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Basel-Dijon-EPFL seminar
Basel, June 4-5, 2019
Schedule
In Alte Universität, Raum 101, Rheinsprung 9, 4051 Basel
Tuesday
June 4
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Wednesday
June 5
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11h30-12h30
Immanuel Van Santen
Automorphisms of the Affine 3-space of Degree 3
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10h00-11h00
Ronan Terpereau
Real structures on horospherical varieties
11h30-12h30
Anthony Genevois
Groups and CAT(0) cube complexes
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| lunch |
lunch |
14h00-15h00
Frank Kutzschebauch
Factorization of matrices over algebras of holomorphic and continuous functions
15h15-16h15
Maciej Zdanowicz
On Bogomolov--Beauville decomposition in characteristic p>0
coffee break
17h00-18h00
Lukas Braun
Gorensteinness and iteration of Cox rings
social dinner
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14h00-15h00
Julia Schneider
Relations in the Cremona group over perfect fields
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Lukas Braun (Tuebingen) - Gorensteinness and iteration of Cox rings
We show that finitely generated Cox rings are 1-Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of Fano type and Kawamata log terminal quasicones, iteration of Cox rings is finite with factorial master Cox ring. Moreover, we prove a relative version of Cox ring iteration for solvable G-(quasi-)torsors.
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Anthony Genevois (Orsay) - Groups and CAT(0) cube complexes
In this talk, I will motivate the idea that CAT(0) cube complexes are useful in order to study groups arriving from various areas of mathematics. After introducing general definitions, examples and central theorems, I will illustrate this idea by explaining how to prove that polycyclic subgroups of braided Thompson's group brV, a specific subgroup of the mapping class group of the plane minus a Cantor set, are all virtually abelian.
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Frank Kutzschebauch (Bern) - Factorization of matrices over algebras of holomorphic and continuous functions
We give results of factorization of matrices in the special linear group
and the symplectic group over certain algebras of holomorphic functions as products of elementary matrices over those algebras.
Also we consider the problem of writing matrices in the general linear group as
products of exponentials.
In both factorization problems the number of factors is a very difficult problem, we give some optimal results.
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Julia Schneider (Basel) - Relations in the Cremona group over perfect fields
The group of birational transformations of the projective space is called Cremona group. For perfect fields whose extension degree of the algebraic closure is infinite, we construct a new normal subgroup of the plane Cremona group. The construction follows the melody of the recent proof that the Cremona group in high dimensions is not simple for subfields of the complex numbers by Blanc, Lamy and Zimmermann.
On the way we study Sarkisov links (i.e. ?easy? birational maps) and relations in the groupoid they generate.
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Ronan Terpereau (Dijon) - Real structures on horospherical varieties
In this talk we will consider the real structures of certain complex algebraic varieties equipped with a reductive algebraic group action: the horospherical varieties. We will see how to determine when such structures exist and, if so, how to describe them. In particular, we will try to illustrate our approach on two classical families of horospherical varieties: the flag varieties and the toric varieties. This is a joint work with Lucy Moser-Jauslin (IMB, Dijon).
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Immanuel Van Santen (Basel) - Automorphisms of the Affine 3-space of Degree 3
We study cubic hypersurfaces in the affine 3-space in order to understand automorphisms of degree 3 of the affine 3-space.
In fact, we will obtain a classification of all such automorphisms up to composition of affine automorphisms at the source and the target.
If time permits, I will also speak about their dynamical degrees. This is joint work with Jérémy Blanc.
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Maciej Zdanowicz (EPFL) - On Bogomolov--Beauville decomposition in characteristic p>0
The Bogomolov--Beauville decomposition in characteristic
zero is a structure result for varieties with trivial canonical class.
It states that every such variety can be decomposed, after a finite
étale cover, as a product of abelian, Calabi-Yau and hyperkähler
varieties.
In the talk I will show how to obtain a partial result - split off
the abelian part - in characteristic p>0 under arithmetic assumption
of weak ordinarity.
This is a joint work in progress with Zsolt Patakfalvi.
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Participants
Emelie Kerstin Arvidsson (EPFL)
Jérémy Blanc (Basel)
Lukas Braun (Tuebingen)
Javier Alonso Carvajal Rojas (EPFL)
Frédéric Deglise (Dijon)
Roberto Diaz (Dijon)
Daniele Faenzi (Dijon)
Pascal Fong (Basel)
Anthony Genevois (Orsay)
Pierre-Alexandre Gillard (Dijon)
Mattias Hemmig (Basel)
Hanspeter Kraft (Basel)
Frank Kutzschebauch (Bern)
Anne Lonjou (Basel)
Zsolt Patakfalvi (EPFL)
Marta Pieropan (EPFL)
Pierre-Marie Poloni (Basel)
Julia Schneider (Basel)
Ursina Schweizer (EPFL)
Ronan Terpereau (Dijon)
Immanuel Van Santen (Basel)
Egor Yasinky (Basel)
Sokratis Zikas (Basel)
Maciej Zdanowicz (EPFL)
Send an email to Jeremy  Blanc  unibas ch if you would like to participate.
Organisers
Jérémy Blanc (Basel)
Adrien Dubouloz (Dijon)
Zsolt Patakfalvi (EPFL)
Ronan Terpereau (Dijon)
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