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 hope to fill this site with some interesting math content in the future :)

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)

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

Spherical Representations of $p$-adic groups
Representations of GL_2 over Nonarchimedean Fields
The Spectral Theorem
Primitive roots using $p$-adic numbers
A nice application of the Krein-Milman theorem

Teaching

Math 54, Spring 2025

Office hours: TBD (both in person in Evans 835)
Official course website
Some more links for Math 54:
Tau Beta Pi's folder with past exams
Hanson Hao's website with some resources for Math 54
Alexander Paulin's website for Math 54 (Spring 22), with some resources such as lecture videos and past exam papers
YouTube Playlist with videos on the content

Math 1B, Fall 2024

Office hours: Tuesday 9:00AM - 10:00AM, Thursday 2:00PM - 3:00PM both in person in Evans 835
Official course website
Some more links for Math 1B:
Tau Beta Pi's folder with past exams
Hanson Hao's website with some handouts for Math 1B
Alexander Paulin's website for Math 1B (Spring 24), with some resources such as lecture videos and past exam papers

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