Welcome!
I am an Instructor (≈ departmental postdoc) in Applied Mathematics at MIT's Department of Mathematics.
I completed my PhD at the Einstein Institute of Mathematics and the Federmann Center for the Study of Rationality at the Hebrew University of Jerusalem, Israel. I had the great fortune of being supervised by Prof. Nati Linial. Following my PhD, I spent three years as a postdoctoral fellow at Harvard's Center of Mathematical Sciences and Applications.
I am interested in using randomized algorithms to answer existential, enumerative, and structural questions in combinatorics. I especially enjoy thinking about combinatorial designs, and random graph and hypergraph thresholds.
My research is supported by National Science Foundation grant DMS-2349024.
Here is my curriculum vitae.
Research Highlights
Here is a Quanta magazine article about my work on the $n$-queens problem. And here is an article in the Harvard Gazette.
Quanta magazine also covered my joint work (published in Annals of Mathematics) with Matthew Kwan, Ashwin Sah, and Mehtaab Sawhney, which resolved a 1973 conjecture of Erdős on the existence of high girth Steiner triple systems.
Contact Information
Email: msimkin followed by @ followed by mit.edu
Office: 2-347, 77 Massachusetts Ave.
My Favorite Open Problem
An order-$n$
Latin square is an $n \times n$ matrix in which every column and every row contains all the values from $[n]$. This is equivalent to an $n \times n \times n$ $\{0,1\}$-array in which every row, column, and "shaft" contains a single $1$. Let $A$ be a random $n \times n \times n$ $\{0,1\}$-array in which the $n^3$ entries are independent random variables that equal $1$ with probability $p$. What is the threshold function $p(n)$ above which $A$ contains a Latin square with high probability?
Update (April 2022): Ashwin Sah, Mehtaab Sawhney, and I have
determined this threshold up to a subpolynomial factor!
Update (June 2022): Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abshishek Methuku, and Deryk Osthus have
determined the threshold up to a logarithmic factor!
Update (December 2022): Peter Keevash and, independently,
Vishesh Jain and Huy Tuan Pham have determined the threshold up to a constant factor! Congratulations! Some questions remain, such as finding the correct constant or proving a hitting time result. These will likely require significant new ideas. However, as far as my original intent when posing the question, it has now been completely answered! Stay tuned for a new problem...