My name is Michael Klyachman and I am a 19 year old aspiring mathematician. I’m a student at the University of Chicago majoring in Math and Russian, and you can email me at uchicago@klyachman.edu (flip as needed)
I come from a pure mathematics background, and have expeirnece in Algebraic Geometry and Algebraic Topology. I’ve recently been looking into applying my mathematical knoweldge to financial markets, and am actively looking for opportunities in Quantitative Trading and Quant Research. Outside of mathematics I’m interested in running, yellow pigs, and public transit.
Motivation/personal synopsys
In my mathematical studies, I’ve come across a lot of interesting concepts. It’s always interesting to me to see how interdisciplinary mathematics can be- applications of topological methods in algebraic geometry (or vice versa) always lead to a richer body of knowledge. Looking at specifically intersections of different fields has allowed me to be creative with my approach to problems, and has allowed me to develop very good intuition specifically with regards to decontructing sub-problems.
I’ve found that the most personally rewarding questions are answered when high-level concepts are able to crack real questions because of the specific process of problem-solving.
Mathematical Interests
- I’m broadly interested in algebraic topology but more specifically in:
- how homotopy theory relates to higher category theory. I’m currently working through learning about higher algebra and topoi, and am fascinated by them (although I don’t know nearly as much as I want to).
- higher dimensional sphere homotopy calculations how those computations interact with spectral sequences. I’m also tenatively interested in motivic stuff.
- spectra, generalized cohomology, and chromatic homotopy.
- I like finite groups a lot, and am interested in classifying p-groups and p-group isomorphism testing.
- In the summer of 2020, I was part of the Boulder CS Theory research group. I worked on using methods from Algebraic Geometry and Finite Group Theory to solve problems of interest in Theoretical CS (mainly GpI and TI)
- I’m also interested in counting points on varieties over the rationals. Currently, I’m working on writing up an expository paper on Mazur’s Torsion theorem.
Miscellaneous
- I participated in the Hampshire College Summer Studies in Mathematics as a student in 2018, and came back as a staff member in 2022. I cannot begin to emphasize how much this summer program impacted my life, and if you are a high schooler interested in “real” mathematics, I strongly suggest applying.
- I care about equity in CS education. I was part of the (now-defunct) Chicode which organized several hackathons for CPS students, and used to be involved in Codeday Chicago.
- I enjoy running in my free time. You can find my strava here.
My blog, which will be filled with mathematical and nonmathematical thoughts alike, is forthcoming.