I am a third year Ph.D. student in the ACO (Algorithms, Combinatorics, and Optimization) program at Carnegie Mellon University.

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

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

Email: mlavrov@andrew.cmu.edu

Office: Wean Hall 6201

- Spring 2014: 21-257 Models and Methods for Optimization (TA)
- Spring 2013: 21-228 Discrete Mathematics (TA)
- Spring 2012: 21-240 Matrix Algebra with Applications (TA)
- Spring 2012: 15-139 Probability and Computing (TA)
- Spring 2012: 21-238 Math Studies Algebra II (Grader)
- Fall 2011: 21-120 Calculus (TA)

**Office hours:** None at the moment.

I am one of the coaches for the Western Pennsylvania ARML Team. Here are some of the materials from my practice sessions:

- (May 18, 2014) Generating Functions 2.1. A practice power round about Lucas's theorem.
- (May 11, 2014) Generating Functions 2. Featuring common sense, trickery, and persistence.
- (May 4, 2014) Generating Functions 1. Featuring non-standard dice and negative binomial coefficients.
- (March 16, 2014 and March 23, 2014) Writing more proofs. Many things.
- (March 2, 2014) Writing proofs. HMMT 2009 Team Round.
- (February 9, 2014) Algebra. Vieta's formulas.
- (February 2, 2014) Algebra. Solving recurrence relations.
- (January 26, 2014) Algebra. Simplifying finite sums.
- (January 19, 2014) Miscellaneous problems.
- (December 15, 2013) Geometry. Theorems about triangles.
- (December 8, 2013) Geometry. Circles!
- (November 10, 2013) Combinatorics. Optimization problems.
- (November 3, 2013) Combinatorics. Introduction to graph theory.
- (October 27, 2013) Combinatorics. Induction, pigeonhole, and brute force.
- (October 20, 2013) Combinatorics. PIE and binomial coefficients.
- (October 6, 2013) Number Theory. Divisors and modular exponentiation (
**Homework**). - (September 29, 2013) Number Theory. Divisors and the beginning of solving integer equations.
- (September 22, 2013) Number Theory. Modular arithmetic and GCD (
**Homework**). - (September 15, 2013) Geometry. Thinking about axioms.
- Material from the previous year...

- M. Lavrov and P. Loh. Hamiltonian increasing paths in random edge orderings. Submitted.
- M. Lavrov, M. Lee, and J. Mackey. Improved upper and lower bounds on a geometric Ramsey problem. Submitted.
- A. Frieze, S. Haber, and M. Lavrov. On the game chromatic number of sparse random graphs. SIAM Journal on Discrete Mathematics, vol. 27, no. 2, 768-790, 2013.
- M. Lavrov and D. Rutherford. On the S¹ x S² HOMFLY-PT invariant and Legendrian links. Journal of Knot Theory and Its Ramifications, vol. 22, no. 8, 1350040 [21 pages], 2013.
- M. Lavrov and D. Rutherford. Generalized normal rulings and invariants of Legendrian solid torus links. Pacific Journal of Mathematics, vol. 258, no. 2, 393-420, 2012.

- On "On a combinatorial problem". An explanation of a theorem of de Bruijn and Erdős to accompany an ARML practice session.
- Remarks on "Remarks on non linear type and Pisier's inequality". An expository note on a paper of Naor and Schechtman, written for a class taught by Ryan O'Donnell; it provides additional background detail and uses notation matching Analysis of Boolean Functions.
- Chess-themed math problems. Not about chess, but about math about chess.
- Donut Quest. A puzzle game for the TI-83+ series of calculators. Includes a level editor.
- 4 In A Row: 3D. Tic-tac-toe on a 4 by 4 by 4 grid for the TI-83+ series of calculators.

Last updated May 18, 2014. Misha Lavrov <mlavrov@andrew.cmu.edu>