Max Weinreich



About me

I am an NSF Postdoctoral Fellow at Harvard University, working at the intersection of dynamical systems, algebraic geometry, and number theory. I received my Ph. D. from Brown University in May 2022, advised by Joe Silverman. My NSF supervisor is Laura DeMarco.

I am on the job market for positions that start in Fall 2025.

Pronouns: he/him

Curriculum Vita (CV)

Contact Info

Email: mweinreich [at] math [dot] harvard [dot] edu

Papers

7. Algebraic billiards in the Fermat hyperbola. Preprint, submitted, 34 pages, 2024.

6. The dynamical degree of billiards in an algebraic curve. To appear in Journal of Geometric Analysis, 2024. 46 pages. talk video

5. GIT stability of linear maps on projective space with marked points. To appear in Illinois J. Math., 2024. 39 pages.

4. Dynamical moduli spaces and polynomial endomorphisms of configurations. With Talia Blum, John Doyle, Trevor Hyde, Colby Kelln, and Henry Talbott. Arnold Math Journal, 33 pages, 2022. arxiv

3. The algebraic dynamics of the pentagram map. Ergodic Theory and Dynamical Systems, 46 pages, 2022. arxiv

2. Automorphism groups of endomorphisms of P^1(F_p). With Julia Cai and Benjamin Hutz and Leo Mayer. Glasgow Math Journal, 34 pages, 2022. arxiv

1. Counting arcs in projective planes via Glynn's algorithm. With Nathan Kaplan, Susie Kimport, Rachel Lawrence, and Luke Peilen. Journal of Geometry, 17 pages, 2017. arxiv


About my math

I study arithmetic dynamics, which is the study of iteration of functions in number theory. My particular interests include dynamical degrees, billiards, moduli spaces, integrable systems, finite fields, and projective configurations.

The image shows a three-circle Venn diagram. The intersection of Algebraic Geometry and Dynamical Systems is Algebraic Dynamics. The intersection of Algebraic Geometry and Number Theory is Arithmetic Geometry. The intersection of Number Theory and Dynamical Systems is Arithmetic Dynamics. My research is in the triple intersection.

My recent work is on billiards in algebraic curves. Watch a video that illustrates my work!

The onset of chaos in the billiard inside an elliptic curve, but not an ellipse.

Notes

Topics course notes on dynamical degrees

Mapping classes and character varieties

Julia sets in Berkovich space

NSF Information

My work is currently supported by NSF Grant No. 2202752. My graduate work was supported by NSF Grant No. 2040433.