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Computing Congruence Quotients of Zariski Dense Subgroups
[OWP-2018-22] (Mathematisches Forschungsinstitut Oberwolfach, 2018-10-26)
We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq ...
Real Analyticity is Concentrated in Dimension 2
[OWP-2018-23] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-05)
We prove that a real-valued function on a real analytic manifold is analytic whenever all its restrictions to $2$-dimensional analytic submanifolds are analytic functions. We also obtain analogous results in the framework ...
Global Variants of Hartogs' Theorem
[OWP-2018-24] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-06)
Hartogs' theorem asserts that a separately holomorphic function, defined on an open subset of $\mathbb{C}^n$, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open ...
Herbrand’s Theorem as Higher Order Recursion
[OWP-2018-01] (Mathematisches Forschungsinstitut Oberwolfach, 2018-02-19)
We provide a means to compute Herbrand disjunctions directly from sequent calculus proofs with cuts. Our approach associates to a first-order classical proof $\pi \vdash \exists v F$, where $F$ is quantifier free, an ...
Criteria for Algebraicity of Analytic Functions
[OWP-2018-25] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-12)
We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend ...
The Martin Boundary of Relatively Hyperbolic Groups with Virtually Abelian Parabolic Subgroups
[OWP-2018-03] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-19)
Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green's function of the corresponding random walk. We give a complete topological characterization ...
Sur le Minimum de la Fonction de Brjuno
[OWP-2018-26] (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-11)
The Brjuno function attains a strict global minimum at the golden section.
Generalized Vector Cross Products and Killing Forms on Negatively Curved Manifolds
[OWP-2018-17] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-17)
Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on $\mathbb{R}^n$ and give their classification. Using ...
Max-Linear Models on Infinite Graphs Generated by Bernoulli Bond Percolation
[OWP-2018-09] (Mathematisches Forschungsinstitut Oberwolfach, 2018-05-17)
We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs, and investigate their relations to classical percolation theory. We formulate results for the oriented square lattice graph ...
A Well-Posedness Result for Viscous Compressible Fluids with Only Bounded Density
[OWP-2018-10] (Mathematisches Forschungsinstitut Oberwolfach, 2018-05-28)
We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and ...