Leonard Tomczak

About

Hi, I am Leonard, I am a math student at UC Berkeley, interested mainly in number theory. Besides number theory I am also curious about various other areas in mathematics, in particular some topics in analysis. I am currently studying automorphic L-functions and trace formulae.

Email: first name DOT last name AT berkeley DOT edu
Office: Evans 835

Lecture Notes

Here are some lecture notes I took.

Math stuff

Math fact of the week

Artin's Conjecture for Abelian Varieties with Frobenius Condition (with F. Heß)

My Qualifying Exam Syllabus is here and rough transcript here.

Some interesting math things I learned about at some point and decided to write up:

Automorphic Stuff:
Automorphic Forms, Representations and other things (Qualifying Exam preparation notes)
Adelic Fourier Series
Spherical Representations of $p$-adic groups
Representations of GL_2 over Nonarchimedean Fields
Other Number Theory:
Igusa's Zeta Functions and Generalizations (Notes for a talk)
Primitive roots using $p$-adic numbers
Functional Analysis:
The Spectral Theorem
A nice application of the Krein-Milman theorem
Linear Algebra:
A formula for the orthogonal projection.

Since I found it extremely annoying to have to download the chapters in books on De Gruyter one by one, I wrote this little script to automate the process.

Teaching

Math 1B, Summer 2025

Course webpage is here.

Directed Reading Program (DRP)

I was a DRP mentor:
Spring 2024: Dirichlet's Theorem on Primes in Arithmetic Progressions

Other stuff

pi-base: data base with bunch of examples and properties of topological spaces
ringtheory: data base with bunch of examples and properties of rings and modules
adjectivesproject: data base with bunch of examples and properties of schemes and their morphisms
SL2(Z)
Approach0: a search engine suitable for math expressions
Proof of the Snake lemma
Classics Explained: YouTube channel with nice animated videos explaining the context of some famous classical musical works.
Skat Lernen: (in German) YouTube channel with lots of videos on the German card game Skat