Alternatively have a look at the program.

## Jacobi forms of degree two

After reviewing a theory of Taylor expansion of scalar valued Jacobi forms of higher degree and

several structure theorems obtained before, we talk new results on vector valued Jacobi forms

of degree two. By using the Taylor expansion and a result on the image of Witt operator, we

determine the module structure of vector valued Jacobi forms of degree two of index one over

the ring of scalar valued Siegel modular forms. We also obtain an explicit dimension formula

for $k > 8$ and confirm Tushima's conjecture.

## Siegel modular forms mod $p$ and their $U(p)$ congruences

We discuss Jacobi coefficients with $p$-integral coefficients, and device them to study Siegel modular forms for the full Siegel modular group of arbitrary genus.

We revisit classical results on Jacobi forms due to Eichler and Zagier, and Sofer. Extensions of them to Jacobi forms of matrix index can be obtained by the recently much refined method of restriction. In particular, we will show that the module of Jacobi forms of fixed index with $p$-integral coefficients is free for all $p$ greater than 3.

## Combinatorics related to Modular Forms and Multiple Zeta Values

In this talk we discuss combinatorial structures, encoded by Hopf algebras, which are related to modular forms and multiple zeta values. In particular we shall also consider their connections with Monstrous Moonshine. These Hopf algebras equally capture the notion of `freeness` in non-commutative probability theory. The talk is based on material from joint work with McKay.

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