** Algebraic Dynamics Seminar at Harvard **

We meet in Room 232 of the Science Center, usually on Thursdays at 4pm. Seminars are typically ** two hours ** long, with a break in the middle and the second hour for more details. Please email me (Laura DeMarco) if you are interested in joining the email list, so I can send you announcements (and Zoom links if the talk is remote). The math department is locked, so let me know if you are not from Harvard but would like to attend a lecture.

Next talk:

**Tuesday, December 6**, 3-5pm in **Room 530**

Jit Wu Yap (Harvard)

Distribution of n-cycles of polynomials over finite fields
Abstract: Let d,n be positive integers. Given a polynomial f of degree d over a finite field Fq, one can view it as a discrete dynamical system on the points of Fq. A natural question to ask if how many n-cycles does a random such f have. We show that if one fixes d,n then as q goes to infinity, the distribution of n-cycles converges to a natural limiting distribution. A key input in our proof is a theorem regarding the Galois group of periodic points. In the second half, I will try to explain how to prove this using the geometry of the Mandelbrot set. This is joint work with Michael Kural.

** Fall 2022 schedule**

September 15. Kathryn Lindsey, Boston College

September 22. Alex Kapiamba, University of Michigan

October 13. Philip Engel, University of Georgia

October 27. Becca Winarski, College of the Holy Cross

November 3. Max Weinreich, Harvard

November 17. Rafael Saavedra, Harvard

December 6 (Tuesday), 3-5pm. Jit Wu Yap, Harvard