# mixedmath

Explorations in math and programming
David Lowry-Duda

# What I'm doing Now

Last updated 8 July 2022.

This is a now page. It is a written version of what I might say if we met in person and you asked me what I'm up to. The date at the top is important: it helps the reader determine if this is a now page or a then page.

## Research Travel

Other than that, I'm typically in either Boston or Providence before September.

I was unexpectedly in Portugal for most of May and half of June due to COVID.

## Research

I'm currently actively working on several projects.

• I'm working to develop methods to explicitly and rigorously compute Maass forms. I'm currently implementing a rigorous form of Hejhal's algorithm for weight $0$ Maass forms in arb.
• At the same time, I'm currently writing down interrelated things about Maass forms, including implementation notes for my computational work, the theory behind rigorous evaluation, and work towards an explicit and computable trace formula for forms of nontrivial character on non-squarefree level.
• I'm working on a paper related to half-integral weight modular forms and their computation. This is joint with Mehmet Kiral, Li-Mei Lim, and Thomas Hulse.
• With my frequent collaborators Chan Ieong Kuan and Alex Walker, I'm investigating discrete reduction problems for the divisor function.

## Teaching

I'm not currently teaching.