Seminar Algebra and Geometry - Fall 2018

DateSpeakerTitleAbstract
September 18
11.00-11.30
Pascal Fong
(Basel)
Vector/projective bundles over curves Talk to present past and current work.
September 18
11.30-12.00
Sokratis Sikas
(Basel)
Birational Geometry of Algebraic Surfaces Talk to present past and current work.
September 25
10.30-11.00
Julia Schneider
(Basel)
A_k-singularities of plane curves of fixed bidegree Talk to present past and current work.
September 25
11.00-11.30
Egor Yasinsky
(Basel)
What transformation groups in algebraic, differential and metric geometry have in common? Talk to present past and current work.
September 25
11.30-12.00
Philipp Mekler
(Basel)
Algebraic Statistics: Gaussian Mixtures and Beyond Talk to present past and current work.
October 2
10.30-11.00
Immanuel van Santen
(Basel)
Embeddings and tame automorphisms in affine geometry Talk to present past and current work.
October 2
11.00-11.30
Anne Lonjou
(Basel)
Cremona group and geometric group theory Talk to present past and current work.
October 2
11.30-12.00
Jérémy Blanc
(Basel)
Birational geometry of surfaces and threefolds Talk to present past and current work.
October 9 no talk
   
October
10-11
Dijon-Basel-EPFL meeting
(Conference in Dijon)
   
October 16
10.30-11.15
Pierre-Marie Poloni
 
  Talk to present past and current work.
October 16
11.15-12.00
Richard Griffon
(Basel)
  Talk to present past and current work.
October 23  
 
   (Jérémy away)
October 30 Fano varieties and their automorphisms
(conference in Loughbourough)
   
November 6 Juliette Bavard
(Rennes)
Around a big mapping class group The plane minus a Cantor set and its mapping class group appear in many dynamical contexts, including group actions on surfaces, the study of groups of homeomorphisms on a Cantor set, and complex dynamics. In this talk, I will motivate the study of this 'big mapping class groups'. I will then present the 'ray graph', which is a Gromov-hyperbolic graph on which this group acts by isometries.
November 13 Lukas Lewark
(Bern)
Positivity, Graphs and Unknotting This talk will explore different notions of positivity of knots, how to encode such knots as graphs, and how to unknot them. Joint results with Baader/Liechti and Feller/Lobb will make appearances. No prerequisites in knot theory will be necessary.
November 20 Nikon Kurnosov
(University of Georgia, Athens, US)
Hyperkähler manifolds and their Betti numbers Hyperkähler manifolds are higher-dimensional generalizations of K3 surfaces. The Beauville conjecture predicts that the number of deformation types of compact irreducible hyperkähler manifolds is finite in any dimension. In this talk I will briefly discuss some basic notions of the theory, explain why hyperkähler manifolds play a very important role in classification of complex manifolds, and then explain what are the evidences for Beauville's conjecture.
November
26-30
Groups of birational transformations
(Conference in Rennes)
   
December 4 Bruno Laurent
(Grenoble)
Almost homogeneous curves and surfaces The varieties which are homogeneous under the action of an algebraic group are very symmetric objects. More generally, we get a much wider class of objects, having a very rich geometry, by allowing the varieties to have not a unique orbit, but a dense orbit. Such varieties are said to be almost homogeneous; this includes the case of toric varities, when the group is an algebraic torus.

In this talk, I will explain how to classify the pairs (X,G) where X is a curve or a surface and G is a smooth and connected algebraic group acting on X with a dense orbit.

For curves, I will mainly focus on the regular ones, defined over an arbitrary field. Over an algebraically closed field, the "natural" notion of non-singularity is "smoothness". However, over an arbitrary field, the weaker notion of "regularity" is more suitable. I will recall the difference between those two notions and show that there exist regular homogeneous curves which are not smooth.

For surfaces, I will restrict to the smooth ones, defined over an algebraically closed field. The situation is more complicated than for curves. Moreover, new phenomena and several difficulties appear in positive characteristic, and I will highlight them.
December 11 Luca Studer
(Bern)
Equations with complex analytic coefficients In the talk we discuss how Oka theory helps to solve systems of equations with complex analytic entries. A classical example is the fact that for every pair of complex analytic functions a, b: C^n -> C with no common zero there are complex analytic functions x, y: C^n -> C satisfying the B├ęzout identity ax+by=1. A more recent example is Leiterer's work, where the solvability of xax^{-1}=b for complex analytic matrix-valued maps a, b: C^n -> Mat(n x n, C) is investigated. Both examples are brought into the context of the speakers research.
December 18