Permutation rational functions via Galois theory and elliptic curves
Dr. Zhiguo Ding
2023-05-16 16:30-17:30
MCM610
Speaker: Dr. Zhiguo Ding (Hunan Institute of Traffic Engineering)Time: 16:30-17:30 May 16, 2023 (Tuesday)
Place: MCM610
Title: Permutation rational functions via Galois theory and elliptic curves
Abstract: I will describe all rational functions f(X) in F_q(X) for which the map c-->f(c) induces a bijection P^1(F_q)-->P^1(F_q), under certain hypotheses on the degree of f(X). The main source of such functions is coordinate projections of elliptic curve isogenies. The proofs use Galois theory, group theory, and arithmetic geometry, and address new types of questions about elliptic curves.
