Let K be a number field. The Grunwald problem for a finite group (scheme) G/K asks what is the closure of the image of H^1(K,G) → ∏_{v ∈ M_K} H^1(K_v,G). For a general G, there is a Brauer—Manin obstr...
Given a topological space X and a Lie group G, topologists investigated the class of principal G-bundles arising from homomorphisms from the fundamental group of X to G. The analogous construction wor...
I will talk about the following problem: which systems of Diophantine
equations have the property that, in every finite colouring of the
natural numbers, there is always a monochromatic solution of th...
Let $k \geq 1$ be an integer and let $f\colon \mathbb C\mathbb P^k \to \mathbb C\mathbb P^k$ be a holomorphic endomorphism of algebraic degree at least 2. Let $\nu$ be an invariant ergodic probability...
Let G be an algebraic group acting on a finite-type scheme X; a natural question is whether there exists a categorical quotient $X // G$ of this action as a finite-type scheme. When G is reductive, th...
The Kirchhoff equation with periodic boundary conditions offers a rich and elegant model for capturing the transverse oscillations of a nonlinear elastic medium. Since its origin in 1876, it has intri...
Since the seminal work of Gidas, Ni & Nirenberg [Math. Anal. Appl. Part A, 1981], considerable effort has been devoted to the classification of positive solutions to the critical $p$-Laplace equat...
We provide a characterization of rotationally symmetric solutions to the Serrin problem on ring-shaped
domains in $R^n$ ($n ≥ 3$). Our approach is based on a comparison-geometry argument. By exploitin...
Supersymmetric nonlinear sigma models arise in the theory of disordered systems and are expected to share key features with O(N)-type models. They also reveal surprising connections with probabilistic...
Classical Galois theory of algebraic equations has been extended to a Galois theory of linear differential equations [vS03] and more recently to the Galois theory of various kind of linear difference ...
