Number Theory Seminar HS 2019
Unless otherwise stated, all talks start at 14.15 and take place in Seminarraum 05.001, Spiegelgasse 5,
Information for speakers
| Date | Speaker | Title | Abstract |
|---|---|---|---|
| 10.10.2019 | Non-vanishing of cubic Dedekind zeta functions | In this talk I will discuss the first steps towards understanding the amount of non-vanishing at the central point of cubic Dedekind zeta functions. In particular I will describe some of the challenges we face in trying to generalize well-known results for quadratic Dirichlet L-functions to the cubic case. This is work in progress with Arul Shankar and Nicolas Templier. | |
| 31.10.2019 | Local Volumes and Monge-Ampère measures over a non-archimedean field | In algebraic geometry, the volume measures the size of the space of global sections of a line bundle. Similarly, the arithmetic volume measures the number of small global sections in Arakelov geometry. There is a local version of this volume over any non-archimedean field. We will show differentiability of such volumes and the connection to the non-archimedean Monge-Ampère problem. | |
| 07.11.2019 | Towards an "arithmetic" André-Oort conjecture | We present a not trivially false generalisation of the André-Oort conjecture. Indeed we prove it in two non trivial cases (one, under GRH, j.w. Edixhoven). We relate it to, and motivate it by, recents trends in equidistribution. | |
| 05.12.2019 | On Fourier coefficients of Poincaré series | Poincaré series are among the first examples of holomorphic and weakly holomorphic modular forms. They are useful in many analytical questions, but their Fourier coefficients seem hard to grasp algebraically. In this talk, I will discuss the arithmetic nature of Fourier coefficients of Poincaré series by characterizing them as cohomological invariants (periods). | |
| 12.12.2019 | Modular method for solving Diophantine equations | In this talk I will present the overview of modular approach to certain Diophantine equations (for example Fermat's equation). Using the modularity and Ribet's theorem as deep results, I will explain how Frey curves and newforms can be used to deduce information about solutions to Diophantine equations. This was the topic of my Master's thesis. | |
| 19.12.2019 | Semi-abelian varieties and unlikely intersections | In this talk, I will discuss semi-abelian varieties and families thereof. I will present results obtained with Fabrizio Barroero and Lars Kühne as well as Daniel Bertrand and also some with Gareth Jones. On the way I will give a description of Ribet section and their ``special” properties, using the language of generalised Jacobians. |