Guest seminar winter 2017/18
Guest seminar "Arithmetic Geometry"
Time: Thursdays, 2pm4pm
Place: SR 032 Arnimallee 6
Talks:
Date  Speaker(s) 

October 12 
Richard Griffon Title: A BrauerSiegel theorem for Fermat surfaces The classical BrauerSiegel theorem gives asymptotic upper and lower bounds on the product of the classnumber times the regulator of units of a number field in terms of its discriminant. In this talk, I will describe an analogous result in a more geometric context. Namely, for a Fermat surface F over a finite field, we consider the product of the order of its Brauer group (which is known to be finite) by the Gram determinant of a basis of its NéronSeveri group for the intersection form, and we describe the growth of that product in terms of the geometric genus of F when the latter grows to infinity. As in the classical setting, the proof of the asymptotic estimate is rather analytic: it relies on obtaining asymptotic bounds on the size of the ``residue’’ of the zeta function of F at its pole at s=1. 
October 19 
Markus Röser (Hannover) Minicourse nonabelian Hodge theory 
October 26 
Markus Röser (Hannover) Minicourse nonabelian Hodge theory 
November 2 (1/2)  Yves André (Paris) Title: Perfectoid spaces and the homological conjectures 
November 2 (2/2)  Oliver Braunling (Freiburg) Title: Ktheory of locally compact (instead of finitely generated) modules We discuss a generalization of a March 2017 theorem of Dustin Clausen, 
November 9 
Jungkai CHEN (National Taiwan University) Title: Pluricanonical maps of higher dimensional varieties.

November 16 (Special Time: 10:30 am sharp, SR140/A7) 
Gereon Quick (Norwegian University of Science and Technology) Title: Examples of nonalgebraic classes in the BrownPeterson tower 
November 23 
Michael Gröchenig A short talk offseminar. 
November 30. (Time: 15:00 Sharp) 
Shane Kelly Title: Introduction to (stable) motivic homotopy theory. 
11. January 
Marco d'Addezio Title: Lisse sheaves and Fisocrystals. 
18. January 
Michel van Garrel (University of Hamburg) Title: A constructive approach to a conjecture by Voskresenskii Voskresenskii conjectured that stably rational tori are rational. Klyachko proved this assertion for a wide class of tori by general principles. In this joint work with Mathieu Florence, we reprove Klyachko’s result by providing simple explicit birational isomorphisms. 
25. Jan. 
Giulio Bresciani (Scuola Normale Superiore, Pisa) Title: The dimensional section conjcture. Abstract: Vistoli observed that, if Grothendieck's section conjecture is true, there should be some notion of dimension such that for an hyperbolic curve over a field finitely generated over Q the space of sections has dimension 1. If one could prove this, it would give a dimensional obstruction to the existence of sections. We propose such notion as a modification of essential dimension, and make some steps toward proving that this dimension is 1 for the space of sections of P^1 minus three points. 
1. Feb 
Michael Gröchenig Title: padic integration for Hitchin systems 