Rational Point Count Distributions for Varieties over Finite Fields via Coding Theory
Event details
| Date | 22.10.2014 |
| Hour | 15:15 › 16:15 |
| Speaker | Nathan Kaplan |
| Location | |
| Category | Conferences - Seminars |
We will discuss an approach of Elkies to counting points in families of varieties over a fixed finite field. A vector space of polynomials gives a linear subspace of (F_q)^N, a linear code, by the evaluation map. Studying properties of this code and its associated dual code gives information about the distribution of rational point counts for the family of varieties defined by these polynomials. We will describe how this approach works for families of genus one curves and del Pezzo surfaces. We will explain how Fourier coefficients of modular forms appear in these enumerative questions and will discuss further problems related to rational points on intersections of varieties. No previous familiarity with coding theory will be assumed.
Practical information
- Informed public
- Free
Organizer
- Natascha Fontana