Ivan Arzhantsev - Werner Bley - Ulrich Derenthal - Andreas Rosenschon - Eva Viehmann
Summer 2012, Wednesdays, 16:30, room B 040 (Mathematisches Institut, Theresienstr. 39, 80333 München)
Previous semester: Winter 2011/12
| Termin | Vortragende/r | Titel | Bemerkungen |
|---|---|---|---|
| 18.4.12 | Fei Xu (Capital Normal University, Beijing) | Very strong approximation with Brauer-Manin obstruction for certain algebraic varieties | |
| 25.4.12 | Ivan Arzhantsev (Moscow State University / LMU München) | Additive structures on projective varieties and local algebras | |
| 9.5.12 | Kazim Buyukboduk (Koç University) | Deformations of Kolyvagin systems | |
| 16.5.12 | Ulrich Görtz (Universität Duisburg-Essen) | Affine Deligne-Lusztig varieties in the Iwahori case | |
| 30.5.12 | Sujatha Ramdorai (Tata Institute of Fundamental Research) | Doppelvortrag ab 15:30 Uhr an der TU München | |
| 30.5.12 | Alexis Bouthier (Université Paris-Sud, Orsay) | (Leibniz-Rechenzentrum, HE 008) | |
| 13.6.12 | Marc Nieper-Wißkirchen (Universität Augsburg) | ||
| 20.6.12 | Alfred Weiss (University of Alberta) | ||
| 20.6.12 | Thanasis Bouganis (Universität Heidelberg) | ||
| 27.6.12 | Kapil Paranjape (Indian Institute of Science Education and Research, Mohali) | ||
| 27.6.12 | Mathias Lederer (Universität Bielefeld) | ||
| 4.7.12 | Chad Schoen (Duke University) | ||
| 18.7.12 | Urs Hartl (Universität Münster) | ||
| 18.7.12 | Yuri Prokhorov (Moscow State University) | Subgroups of Cremona groups |
By using Manin's idea, one can refine the classical strong approximation to the strong approximation with Brauer-Manin obstruction. Several achievements have been made recently for homogeneous spaces and some families of homogeneous spaces with some application to study the existence of the integral points. In this talk, we will explain that for certain algebraic varieties one can have even stronger property than strong approximation with Brauer-Manin obstruction. We will also discuss a conjecture proposed by Harari and Voloch.
Let C be the additive group of the field of complex numbers. An additive structure on an n-dimensional complex projective variety X is a regular action of Cn on X with an open orbit. Such a structure allows to consider X as an equivariant compactification of Cn. This way we obtain an additive version of toric geometry.
In 1999 Hassett and Tschinkel established a remarkable correspondence between additive structures on projective spaces and Artinian local algebras. This correspondence implies that the number of equivalence classes of additive structures on Pn with n>5 is infinite.
We will discuss the Hassett-Tschinkel correspondence and related numerical invariants of local algebras together with some classification results. A generalization of the correspondence to projective hypersurfaces will be given and additive structures on flag varieties of semisimple algebraic groups will be described. Also we will discuss some results on equivariant compactifications of arbitrary commutative linear algebraic groups.
Mazur's theory of Galois deformations, inspired by Hida's earlier work on families of modular forms, has led to the resolution of many important conjectures in Number Theory, such the Taniyama-Shimura conjecture or many cases of the strong Artin conjecture for GL2. In this talk, I will first give a general outline of Mazur's abstract theory and talk about a recent result that Kolyvagin systems (which Mazur and Rubin prove to exist for mod p Galois representations) do often deform to a big Kolyvagin system for the "Universal Galois deformation" representation. I will touch upon arithmetic applications of this result.
Affine Deligne-Lusztig varieties are a group-theoretic tool to study arithmetic properties of Shimura varieties. They are analogs in the setting of an affine root system of classical Deligne-Lusztig varieties, which have significant applications in the representation theory of finite groups of Lie type.
I will explain the basic notions, some results and open questions in elementary terms, and report on recent work with Xuhua He and Sian Nie.
The Cremona group Crn is the group of automorphisms of the rational function field k(t1,t2,..., tn). I describe the method that allows to find finite subgroups of Crn. I introduce minimal models (G-Fano-Mori models), outline the classification in dimension 2, and give a lot of examples in dimension 3. Relation to the notion of essential dimension will also be discussed.
