**About me:**

I'm a first-year math PhD student at Brown University. I research number theory and related areas, and I'm particularly interested in automorphic forms, L-functions, and cryptography.

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 harmonic analysis and analytic number theory trimester program at the Hausdorff Research Institute for Mathematics in Bonn (covid-permitting)

Fall 2021: I'll attend the post-quantum algebraic cryptography trimester program at the Henri Poincaré Institute in Paris (covid-permitting)

**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, Tamás 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)

**Other links:**

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