## 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 Erdős 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... I have TAed the following courses, all at Hebrew University:

• Spring 2020: Discrete Mathematics: First year undergraduate course for math and CS students.
• Spring 2019: Linear Algebra 2: Second undergraduate course in linear algebra.
• Spring 2018: Linear Algebra 1: First year undergraduate course in linear algebra.
• Fall2019, Fall 2018, Fall 2017, and Fall 2016: Mathematical Tools in Computer Science: Graduate course for CS students. Topics include:
• Probability (emphasizing the probabilistic method).
• Linear algebra: Spectral theorems and singular value decomposition for real matrices.
• Markov chains.
• Linear programming.
• Spring 2017 and Fall 2015: Topics in Analysis for Computer Science Students: Second year undergraduate course for CS students. Topics include:
• Convexity.
• Norms, inner products, Banach and Hilbert spaces.
• Notions of convergence for function sequences.
• Fourier series.
• Spring 2016 and Spring 2015: Infinitesimal Calculus 2 for Computer Science Students: Second course in undergraduate calculus.

Photo credit: Stephanie Mitchell/Harvard University.

Noam Yonat learns about triangle decompositions.

With Shanee in the French Alps.

Carrying Noam up Har HaTayasim.

Aqaba... seems more colorful in real life.