School of Mathematical Sciences

University of Nottingham

All are welcome.

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
- 11:00-12:00
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.

- 12:10-1:10
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.

- 2:50-3:50
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.

- 4:00-4:30
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.

- 4:35-5:05
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