Rational Points - Geometric, Analytic and Explicit Approaches

University of Warwick, 27 May - 31 May 2013
Organizers: Roger Heath-Brown (Oxford), John Cremona (Warwick), Samir Siksek (Warwick), Michael Stoll (Bayreuth), Damiano Testa (Warwick)

All talks will be in Room MS.01, Mathematics department, Zeeman Building (building no. 38 on this map).

Abstract are available here.

Monday 27 May

• 8.00-9.15 Registration (in the Mathematics Research Centre office, Zeeman Building).
  Coffee in the common room.
• 9.15-10.15 Trevor Wooley (Bristol)
  Systems of diagonal cubic equations
  
• 10.15-11.00 Coffee
• 11.00-12.00 Olivier Wittenberg (CNRS/ENS)
  On a conjecture of Kato and Kuzumaki about $p$-adic fields
  
• 12.00-14.00 Lunch
• 14.00-15.00 Jonathan Pila (Oxford)
  On atypical intersections in powers of modular curves
  
• 15.00-16.00 Tea
• 16.00-17.00 David M^cKinnon (Waterloo)
  Theorems of Roth and Liouville, only bigger
  
• 17.00 Reception
• 18.00 Dinner

Tuesday 28 May

• 9.15-10.15 Jean-Louis Colliot-Thélène (CNRS et Université Paris-Sud)
  Rational points on one-parameter families of 2-dimensional quadrics
  
• 10.15-11.00 Coffee
• 11.00-12.00 Martin Bright (American University of Beirut)
  Bad reduction of the Brauer-Manin obstruction
  
• 12.00-14.00 Lunch
• 14.00-15.00 Bianca Viray (Brown)
  Two-torsion Brauer classes on double covers of ruled surfaces
  
• 15.00-15.45 Tea
• 15.45-16.45 Alexei Skorobogatov (Imperial)
  Diagonal quartic surfaces, complex multiplication, and the Brauer-Manin obstruction
  
• 16.45-17.00 Break
• 17.00-17.30 Jan Steffen Müller (Hamburg)
  $p$-adic heights and integral points on hyperelliptic curves

Wednesday 29 May

• 9.15-10.15 David Harari (Orsay)
  Linear algebraic groups over the function field of a $p$-adic curve
  
• 10.15-10.45 Coffee
• 10.45-11.45 Jeroen Sijsling (Warwick)
  Galois descent and rational points
  
• 11.45-12.00 Break
• 12.00-13.00 Tim Dokchitser (Bristol)
  L-functions of hyperelliptic curves
  
• Free afternoon

Thursday 30 May

• 9.15-10.15 Tom Fisher (Cambridge)
  Computing the Cassels-Tate pairing
  
• 10.15-11.00 Coffee
• 11.00-12.00 Nils Bruin (Simon Fraser)
  TBA: Torsion in ideal class groups By Algebraic geometry
• 12.00-14.00 Lunch
• 14.00-15.00 Ulrich Derenthal (München)
  Integral Brauer-Manin obstructions for sums of two squares and a power
  
• 15.00-15.45 Tea
• 15.45-16.45 David Holmes (Leiden)
  Rational points on Kummer varieties
• 16.45-17.00 Break
• 17.00-17.30 Maciej Ulas (Jagellonian)
  Rational solutions of certain Diophantine equations involving norms
  

Friday 31 May

• 9.15-10.15 Tim Browning (Bristol)
  Rational points on the intersection of a cubic and quadric hypersurface
  
• 10.15-11.00 Coffee
• 11.00-12.00 Ronald van Luijk (Leiden)
  Density of rational points on Del Pezzo surfaces of degree one
  
• 12.00-14.00 Lunch and Departure