Random Polynomials, Probabilistic Galois Theory, and Finite Field Arithmetic
Lior Bary-Soroker (School of Mathematical Sciences of Tel Aviv University)
17-Dec-2020, 13:00-14:00 (3 years ago)
Abstract: We will discuss recent advances on the following two question: Let A(X) =Σ ±Xi be a random polynomial of degree n with coefficients taking the values -1, 1 independently each with probability 1/2. Q1: What is the probability that A is irreducible as the degree goes to infinity Q2: What is the typical Galois of A? One believes that the answers are YES and THE FULL SYMMETRIC GROUP, respectively. These questions were studied extensively in recent years, and we will survey the tools developed to attack these problems and partial results.
algebraic geometrynumber theory
Audience: researchers in the topic
Algebraic Geometry and Number Theory seminar - ISTA
Organizers: | Tamas Hausel*, Tim Browning* |
*contact for this listing |
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