**About me:**

Howdy!! I'm a PhD student at Brown University. I currently research the mathematical foundations of artificial intelligence.

In Brown's Department of Mathematics, I do cryptography research under the guidance of Jeffrey Hoffstein.

In Brown's Department of Computer Science, I do natural language processing research under the guidance of Carsten Eickhoff.

The above image is taken from an advertisement for Wesleyan University, where I completed my undergraduate degree. I also spent one semester at the Math in Moscow program and another at the Budapest Semesters in Mathematics program.

Email: ngillman[at]brown[dot]edu

**Links to my work on...**

**Publications/preprints (artificial intelligence, ****machine learning****):**

6. IsoScore: Measuring the Uniformity of Vector Space Utilization (with William Rudman, Taylor Rayne, and Carsten Eickhoff), 2021. (arXiv)

**Publications/preprints (mathematics):**

5. Explicit subconvexity savings for sup-norms of cusp forms on PGL(n,R). *Journal of Number Theory* (2020) **206**, 46-61*.* (arXiv, journal, MathSciNet)

4. Patterns of primes in the Sato-Tate conjecture (with Michael Kural, Alexandru Pascadi, Junyao Peng, and Ashwin Sah). *Research in Number Theory* (2020) **6**, No. 9. (arXiv, journal, MathSciNet)

3. Large sets with small injective projections (with Frank Coen, TamĂˇs Keleti, Dylan King, and Jennifer Zhu). *Annales Fennici Mathematici *(2021) **46**, No. 2. (arXiv, journal)

2. From partitions to Hodge numbers of Hilbert schemes of surfaces (with Xavier Gonzalez, Ken Ono, Larry Rolen, and Matthew Schoenbauer). *Philosophical Transactions of the Royal Society, Series A* (2019) **378.** (arXiv, journal, MathSciNet)

1. Exact formulas for invariants of Hilbert schemes (with Xavier Gonzalez and Matthew Schoenbauer). *Research in Number Theory *(2018) **4**, No. 39. (arXiv, journal, MathSciNet)

**Notes and u****npublished expository papers (mathematics):**

An introduction to arithmetic geometry and elliptic curves (spring 2021)

An introduction to analytic number theory on GL(2) (fall 2020)

Formulations and generalizations of Eisenstein series (summer 2020)

The trace formula of Petersson (summer 2020)