Welcome!
I am a postdoctoral fellow at Harvard University's Center of Mathematical Sciences and Applications.
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.
I am interested in high-dimensional combinatorics, especially random high-dimensional permutations and designs. I also enjoy thinking about random (hyper) graphs and (hyper) graph processes. Lately I have been applying functional-analytic methods to study these objects.
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 with Matthew Kwan, Ashwin Sah, and Mehtaab Sawhney, which resolved a 1973 conjecture of ErdÅ‘s on the existence of high girth Steiner triple systems.
Contact Information
Email: msimkin followed by @ followed by cmsa.fas.harvard.edu
Office: 20 Garden St. 115C.
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...