Explicit Methods in Number Theory: Conference in Honour of Cremona's 60th Birthday, University of Warwick, 4-8 April 2016

Organizers: Lassina Dembele (Warwick), Tom Fisher (Cambridge), Haluk Sengun (Sheffield), Samir Siksek (Warwick)

All talks take place in room MS.02, Mathematics Institute, Zeeman Building.

Monday 4 April

• 8:30--9:15 registration and coffee in the Mathematics Institute Common Room
• 9:15--10:15 Hendrik Lenstra (Leiden)
  "Abelian automorphisms towers"
• 10:15--11:00 Coffee and tea break in A0.05
• 11:00--12:00 Henri Cohen (Bordeaux)
  "L-functions and modular forms in Pari/GP"
  
• 12:00--14:00 Lunch in A0.05
• 14:00--15:00 Haluk Sengun (Sheffield)
  "Mod p automorphic forms"
• 15:00--15:45 Coffee and tea break in A0.05
• 15:45--16:45 Tony Scholl (Cambridge)
  "Special values of L-functions"
• 17:00--18:15 Wine reception in the Mathematics Institute Common Room
• Conference dinner at Scarman

Tuesday 5 April

• 9:15--10:15 Tom Fisher (Cambridge)
  "Binary quartics and the Cassels-Tate pairing"
• 10:15--11:00 Coffee and tea break in A0.05
• 11:00--12:00 Lassina Dembele (Warwick)
  "On the existence of abelian surfaces with everywhere good reduction"
• 12:00--14:00 Lunch in A0.05
• 14:00--15:00 Lynne Walling (Bristol)
  "Explicit action of Hecke operators on half-integral weight Siegel Eisenstein series"
• 15:00--15:45 Coffee and tea break in A0.05
• 15:45--16:45 Ariel Pacetti (Leverhulme Trust Visiting Professor)
  "Computing tables of elliptic curves over $\mathbb{Q}(i)$"

Wednesday 6 April

• 9:15--10:15 Michael Stoll (Bayreuth)
  "The Generalized Fermat equation $x^2 + y^3 = z^{11}$"
• 10:15--11:00 Coffee and tea break in A0.05
• 11:00--12:00 Samir Siksek (Warwick)
  "Semistability and Serre's uniformity"
• 12:00--13:00 Lunch in A0.05.
  Free Afternoon.

Thursday 7 April

• 9:15--10:15 Andrew Sutherland (MIT)
  "Torsion subgroups of rational elliptic curves over the compositum of all cubic fields"
• 10:15--11:00 Coffee and tea break in A0.05.
• 11:00--12:00 Barinder Banwait (Essen)
  "Traces of Frobenius and an inverse Galois Problem for cubic surfaces over finite fields"
• 12:00--14:00 Lunch in A0.05.
• 14:00--15:00 Denis Simon (Caen)
  "Squares represented by cubic forms"
• 15:00--15:45 Coffee and tea break in A0.05.
• 15:45--16:45 Soma Purkait (Kyushu)
  "Hecke algebras, new vectors and characterization of the new space"

Friday 8 April

• 9:15--10:15 Manjul Bhargava (Princeton)
  "A positive proportion of plane cubics fail (respectively satisfy) the Hasse principle"
• 10:15--11:00 Coffee and tea break in A0.05.
• 11:00--12:00 Bryan Birch (Oxford)
  "Insoluble curves"
• 12:00--13:00 Lunch in A0.05.
  Departure