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This Week’s Discoveries | 6 February 2018

6 februari 2018
Oort Building
Niels Bohrweg 2
2333 CA Leiden
De Sitterzaal

First Lecture

Jupiter internal structure and the first Juno results

Yamila Miguel ( Leiden Observatory)
Yamila is originally from Buenos Aires, Argentina, where she completed her PhD studying planetary systems formation. From 2011 to 2014 she was a postdoctoral Fellow at the Max Planck Institute for Astronomy, where she started studying chemistry in exoplanets’ atmospheres (rocky and giant planets). She was at the Observatoire de la Côte d’Azur between 2015 and 2017 (as a Henri Poincaré Postdoctoral Fellow and later a CNES Postdoctoral Fellow), studying the interior structure of giant planets and as a part of the Juno mission science team. This year she started as an assistant professor at Leiden Observatory where she will continue studying (exo)planet atmospheres and their interiors, towards a better understanding of their origins. her main interests are the study of atmospheres, interior and formation of exoplanets and planets in our solar system. 

The key to understand our origins is in the interiors and atmospheres of the giant planets. Jupiter is the biggest planet in our system and the most influential one: its large mass shaped the architecture of the solar system and due to its fast formation it contains valuable information of the solar system formation history. In orbit since July 2016, the first orbits of Juno mission had led to a remarkable improving of the planet gravity data, changing our knowledge of the planetary interior and leading to a much better comprehension of the giant planet and its role in the solar system. In this talk, I will present the last Juno results and the models we use to understand Jupiter interior.

Second Lecture

Formulas of Tamagawa type in positive characteristic

Maxim Mornev (MI)
Maxim is a ALGANT PhD student in the Arithmetic Geometry group of Bas Edixhoven. His supervisors are Lenny Taelman (Leiden, now in Amsterdam) and  Fabrizio Andreatta (Milan). He will defend his thesis entitled “Shtuka cohomology and special values of Goss L-functions” on February 13.

The equivariant Tamagawa number conjecture (ETNC) aims to express special values of L-functions via motivic cohomology. It generalizes classical results such as the Leibniz formula for π and Euler's Basel identities, as well as the famous conjecture of Birch and Swinnerton-Dyer, one of the Millenium prize problems. The ETNC is wide open and is out of reach of current methods.

Recent research suggests that a similar problem makes sense and is much more amenable for certain unusual number systems, the so-called rings of positive characteristic. Lenny Taelman discovered that an analog of the BSD conjecture holds for one number system of this sort, the ring of polynomials with coefficients in a finite field. Inspired by the original ETNC I generalized his result to a wide class of similar number systems. In this talk I will discuss examples of the beautiful and deep formulas which follow from the equivariant Tamagawa number conjecture and its analog in positive characteristic.

This Week's Discoveries