Related papers: Continuous analytic capacity and holomorphic motio…

We give a simple description of the classical moduli space of vacua for supersymmetric gauge theories with or without a superpotential. The key ingredient in our analysis is the observation that the lagrangian is invariant under the action…

We consider compact objects in a classical and non-relativistic generalisation of Newtonian gravity, dubbed bootstrapped Newtonian theory, which includes higher-order derivative interaction terms of the kind generically present in the…

We identify a canonical structure J associated to any first-order theory, the {\it space of definability patterns}. It generalizes the imaginary algebraic closure in a stable theory, and the hyperimaginary bounded closure in simple…

The purpose of this paper is to develop a Lie algebraic approach to obtain new proofs of important results of H.-C. Wang, Tits and Wolf-Wang-Ziller on compact complex homogeneous manifolds emphasizing only those that admit a transitive…

A new exact analytically solvable Eckart-type potential is presented, a generalisation of the Hulthen potential. The study through Supersymmetric Quantum Mechanics is presented together with the hierarchy of Hamiltonians and the shape…

In the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among all sets with a given diameter. In particular, given an…

The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…

Let $f:X\to X$ be a continuous map on a compact metric space with finite topological entropy. Further, we assume that the entropy map $\mu\mapsto h_\mu(f)$ is upper semi-continuous. It is well-known that this implies the continuity of the…

We show that, given a family of discs centered at a chord-arc curve, the analytic capacity of a union of arbitrary subsets of these discs (one subset in each disc) is comparable with the sum of their analytic capacities. We show a sort of…

Given a collection of K\"ahler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equilibrium measures which coincide with classical notions when…

We take the first steps towards a better understanding of continuous orbit equivalence, i.e., topological orbit equivalence with continuous cocycles. First, we characterise continuous orbit equivalence in terms of isomorphisms of C*-crossed…

We construct an equivariant version of Ray-Singer analytic torsion for proper, isometric actions by locally compact groups on Riemannian manifolds, with compact quotients. We obtain results on convergence, metric independence, vanishing for…

We construct a measure in the hamiltonian function level sets that is invariant under the hamiltonian flow for short times and flow preserving for arbitrarily long times. This allows a probabilistic approach to the study of hamiltonian…

In connection with the results of Tim Austin, and Wen Huang, Song Shao, Xiangdong Ye we present the following assertion: there are infinite automorphisms $S,T$, some set $A$ of positive finite measure and a sequence $N_m$ with…

We extend certain classical theorems in pluripotential theory to a class of functions defined on the support of a $(1,1)$-closed positive current $T$, analogous to plurisubharmonic functions, called $T$-plurisubharmonic functions. These…

This paper is concerned with sample path properties of isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field based on the…

We give a systematic presentation of the stability theory in the non-algebraic Kaehlerian geometry. We introduce the concept of "energy complete Hamiltonian action". To an energy complete Hamiltonian action of a reductive group G on a…

This paper proves that the two homotopy theories for orbispaces given by Gepner and Henriques and by Schwede, respectively, agree by providing a zig-zag of Dwyer-Kan equivalences between the respective topologically enriched index…