Alternatively have a look at the program.

## Number theory with Magma: for performant and flexible computation

Magma (distributed at the U. Sydney) is a software designed for computations in algebra, number theory,

and arithmetic geometry. In this talk, we will introduce Magma and extensive projects with packages we

created (or collaborated) with short demos.

## Selberg's orthonormality conjecture and joint universality of L-functions

In this talk, we introduce the new approach how to use an orthonormality relation

of coecients of Dirichlet series dening given L-functions from the Selberg class to

prove joint universality (joint work with Yoonbok Lee, Lukasz Pankowski).

## Explicit trace formulas for symmetric square L-functions for GL(2) and some applications

Zagier exhibited an indentity between meromorphic functions as a generalization of the Eichler-Selberg

trace formula for elliptic modular forms. Later, Jacquet and Zagier described such a kind of trace formula

with complex parameter for adelic GL(2), containing abstractness of its spectral and geometric terms. In

this talk, we give a generalization of Zagier's formula to the case of holomorphic Hilbert modular forms

in a new way. As applications, we discuss an equidistribution result for Hecke eigenvalues of Hilbert

## A certain level-index changing operator on Jacobi cusp new forms

Let $N$ be an odd square-free integer. We give a Hecke isomorphism map from the space of Jacobi cusp new forms of level $1$ and index $N$ satisfying a certain condition into the space of Jacobi cusp new forms of level $N$, index $1$ and the character after reviewing about some known properties of level-index changing operators.

## Arithmetic formulas for the coefficients of the McKay-Thompson series

By the work of R. Borcherds we know the Fourier coefficients of the elliptic modular $j$-function are closely related

to the Monster group. As a new perspective, M. Kaneko gave an arithmetic formula for the Fourier coefficients expressed

in terms of the traces of the CM values of the $j$-function in 1996. In this talk, we consider analogues of this formula for

the McKay-Thompson series. Our main result is an explicit formula for the coefficients expressed in terms of the CM

values of certain hauptmoduln. Furthermore, we give some applications.

## On Charlton's conjecture about the multiple zeta values

In this talk, we give a proof of a special case of the generalized cyclic insertion conjecture on the MZVs, which was formulated by Steven Charlton in his thesis. The conjecture is stated in terms of the block notation for MZVs introduced by himself. Charlton's conjecture is a broad generalization of several long unproven families of identities such as Borwein-Bradley-Broadhurst-Lisoněk's cyclic insertion conjecture and certain conjectural identities posed by Hoffman.

## Average values of higher Green's functions and their factorizations.

By the classical theory of complex multiplication, the Klein $j$-invariant takes algebraic

values at CM points. In their seminal work on singular moduli, Gross and Zagier gave a

factorization of the difference between two such values, which can be viewed as the exponential

of a special value of a Green's function on the upper half plane. From numerical computations,

they conjectured that the special values of certain higher Green's functions also enjoy similar

algebraicity property. We will revisit this conjecture and discuss some recent progress.

## Explicit constructions of non-tempered cusp forms on orthogonal groups of low split ranks

The aim of this talk is to report a recent research on explicit constructions of cusp forms on orthogonal groups of split rank one or two by some lifts from cusp forms on the complex upper half plane. We also discuss cuspidal representations generated by them in terms of the explicit determination of their local components. As for the representation theoretic treatment, the point is to use Sugano’s non-archimedean local theory of ``Jacobi form formulation” of Oda-Rallis-Schiffman lifting to orthogonal groups of rank two.

## On the Miyawaki lifts of hermitian modular forms

We construct a lifting from a elliptic modular cusp form *f* and a hermitian modular cusp

form *g* of degree *r* to a hermitian modular cusp form of degree *n + r*. This lift is the

so-called Miyawaki lift. When *f* and g are "Hecke eigenforms", its lift is also a "Hecke eigenform"

(if it is not identically zero). Moreover, we determine explicitly the standard *L*-function and*A*-parameter associated to the Miyawaki lift.

## The Hermitian modular group and the orthogonal group

The Hermitian modular group of degree $n$ over an imaginary quadratic field

$K=\mathbb{Q}(\sqrt{-m})$ was introduced by Hel Braun in the 1940s

as an analogue for the well known Siegel modular group. It acts on the

Hermitian half space and the accociated Hermitian modular forms have

been studied thoroughly in the past. However, this talk does not concentrate

on the modular forms but on the modular group itself. For $n=2$ and $m \neq 1,3$,

$m$ squarefree, we will prove that the Hermitian modular group $U(2,2;\mathcal{O}_K)$,