I am a fourth 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 2015: 21-228 Discrete Mathematics (TA)
- Summer 2014: Canada/USA Mathcamp!
- 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:** Thursday 12:30-3:30pm in Wean Hall 6201.

I am one of the coaches for the Western Pennsylvania ARML Team. Here are the problem sets for this year's practices:

- (March 29, 2015) Generating functions. Solving counting problems with convolutions.
- (March 15, 2015) Generating functions. Introduction. Also, AIME from 1996.
- (March 1, 2015) Algebra. Solving recurrence relations.
- (February 22, 2015) AHSME and AIME from 1997. (You can find these contests on Art of Problem Solving.)
- (February 8, 2015) Number theory. Number theory on the AMC.
- (February 1, 2015) AHSME and AIME from 1998. (You can find these contests on Art of Problem Solving.)
- (January 25, 2015) Number theory. Divisors and factors.
- (December 7, 2014) Assorted problems about chess.
- (November 30, 2014) Algebra. Polynomials and a bit of interpolation.
- (November 2, 2014) Geometry. Three-dimensional geometry.
- (October 19, 2014) Geometry. Coordinate geometry.
- (October 12, 2014) Mock ARML Team Round and Individual Round, loosely based on ARML 2010.
- (September 28, 2014) Combinatorics. Equivalence relations.
- (September 14, 2014) Combinatorics. Markov chains!

You can also explore practice materials from previous years.

- M. Lavrov. An upper bound for the Hales-Jewett number HJ(4,2), submitted.
- M. Lavrov and P. Loh. Increasing Hamiltonian paths in random edge orderings. Random Structures and Algorithms, to appear.
- M. Lavrov, M. Lee, and J. Mackey. Improved upper and lower bounds on a geometric Ramsey problem. European Journal of Combinatorics, vol. 42, 135-144, 2014.
- 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 April 12, 2015. Misha Lavrov <mlavrov@andrew.cmu.edu>