Hi! I'm Misha. I do research in combinatorics and teach math, occasionally to high-school students.

You may occasionally also see my name written as Mikhail Lavrov. This is still me. Mikhail and I are the same person.

There are many ways to reach me, but sending an email to misha.p.l@gmail.com is one of the most reliable.

My research is in Ramsey theory and probabilistic combinatorics, a large part of both being focused on problems in graph theory. I received my Ph.D. from the ACO (Algorithms, Combinatorics, and Optimization) program at Carnegie Mellon University, in May 2017. My Ph.D. advisor was Po-Shen Loh.

From 2017 to 2020, I was a J.L. Doob postdoc in the Math Department of the University of Illinois at Urbana-Champaign. I am now on my way to Kennesaw State University.

You may be interested in:

- A list of my publications
- My CV (last updated December 2019)

I've done a lot of teaching here and there, including:

- At the University of Illinois. I am particularly proud of my lecture notes for
- Math 482: Linear programming, as taught in spring 2020, and
- Math 484: Nonlinear programming, as taught in spring 2019.

- At Canada/USA Mathcamp! I was first a mentor there in 2014, and have returned every summer so far.
- For the Western PA ARML team, a math team for middle- and high-school students in the Pittsburgh area that is now in the capable hands of C.J. Argue.

I use Mathematica in my research, but sometimes I also use it just to draw pretty pictures.

On the other hand, the fractal you can see in the background of this webpage was created in MS Paint. Here's an enlarged version of the tile after 7 doubling steps. See if you can figure out how I did it!

When I want to do a little bit of math, but not too much math, I answer questions on Math StackExchange (and occasionally ask them, too). Some highlights, judged entirely by how fun I think they are:

- Did you know that you can 4-color a map of the US and use the color green only twice?
- Several teams of varying size play team-on-team matches. When one team beats another, the leader of the losing team joins the winners, and the rest of the losing team splits into 1-person teams. Starting from
*n*1-person teams, how many games does it take on average to form one*n*-person team? Here is a solution using Markov chains. - Is it possible to decompose K
_{12,12}into four edge-disjoint copies of 3(K_{4,4}-I)? We can find the answer using simulated annealing. - Some Pythagorean triples a
^{2}+b^{2}=c^{2}also satisfy φ(a^{2})+φ(b^{2})=φ(c^{2}). Is it just the ones we expect, or are there more? I wrote this question for a math contest, but my solution was wrong, and years later MSE still doesn't know the answer.

Last updated June 10, 2020. Misha Lavrov <misha.p.l@gmail.com>