Talk

The aim of the talk is to discuss the construction of an isocrystal associated to abelian schemes over p-adic fields using the arithmetic jet space theory. Isocrystals are objects in p-adic Hodge theory that lead to Galois representations. A well-known example of isocrystals coming from geometry are the ones obtained from the de Rham cohomology of the scheme. We will also talk about the interaction of our object with the first deRham cohomology of the abelian scheme. This is a joint work with Jim Borger.

In the late seventies, Casson and Gordon developed several knot invariants that obstruct a knot from being slice, i.e. from bounding a disc in the 4-ball. In this talk, we use twisted Blanchfield pairings to define twisted signature functions for knots, and describe their relation to the Casson-Gordon invariants. If time permits, we will describe how this can be used to obstruct the sliceness of some algebraic knots. This is joint work with Maciej Borodzik and Wojciech Politarczyk.

In this talk, we will briefly review the theory of characters of Demazure modules which are modules for the standard maximal parabolic subalgebra of an affine Lie algebra. The discussion will be followed by some connections that I have discovered(with collaborators) in my own research between algebraic combinatorics and other areas of mathematics such as representation theory and number theory. For instance, we show that the graded multiplicities of higher level Demazure modules in Demazure flags can be expressed in terms Dyck paths.

This mini-course is on the basis of the speaker's monograph "a mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory" (The MPIM-preprint series 2018-65). I plan to explain the construction of a new Hopf algebraic formalism on graphons derived from the Kreimer's renormalization coproduct. Then I will show the application of this new mathematical object in dealing with non-perturbative parameters.
 

This mini-course is on the basis of the speaker's monograph "a mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory" (The MPIM-preprint series 2018-65). I plan to explain the construction of a new Hopf algebraic formalism on graphons derived from the Kreimer's renormalization coproduct. Then I will show the application of this new mathematical object in dealing with non-perturbative parameters.
 

We will report on ongoing joint work with Martin Gonzalez (MPIM) about analogues of cyclotomic multiple zeta values for complex elliptic curves with level structure. These are holomorphic functions on the upper half plane which degenerate to cyclotomic multiple zeta values at cusps. One of the motivations for their study is the existence of several modular phenomena for cyclotomic multiple zeta values.