George M. Walker

Principal areas of interest

Computational Number Theory and Arithmetic Algebraic Geometry, specifically in computing Zeta functions of varietes over finite fields using p-adic cohomology. I am currently working on implementing Lauder's "Fibration Algorithm" in new cases. I completed my DPhil under the supervision of Alan Lauder at the University of Oxford in 2009.

• Curriculum vitae
(email me for a copy)

Papers, preprints and publications

• Thesis
• Explicit lattices in crystalline cohomology
(submitted)
• Point counting using fibration in $p$-adic cohomology
(submitted)
• Average behaviour of elliptic curves over function fields of positive characteristic
(in preparation)

Software

• The fibration algorithm for curves
• The fibration algorithm for surfaces fibred into C_ab curves
(coming soon)

Talks and presentations

• Mon 8/12/08, TCC Number Theory Day, University of Oxford, "Computing zeta functions of varieties over finite fields using p-adic cohomology"
• 6-10/07/09, Journées de Géométrie Arithmétique, Rennes, "Minimalism on elliptic curves and computing ranks using p-adic cohomology"
• Wed 27/01/10, University of Bristol Heilbronn seminar, "Counting points on varieties over finite fields by fibration"
• Thurs 4/02/10, University of Oxford Number Theory Seminar, "Point counting via fibration and minimalism on elliptic curves"
• Wed 17/03/10, Effective methods in p-adic cohomology workshop, Oxford, "Minimalism on Ellipic curves"
• Wed 19/05/10, Workshop on Computational Number Theory and Arithmetic Geometry, K.U. Leuven, "Counting points on curves by fibring into zero dimensions"
• Tues 01/06/10, Warwick University Number Theory Seminar, "Computing the number of points on varieies over finite fields using $p$-adic cohomology".
• Tues 18/05/11, University of Bristol Junior Number Theory Seminar, "Average behaviour of elliptic curves over global fields".
• Tues 08/06/11, Goettingen University Algebraic Number Theory Seminar, "A survey of point counting on varieties over finite fields using $p$-adic cohomology".
• Tues 14/06/11, Humboldt University, Berlin, Arithmetic Geometry Seminar, "Zeta functions of plane curves".

University of Oxford Junior Number Theory Seminar talks given:

• Mon, 16/10/2006: Introduction to the Riemannn hypothesis for curves over finite fields
• Mon, 27/11/2006: Counting rational points and the zeta-function modulo p
• Mon, 29/01/2007: Cyclotomic and Kummer Extensions
• Mon, 07/05/2007: Computing zeta functions using p-adic cohomology
• Mon, 12/11/2007: An excursus in computations in deforming curves in weighted projective spaces
• Mon, 25/02/2008: Resultants, Discriminants and the Principal A-Determinant
• Mon, 09/06/2008: Counting points on surfaces by counting points on curves
• Mon, 16/02/2009: An Elementary Proof of Hasse's Theorem on Elliptic Curves over Finite Fields
• Mon, 01/06/2009: Introduction to the Birch–Swinnerton-Dyer Conjecture. III: Average ranks, the Artin–Tate conjecture and function fields.
• Mon, 16/11/2009: A soupçon of Berkovich spaces

Links

• Walker Architecture
• Chloe Walker jewellery

Address: School of Mathematics,
	 University of Bristol
	 University Walk
	 Bristol, BS8 1TW

e-mail:george.walker@bristol.ac.uk