**Speaker: **Michel Lavrauw, Sabancı University

**Title: ** On linear systems of conics over finite fields

**Date/Time:** 14 October 2020 / 13.40-14.30

**Zoom:Meeting ID: **212 003 6001**Passcode**:

**Abstract:** A form on an n-dimensional projective space P^n is a homogeneous polynomial in (n + 1) variables. The forms of degree d on P^n comprise a vector space W of dimension {n+d \choose d}. Subspaces of the projective space PW are called linear systems of hypersurfaces of degree d. The problem of classifying linear systems consists of determining the orbits of such subspaces under the induced action of the projectivity group of P^n on PW. In this talk we will focus on linear systems of quadratic forms on P^2 over finite fields. We will give an overview of what is known and explain some of the recent results. This is based on joint work with T. Popiel and J. Sheeke.

**Bio:**Michel Lavrauw studied Mathematics at Ghent University (Belgium), and obtained a Ph.D. degree in Mathematics from Eindhoven University of Technology (The Netherlands) in 2001 under the supervision of Aart Blokhuis and Andries Brouwer. He worked as a postdoc at the University of Naples (Marie Curie Fellowship), at Universitat Politècnica de Catalunya in Barcelona (EU-project COMBSTRU), at Eindhoven University of Technology (Veni grant (NWO)), at Ghent University (FWO fellowship), and at Vrije Universiteit Brussel (VUB). In 2012, he obtained the Abilitazione Scientifica Nazionale for full professor (settore 01/A1, Algebra/Geomety) from the Italian Ministero dell'Istruzione dell'Università e della Ricerca, and was a faculty member at the University of Padua (Italy) from 2011-2017. In 2017 he joined the Math group of the Faculty of Engineering and Natural Sciences at Sabancı University. The research of Michel Lavrauw is focussed on the areas of combinatorics, algebra, Galois geometry, finite geometry, incidence geometry, finite fields and coding theory. More specifically, arcs in projective spaces, finite semifields (non-associative division algebras), projective planes, Segre varieties, Veronese varieties, geometry of tensor product spaces, translation generalised quadrangles (equivalent to the theory of eggs in projective spaces), polynomial techniques in finite geometry, field reduction techniques, linear sets, MDS codes, MRD codes, and the links between incidence geometry and coding theory. He is one of the organisers of the Irsee conference on Finite Geometries and is one of the authors of the GAP-package FinInG for computation in Finite Incidence Geometry. He is a member of the editorial boards of the journals "Finite Fields and Their Applications" and "Designs, Codes and Cryptography".