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An Identification Therorem for PSU6(2) and its Automorphism Groups
[OWP-2011-08] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-10)
We identify the groups PSU6(2), PSU6(2):2, PSU6(2):3 and Aut(PSU6(2)) from the structure of the centralizer of an element of order 3.
Definable orthogonality classes in accessible categories are small
[OWP-2011-14] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-15)
We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary ...
Classification of totally real elliptic Lefschetz fibrations via necklace diagrams
[OWP-2011-13] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
We show that totally real elliptic Lefschetz brations that admit a real section are classified by their "real loci" which is nothing but an S1-valued Morse function on the real part of the total space. We assign to ...
Steinberg groups for Jordan pairs
[OWP-2011-29] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-26)
We introduce categories of groups with commutator relations with respect to root groups and Weyl elements, permuting the root groups. This allows us to view the classical Steinberg groups, for example the Steinberg group ...
Upper bounds for the number of solutions to quartic thue equations
[OWP-2011-21] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve ϕ(x,y) that allows us to use the theory of linear forms in logarithms. This manuscript ...
On Reflection Subgroups of Finite Coxeter Groups
[OWP-2011-06] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-9)
Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class ...
On Canonical Forms for Two-person Zero-sum Limit Average Payoff Stochastic Games
[OWP-2011-35] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-29)
We consider two-person zero-sum mean payoff undiscounted stochastic games. We give a sufficient condition for the existence of a saddle point in uniformly optimal stationary strategies. Namely, we obtain sufficient ...
Averages of Shifted Convolutions of d3(n)
[OWP-2011-11] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-13)
We investigate the first and second moments of shifted convolutions of the generalised divisor function d3(n).
Products of pairs of Dehn twists and maximal real Lefschetz fibrations
[OWP-2011-32] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic ...
2-Minimal Subgroups in Classical Groups: Linear and Unitary Groups
[OWP-2011-09] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-11)