Positions

Education

Skills

Expert in: Mathematics - in particular, algebraic geometry, number theory, category theory and combinatorics.

Fluent in: Physics, in particular statistical mechanics, theory of computation, programming (Python, Sage, Lean), Machine Learning research, Cognitive Science.

Interests

Machine learning, cognitive science, theory of intelligent agents, evolutionary biology, arithmetic geometry.

Papers

1. Matrix Points on Varieties; joint with Yifeng Huang, Ruofan Jiang, and Yifan Wei. [arxiv]
2. A Chebotarev Density Theorem over Local Fields; joint with Yifan Wei and John Yin. [arxiv]
3. Configuration spaces, graded spaces, and polysymmetric functions; joint with Andrew O'Desky. [arxiv] (submitted)
4. On the variation of the Frobenius in a non abelian Iwasawa tower. [arxiv] (Algebra and Number Theory)
5. Unlikely and just-likely intersections for high dimensional families of elliptic curves. [arxiv] (submitted)
6. Just-likely intersections on Hilbert modular surfaces; joint with Qiao He and Ananth N. Shankar. [arxiv] (Math. Annalen)
7. Supersingularity of Motives with Complex Multiplication and a Twisted Polarization. [arxiv]

Awards

1. Excellence in Research, Graduate Student Award, 2021.
2. Henry Schaerf Mathematics Graduate Award, 2022.

Research Talks

1. (May 2023) Hebrew University of Jerusalem. A Chebotarev Density Theorem over Local Fields.
2. (May 2023) Brown University. A Chebotarev Density Theorem over Local Fields.
3. (Jan 2023) JMM, Special Session - Excursions in Arithmetic Geometry. Just-likely and unlikely intersections on Shimura varieties.
4. (Dec 2022) John Hopkins Junior Number Theory Days 2022. On a p-adic Chebotarev density theorem.
5. (May 19, 2022) IISC Number Theory seminar, Bangalore. On the space of irreducible polynomials in many variables.
6. (April 30, 2022) ADDING seminar, Georgia. The variation of Frobenius eigenvalues in ℓ-adic towers of curves over a finite field.
7. (Nov 22, 2021) UW Madison Singularities seminar. On topological invariants of the space of irreducible polynomials in many variables.
8. (Oct 22, 2021) UW-Madison Algebraic Geometry seminar. A generalization of the ring of Symmetric functions and an application to computing topological invariants of graded monoid spaces.
9. (Oct 14, 2021) UW-Madison Number Theory seminar. The variation of the characteristic polynomial in ℓ-adic towers.

Expository Talks and Reading Groups

1. (July 28, 2017) Invited talk at TIFR. On mod-p and p-adic modular forms following Swinnerton-Dyer and Serre.
2. (Spring 2018-2019) For a course on Class Field Theory. On Drinfeld Modules.
3. (Spring 2018 - Fall 2019) Math-Physics reading group, UW Madison. Covered various topics such as Quantum cryptography, electromagnetism, statistical physics etc.
4. (Nov 10, 2020) Minnesota reading seminar on perfectoid spaces. On the Weight-Monodromy Conjecture.
5. (Feb 7, 2021) U-Washington reading seminar. On Mori's paper "Projective manifolds with ample tangent bundle."
6. (Winter 2020-21) Reading group on Weil I.
7. (Summer 2021) Reading group on Absolute Hodge Cycles.
8. (Summer 2021) Reading group on p-adic Hodge Theory.
9. Various talks in the Graduate Number Theory and Algebraic Geometry seminars at UW-Madison.

Teaching

1. (Fall 2018-19) Teaching Assistant; Math 221, UW-Madison: Calculus I.
2. (Fall 2018-19) Directed Reading Program for undergraduates, UW-Madison: Algebraic Geometry and Galois Theory.
3. (Spring 2018-19) Teaching Assistant; Math 222, UW-Madison: Calculus II.
4. (Spring 2018-19) Directed Reading Program for undergraduates, UW-Madison: Algebraic Number Theory.
5. (Fall 2019-20) Teaching Assistant; Math 234, UW-Madison: Calculus III.
6. (Spring 2019-20) Teaching Assistant; Math 240, UW-Madison: Discrete Math.
7. (Spring 2019-20) Directed Reading Program for undergraduates, UW-Madison: Galois Theory.
8. (Summer 2019-20) Instructor; Math 234, UW Madison: Calculus III.
9. (Fall 2020-21) Teaching Assistant; Math 340, UW-Madison: Linear Algebra.
10. (Spring 2020-21) Instructor; Math 96, UW Madison: Preparatory Algebra.
11. (Fall 2021-22) Teaching Assistant; Math 321, UW-Madison: Applied Mathematical Analysis.
12. (Spring 2021-22) Teaching Assistant; Math 321, UW-Madison: Applied Mathematical Analysis.