

As a corollary we will find the classical five-term relation for the
dilogarithm in a somewhat
exotic disguise, and discuss some open questions.

 

We discuss how odd Lie and BV structures arise naturally in an operadic/surface setting.
More generally, we present a novel categorical framework where these structures
appear from odd operations.