My primary research interest is arithmetic statistics, especially in shapes of orders and ideals in number fields (and their distributions). I am also interested in additive combinatorics and classical algebraic geometry. I like lattices, in pretty much any shape or form.

*Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves*, Preprint, arXiv:2207. 10522 [July 2022]*Sumsets of sequences in abelian groups and flags in field extensions*, Preprint, arXiv:2207. 10507 [July 2022]*On intersections of symmetric determinantal varieties and theta characteristics of canonical curves*, (joint with Avinash Kulkarni), Submitted , arXiv:2109.08740 [October 2021]*Computing unit groups of curves*, (joint with Justin Chen and Leon Zhang), Accepted by**Journal of Symbolic Computation**, arXiv:1808.02742 [Aug 2018]*Uniform bounds for the number of rational points on symmetric squares of curves with low Mordell-Weil rank*, (joint with Danielle Wang), Accepted by**Acta Arithmetica**, arXiv:1708.07057 [August 2017]

- Arithmetic Statistics Special Session,
**AMS Sectional Meeting at University of Cincinnati**[April 2023] - Algebra and Number Theory Seminar,
**Emory University**[March 2023] - Number Theory Seminar,
**UC San Diego**[February 2023] - Algebra and Number Theory Seminar,
**Dartmouth College**[February 2023] - Number Theory Seminar,
**Princeton University/IAS**[January 2023] - Arithmetic Statistics Special Session,
**Joint Mathematics Meetings**[January 2023] - Palmetto Number Theory Series,
**University of South Carolina**[December 2022] - Algebra/Number Theory Seminar,
**Brown University**[December 2022] - Algebra, Geometry, and Number Theory Seminar,
**Tufts University**:*Bounds on Successive Minima of Orders in Number Fields*[November 2022] - Simons Foundation Conference, Geometry in Arithmetic Statistics,
**Schloss-Elmau, Germany**:*Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves*[September 2022] - SAXAG Seminar,
**Max Planck Institute for Mathematics in the Natural Sciences, Leipzig**:*On intersections of symmetric determinantal varieties and theta characteristics of canonical curves*[July 2022] - Nonlinear Algebra Seminar,
**Max Planck Institute for Mathematics in the Natural Sciences, Leipzig**:*An introduction to arithmetic statistics*[June 2022] - Adopha Seminar,
**Leiden University**:*Asymptotic bounds on successive minima of orders in number fields*[January 2022] - Seminar on Nonlinear Algebra,
**Max Planck Institute for Mathematics in the Natural Sciences, Leipzig**:*Cohen-Lenstra Heuristics*[June 2019] - Number Theory Seminar,
**University of Groningen**:*Rational points on symmetric squares of curves*[July 2018] - Seminar on Nonlinear Algebra,
**Max Planck Institute for Mathematics in the Natural Sciences, Leipzig**:*Counting Unit Groups of Curves*[June 2018]

- Arithmetic Statistics Seminar,
**Princeton University**[November 2022] - Graduate Student Seminar,
**Princeton University**:*Monogenic cubic rings*[November 2022] - Graduate Student Seminar,
**Princeton University**:*An introduction to sumset theorems: Kneser's theorem, Vosper's theorem, and generalizations*[March 2022] - Arithmetic Statistics Seminar,
**Princeton University**:*The Relationship between Segre cubic threefolds, Igusa quartic threefolds, and quintic and sextic etale algebras, P\ t. 2*[November 2021] - Arithmetic Statistics Seminar,
**Princeton University**:*The Relationship between Segre cubic threefolds, Igusa quartic threefolds, and quintic and sextic etale algebras [November 2020]* - Arithmetic Statistics Seminar,
**Princeton University**:*The Relationship between Cayley cubic surfaces, Steiner quartic surfaces, and quartic etale algebras*[November\ 2020] - Arithmetic Statistics Seminar,
**Princeton University**:*The Relationship between Tricuspidal quartic plane curves, nodal cubic plane curves, and cubic etale algebras*\ [November 2020] - Graduate Student Seminar,
**Princeton University**:*Tricuspidal cubic plane curves and cubic etale algebras*[November 2020] - Arithmetic Statistics Student Seminar,
**Stanford University**:*Binary quartic forms having bounded invariants*[June 2020] - Princeton Open House Talk,
**Princeton University**:*Introduction to Arithmetic Statistics*[March 2020] - Arithmetic Statistics Student Seminar,
**Princeton University**:*Asymptotic bounds on successive minima of orders of number fields*[December 2019] - Computatational Tropical Geometry minisymposium,
**2019 SIAM Conference on Applied Algebraic Geometry**:*Computing Unit Groups of Curves*[July 2019] - Graduate Student Seminar,
**Princeton University**:*Higher Composition Laws*[April 2019] - AMS Contributed Paper Session on Research in Geometry, Groups, and Representations by Undergraduate and Post-Baccalaureate Students,
**Joint Mathematics Meetings 2018**:*Uniform Bo\ unds for the Number of Rational Points on Symmetric Squares of Curves with Low Mordell-Weil Rank*[January 2018]