Hi, I’m Johann. I’m interested in mathematics and computer science. More concretely, here is a list with some of my interests, roughly ordered by their usefulness in the real world / industry (which is also roughly the order in which I became interested in them):
- applications of arithmetic geometry in cryptography
- algebraic and elliptic curves
- $p$-adics, and analogs for analytic notions over them
- some algebraic geometry, like Galois Theory of schemes yielding a relation between Galois groups and fundamental groups
- (automorphic forms, Galois representations, their relation to algebraic / geometric objects, noncommutative geometry, quaternion algebras)
- computational aspects of all the previous and computer algebra
- cryptography
- (the language(s) of logic and computation)
- (interactive proof assistants and automatic theorem proving, as well as formal verification of software, and combining computer algebra with formal verification of proofs)
- (applying category theory to computing, data science, engineering, logic, AI, and other sciences)
- “nonlinear algebra”
- applying (real, computational, tropical) algebraic geometry to statistics, optimization, and differential equations
- tensors
- optimization and its relation to data science
- all sorts of (mostly continuous) optimization, also in combination with probability/statistics
- computational optimal transport
- modern probability / statistics / data science
- modern statistics (high-dimensional, computational, robust)
- information theory/geometry
- causality, graphical models, and its interplay with the next two bulletpoints
- machine learning
- artificial intelligence
Over the last three years, attacking elliptic curve based cryptography has been a great motivation for me to learn about arithmetic geometry, and that’s where I learned about the first block above. Now, I look more into applied math and computer science.
I like to combine elegant theory with useful practice.
If time allows (not right now, of course!), I would also be interested in an engineering project outside of my “comfort zone”, for example involving biotech, chemistry, or mechanical engineering. I would also like to learn more about biology and neuroscience at some point.
Feel free to contact me via [firstname].[lastname]@hotmail.de (PGP Public Key), I’m always happy to speak about math, computer science, engineering, life, and everything else.
This subpage was last updated in July 2023.