**About me:**

Howdy. I'm a first-year math PhD student at Brown University. I'm broadly interested in artificial intelligence, cryptography, and number theory.

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

In Brown's computer science department, I do natural language processing research with William Rudman, 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.

Curriculum vitae (as of Feb. 2021)

Email: ngillman[at]brown[dot]edu

**Professional updates:**

Spring 2021: I'm co-organizing Brown's graduate student seminar

Spring 2021: I'm running a directed reading program on lattice-based cryptography

Summer 2021: I'll attend the deep learning theory summer school at Princeton

**Publications:**

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 Academiae Scientiarum Fennicae Mathematica*, to appear. (arXiv)

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)

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

**Notes and u****npublished expository papers:**

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)