Josie Hlavinka

About Me

Hi! My name is Josie (she/her), and I'm a fourth year graduate student in the Mathematics department at UC Berkeley. I am advised by David Nadler. I am a 2026 Simons Dissertation Fellow, and I am grateful to be supported by an NSF GRFP grant.

I work between symplectic and algebraic geometry, focusing largely on the geometry of varieties which have interesting interactions with combinatorics. At the moment I am nearly finished with a project proving a version of mirror symmetry for acyclic cluster varieties.

You can contact me at josephhlavinka AT berkeley DOT edu, and one can find my past papers below.

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I received my Sc. B. from Brown University, magna cum laude. I worked fairly extensively with Melody Chan and Brendan Hassett while I was there.

In my free time I listen to and play a great deal of experimental music. I also recently got 3rd place in a donut eating contest.

Research

Homological Mirror Symmetry for Acyclic Cluster Varieties, in preparation.

Mixed Tateness and Cohomological Vanishing for Cluster Varieties, preprint.

Fence Complexes and Toric Degenerations of Positroid Varieties (with Cameron Chang and Pranav Enugandla), submitted.

Automorphisms of Tropical Hassett Spaces (with Sam Freedman and Siddarth Kannan), in Port. Math. 79 (2022), no. 1/2, pp. 163-197.

Surveys and Proceedings

Talbot 2024: Topological Cyclic Homology of Ring SpThe M. Lecture 3: Computation of THH(F_p) (2025), notes by Akira Tominaga.

Motivic Homotopy Theory and Cellular Schemes (2022), via the UChicago REU.

My undergraduate honors thesis (uncompleted for personal reasons) was slated to describe a generalization of the Fulton-Macpherson compactification of Conf_n(X) to a family of "weighted" compactification of spaces of the form X^n \ a set of small diagonals. While I no longer think this research will see the light of day, I am happy to discuss it with any interested party.

Teaching and Outreach

I was a GSI for Alex Paulin in Math 1A and 1B, Berkeley's Calc I and II courses, in the fall of 2024 (for 1A) as well as the spring of both 2024 and 2025 (for 1B). If I was your GSI and you are in need of further support, please reach out!

For most of the summers between 2019 and 2023 I was very lucky to work as an instructor at Bridge to Enter Advanced Mathematics (BEAM), where I taught under-represented and low-income rising 7th graders some really cool math. Check BEAM out!

I am very excited to be an instructor at Mount Tamalpais College starting this coming Fall.

Organizing

In the 2025-26 school year I was an organizer for David Nadler's Geometric Representation Theory, notes for which are written by the inimitable John S. Nolan and hosted here. The topic of the seminar was equivariant homotopy theory in Fall 2025 and potent categorical representations (in the sense of Ben-Zvi and Nadler's ICM address) in Spring 2026.

I am an ardent believer in Federico Ardila's axioms for mathematical education, outreach, and practice:

Axiom 1. Mathematical potential is equally present in different groups, irrespective of geographic, demographic, and economic boundaries.

Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

Axiom 4. Every student deserves to be treated with dignity and respect.

As Prof. Adrila notes, these statements should not sound revolutionary, and considering the current practices of mathematical society, they are a pressing call to action.

Friends :)

I'm lucky to have some cool mathematical friends. Check out their websites!

Vilas Winstein: https://vilas.us/

Charlotte Keisling: https://sites.google.com/berkeley.edu/keisling

Gabriel Beiner: https://math.berkeley.edu/~gbeiner/

Will Fisher: https://math.berkeley.edu/~willfisher/

Brian Sun: https://math.berkeley.edu/~bsun/

Zarif Ahsan: https://sgs.stanford.edu/news/meet-zarif-ahsan-25

Katalin Berlow: https://katalinberlow.github.io/

Sophie McCormick: https://sites.google.com/view/sophie-mccormick