Photo credit: Henry Baring

Visiting Assistant Professor

Department of Mathematics

Colby College

**Contact Information**

Office: Lovejoy 108

E-mail: jpetok (at) colby (dot) edu

Mailing address: Department of Mathematics, 4000 Mayflower Hill, Waterville , ME 04901

I am a Visiting Assistant Professor at Colby College in Waterville, Maine. From 2020-2024, I was based at Dartmouth College, working under the supervision of Asher Auel. In Fall 2023, I was a visitor at the Hausdorff Research Institute for Mathematics in Bonn, Germany as a participant in the Junior Trimester Program in Algebraic Geometry. I received my PhD in 2020 under the supervision of Anthony Várilly-Alvarado.

In Fall 2023, I co-organizined the STReTCH seminar in Bonn with Xuqiang Qin.

**Research Interests**

General interests: Algebraic Geometry, Arithmetic Geometry, Number Theory

**Papers**

Kodaira dimension of moduli of special K3^[2]-fourfolds of degree 2 (2023, in Journal des Mathématiques Pures et Appliquées). Associated code. Journal version.

A census of cubic fourfolds over F2. (to appear in Mathematics of Computation, with Asher Auel, Avinash Kulkarni, Jonah Weinbaum). Associated code.

On decompositions for Fano schemes of intersections of two quadrics (submitted, with Pieter Belmans, Jishnu Bose, Sarah Frei, Benjamin Gould, James Hotchkiss, Alicia Lamarche, Cristian Rodriguez Avila, Saket Shah).

Zeta functions of K3 categories over finite fields (preprint, with Asher Auel ).

Rational points on modular curves of composite level (preprint, with Catalina Camacho Navarro, Wanlin Li, Jackson Morrow, David Zureick-Brown).

Sections of quadric fourfold bundles over surfaces (with Asher Auel ). In preparation.

**Teaching**

Math 160 - Series and Multivariable Calculus - Fall 2024 - Colby

Math 130 - Calculus I Revisited - Fall 2024 - Colby

Math 8 -Calculus of One and Several Variables - Spring 2023 - Dartmouth

Math 3 -Calculus - Winter 2023 - Dartmouth

Math 9 -Multivariable Calculus with Linear Algebra- Fall 2022 - Dartmouth

Math 11 -Accelerated Multivariable Calculus - Fall 2022 - Dartmouth

Math 8 -Calculus of One and Several Variables - Spring 2022 - Dartmouth

Math 81 - Galois Theory - Winter 2022 - Dartmouth

Math 31 - Topics in Algebra - Fall 2021 - Dartmouth

Math 25 - Number Theory - Fall 2021 - Dartmouth

Math 22 - Linear Algebra - Spring 2021 - Dartmouth

Math 8 - Calculus of One and Several Variables - Winter 2021 - Dartmouth

Math 22 - Fall 2020 - Linear Algebra - Dartmouth

Math 8 - Calculus of One and Several Variables - Fall 2020 - Dartmouth

Math 365 - Number Theory - Summer 2020 - Rice

Math 355 - Linear Algebra - Summer 2018 - Rice

Math 211 - Linear Algebra and Differential Equations Fall 2017 - Rice

** Old stuff**

Some random incomplete notes that some people have occasionally found useful.

- Math 567 - Topics in Algebraic Geometry: Modular Curves (Taught by Richard Shadrach, Fall 2015).
- Math 539: Geometric Topology (Taught by Andrew Putman, Fall 2015).
- Borel subgroups and parabolic subgroups

** Fun stuff**
Some non-mathematical activities that I enjoy: cooking, singing, hiking, biking, and skiing.

**Links**