The second University Nottingham - University College Dublin Number Theory Day
Saturday May 2 2009
School of Mathematical Sciences
University of Nottingham
Organizers: Nigel Boston and Ivan Fesenko
All are welcome.
Dublin participants inlcude N. Boston, L. Caputo, R. Gow, K. Hutchinson, D. McCarthy,
R. Osburn, M. Myers, B. Sahu
Nottingham participants: K. Ardakov, N. Diamantis, I. Fesenko, F. Trihan, C. Wuthrich, A. Diaconu,
P. Lebacque, G. Yamashita, T. Blann, O. Braeunling, A. Camara, M. Morrow, T. Ward
Participants: S. Krishnamoorthy (Sheffield), S.V. Vostokov (St Petersburg)
- 10:30 tea/coffee
Adrian Diaconu (Minnealopis/Nottingham)
Moments of L-functions over rational function fields
Abstract: This talk presents new developments in understanding the analytic continuation of certain Dirichlet series in several complex variables associated to moments of quadratic Dirichlet L-functions. It is known that enough analytic information about these series implies the moment conjecture. We shall discuss this implication, as well as further interesting connections.
Kevin Hutchinson (UCD)
Milnor-Witt K-theory and the homology of the special linear group
Abstract: I will give a brief introduction to Milnor-Witt K-theory and will explain its role in answering some old questions about homology stability for special linear groups of fields.
Christian Wuthrich (Nottingham)
Derivatives of self-points
Abstract: For a cyclic subgroup C of order N of an elliptic curve E of conductor N in our previous work we constructed a modular point on E, called self-point, as the image of (E,C) on X_0(N) under the modular
parametrisation. In many cases (e.g. E is semi-stable), one can prove that
the point is of infinite order in the Mordell-Weil group of E over the field of definition of C.
More generally, we construct points in the PGL_2(Z_p)-tower inside the extension generated by p-primary-part of the torsion of E.
We also introduce derivatives à la Kolyvagin and then get new interesting
elements in Selmer groups.
Luca Caputo (UCD)
On the structure of étale wild kernels of number fields
Abstract: We give some results about the problem of determining if a given abelian p-group appears as étale wild kernels of a number field. Etale wild kernels, which are cohomological generalizations of the classical K-theory wild kernel, are related both with class groups and Iwasawa modules.
Dermot McCarthy (UCD)
On a supercongruence conjecture of Rodriguez-Villegas
Abstract: We discuss recent work concerning a conjectural supercongruence (due to Rodriguez-Villegas) between a special value of an ordinary hypergeometric series and the p-th Fourier coefficient of a modular form.
- 5:30 Ye Old trip to Jerusalem, a historical inn in the Nottingham city centre
- 7:00 Dinner at Mem Saab