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...
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...
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...
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...
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...
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...
In this talk, based on joint work with Stephane Geudens and Marco Zambon, we develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. ...
In this talk, we present an existence result for semilinear elliptic problems of the form
-Delta u + u = f(u), u > 0, u in H^1_0(A),
where A denotes either an annulus or the exterior of a ball in R...
Abstract: We study the limiting case $\gamma\to(1/2)^-$ in dimension one for the fractional Caffarelli-Kohn-Nirenberg inequality, obtaining Onofri's inequality in the unit disk as a limit. An importan...
