##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Rudolph Perkins

## The Many Obstructions to Formulating a Maeda Conjecture for Drinfeld-Goss Modular Forms

##### Abstract:

There are several major obstructions that arise in the attempt to formulate an analog of the Maeda Conjecture in the setting of Drinfeld modular forms. I will report on an undergoing joint work with G. Boeckle and P. Graef wherein we identify various Hecke stable filtrations on the spaces of cuspidal Drinfeld modular forms of full level and a given weight by identifying them with spaces of positive characteristic valued, $SL_2(\mathbb{F}_q[\theta])$-invariant, harmonic cocycles on the oriented edges of the Bruhat-Tits tree for $PGL_2 / \mathbb{F}_q((1/\theta))$ made possible by an isomorphism of Tietelbaum. I will compare with the classical situation along the way and provide some of the relevant background on Drinfeld modular forms in a pre-talk aimed at graduate students and postdocs.

### April 25, 2019

### 2:00 PM

### AP&M 7321

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