Sheds 2016
Münster
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Abstracts:
Barbara Baumeister (Bielefeld), Reflection groups, Hurwitz action and Artin groups
Abstract:
Let W be a well generated reflection group, that is a group W which acts on a complex (or real) vector space
and is generated by n reflections r1,...,rn.
We call T the set of reflections of W
that are conjugates of the generating reflections in W. The reduced factorizations of elements of
W into products of reflections in T are studied by many people in different contexts.
We here discuss the case when W is a Coxeter group and its motivating application to Artin groups.
Bertrand Rémy (Palaiseau), Growth of profinite groups of arithmetic type
Abstract:
This talk will mainly deal with presentations (finite generation, finite presentation, size of presentations)
of profinite groups, when the latter ones come from completions of arithmetic groups.
More precisely, we go back
and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand,
presentations of profinite groups, deducing along the way new results on both. This is joint work with
Inna Capdeboscq and Alex Lubotzky.
Maneesh Thakur (New Delhi), R-triviality of some (exceptional) algebraic groups
Abstract:
In this talk, we will discuss the R-triviality of certain groups of type
E8, E7 and E6,
which are intimately related with Albert division algebras.
Hendrik Van Maldeghem (Gent), About F4 and E6
Abstract:
In this talk we review some similarities between buildings and groups of type F4 and E6.
The main achievement is a geometric construction of the building of type E6 over any field from a split
building of type F4 over that field. This also yields some (geometric and group-theoretic) consequences,
which we will mention.
The main part is joint work with Narasimha Sastry and Anneleen De Schepper.
Stefan Witzel (Bielefeld), On certain Ã2 lattices
Abstract:
My talk will be about lattices on Ã2 buildings that
preserve types and act regularly on panels of each type. We
concentrate on the case where each vertex stabilizer acts on its
residue as a Singer cycle. Jan Essert has shown that this class of
lattices coincides with the class of groups admitting a presentation
of a particular form.
For these lattices one would like to answer the following questions:
* which of the lattices are isomorphic?
* for which lattices is the building Bruhat--Tits?
* for which of the lattices are the buildings isomorphic?
* which of the lattices are commensurable to other known lattices
(constructed by Köhler-Meixner-Wester, Ronan, Tits, and
Cartwright-Mantero-Steger-Zappa)?
I will report on recent progress in answering these questions, mostly
restricted to the case where the branching parameter q is at most
5.
The seminar starts on Friday, March 4, 2016 at 10:00 am in lecture room N2, Orléans-Ring 10 (next to the main math building), Münster.
Schedule
10:00 - 10:50 Hendrik Van Maldeghem (Gent), About F4 and E6.
11:20 - 12:10 Bertrand Rémy (Palaiseau), Growth of profinite groups of arithmetic type.
14:00 - 14:50 Maneesh Thakur (New Delhi), R-triviality of some (exceptional) algebraic groups.
15:20 - 16:10 Barbara Baumeister (Bielefeld), Reflection groups, Hurwitz action and Artin groups.
16:40 - 17:30 Stefan Witzel (Bielefeld), On certain Ã2 lattices.
18:30 Party
The lecture room is room N2 in Orléans-Ring 10, next to the math building (ground floor). Tea and coffee will be served during the breaks in SR0 (entrance level of the math building).
The next bus stop is named 'Coesfelder Kreuz'. From the train station you may take the buses
- Number 4 direction "Alte Sternwarte"
- Number 5 direction "Nienberge"
- Numbers 11,12,22 direction "Gievenbeck"
- Number 13 direction "Technologiepark"
- Number 20 direction "Roxel"
Here is a map centered at the math building.