Michael Zshornack

Contact information

Mathematics Department
Northwestern University
2033 Sheridan Rd
Evanston, IL 60208

Office: Lunt 311
Email: [lastname]@northwestern.edu

About me

I am an RTG Postdoctoral Fellow and Boas Assistant Professor in the Math Department at Northwestern University. I earned my Ph.D. at UC Santa Barbara in June 2024 under Darren Long. A copy of my CV is available here.

I am broadly interested in arithmetic groups and character varieties, and how these objects interact with low-dimensional topology, geometric group theory, number theory and dynamics. For more information on my work, see the research section below.

Research

My research is largely centered around arithmetic groups, their subgroups and character varieties. I am interested in connections between these objects and low-dimensional topology, hyperbolic geometry and dynamics. Some specific things I like to think about include, but are not limited to:

• The structure of infinite-index, Zariski-dense subgroups of lattices in Lie groups.
• Algebro-geometric, topological and dynamical aspects of character varieties of surfaces and hyperbolic \(3\)-manifolds.
• Higher and lower-rank Teichmüller theory.

Preprints and Publications

1. Integral Zariski dense surface groups in \(\operatorname{SL}(n,\R)\). Math. Proc. Cambridge Philos. Soc. 179 (2025) no. 1, 63-78. (arXiv)

2. Rational approximation for Hitchin representations (with Jacques Audibert). Groups Geom. Dyn. To appear (2026). (arXiv)

3. A family of accumulation points of non-free rational numbers (with Christopher (Bobby) Buyalos^†, Jayden Thadani^†, Xinbei Wang^† and Bradley Zykoski). Submitted (2025). (arXiv)

4. Thin surface subgroups of non-uniform arithmetic lattices in \(\operatorname{SO}^+(n,1)\) (with Sara Edelman-Muñoz). Submitted (2026). (arXiv)

^† indicates undergraduate author.

Other selected writings

1. My Ph.D. Thesis.

Teaching

Current Teaching

• Fall 2026: Math 230-2, Multivariable Integral Calculus

Past Teaching

Boas Assistant Professor at Northwestern University

• Spring 2026: Math 240-0, Linear Algebra

• Fall 2025: Math 220-1, Single-Variable Differential Calculus

• Winter 2025: Math 220-2, Single-Variable Integral Calculus

• Fall 2024: Math 220-1, Single-Variable Differential Calculus

Teaching Associate at UC Santa Barbara

• Summer 2023: Math 6A, Vector Calculus

• Summer 2022: Math 6A, Vector Calculus