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Isaac Newton Institute for Mathematical Sciences

Arithmetic Geometry

5 January - 3 July 1998

Organisers: J-L Colliot-Thélène (Orsay); J Nekovár (Cambridge); C Soulé (IHES)

A Newton Institute Workshop

During the programme on Arithmetic Geometry (organizers J-L Colliot-Thélène, J Nekovár, C Soulé)
at the Newton Institute (Cambridge, UK),

Arakelov Theory, Values of L-Functions

29 June to 3 July 1998

Organizers: J Nekovár and C Soulé

Monday 29 June

09.00-11.00 Registration

11.00-11.30 Coffee

11.30-12.30 A Goncharov (Brown)
Multiple $\zeta$-values and modular complexes

13.00-14.00 Lunch

14.00-15.30 Pilgrimage to the bank

15.30-16.30 P Vojta (Berkeley)
On Bu"chi's problem and Hilbert's tenth problem

16.30-17.00 Tea

17.00-18.00 KI Yoshikawa (Nagoya)
Analytic torsion and automorphic forms on the moduli space

18.00-19.00 Wine reception

Tuesday 30 June

10.00-11.00 JB Bost (CNRS, IHES)
Intersection theory on arithmetic surfaces, $L^2_1$-Green functions, and hyperbolic metrics

11.00-11.30 Coffee

11.30-12.30 M Rapoport (Köln)
Height pairings on Shimura curves and p-adic uniformization

13.00-14.00 Lunch

15.00-16.00 N Dan (Paris 13)
Analytic continuation of Green currents

16.00-17.00 Tea

17.00-18.00 A Moriwaki (Kyoto)
Inequalitites for semistable families of arithmetic varieties

Wednesday 1 July

10.00-11.00 H Tamvakis (University of Pennsylvania)
Arithmetic Schubert calculus

11.00-11.30 Coffee

11.30-12.30 U Tipp (Nottingham)
A Gross-Zagier formula over function fields

13.00-14.00 Lunch

15.00-16.00 K Köhler (Bonn)
The arithmetic Lefschetz fixed point formula and heights

16.00-18.30 Free time

18.30- 19.30 Reception at the Cambridge University Press bookstore

Thursday 2 July

10.00-11.00 AJ Scholl (Durham)
Kato's Euler systems and explicit reciprocity laws

11.00-11.30 Coffee

11.30-12.30 SW Zhang (Columbia)
A Gross-Zagier formula over totally real fields

13.00-14.00 Lunch

15.00-16.00 J Kramer (Humboldt University)
Green currents, automorphic forms and L-functions

16.00-17.00 Tea

17.00-18.00 T Tucker (Berkeley)
Dirichlet's theorem, Vojta's inequality, Vojta's conjecture, and related problems

Friday 3 July

10.00-11.00 J Burgos (Barcelona)
Higher Bott-Chern forms and Beilinson's regulator

11.00-11.30 Coffee

11.30-12.30 E Ullmo (Orsay)
Falting's height of quotients of $J_0(N)$ and related topics

13.00-14.00 Lunch

15.00-16.00 P Michel (Orsay)
Non-vanishing of automorphic L-functions (from the analytic point of view) : results and applications

16.00-17.00 Tea

17.00-18.00 M Taylor (UMIST)
Epsilon constants of metrised line bundles

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