4 citations · 6 across the 7 of their papers we have counts for
6 papers · 1 filter
The affine invariant of generalized semitoric systems
Álvaro Pelayo, Tudor S. Ratiu, San Vũ Ngoc
A generalized semitoric system F:=(J,H): M --> R^2 on a symplectic 4-manifold is an integrable system whose essential properties are that F is a proper map, its set of regular valu…
First steps in symplectic and spectral theory of integrable systems
Álvaro Pelayo, San Vũ Ngoc
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian…
Symplectic theory of completely integrable Hamiltonian systems
Álvaro Pelayo, San Vũ Ngoc
This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredi…
Sharp symplectic embeddings of cylinders
Álvaro Pelayo, San Vũ Ngoc
We show that the cylinder Z^{2n}(1):= B^2(1)\times \mathbb{R}^{2(n-1)} embeds symplectically into B^4(R) \times \mathbb{R}^{2(n-2)} if R \geq \sqrt{3}.
Symplectic spectral geometry of semiclassical operators
Álvaro Pelayo
In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spect…
Voevodsky's Univalence Axiom in homotopy type theory
Steve Awodey, Álvaro Pelayo, Michael A. Warren
In this short note we give a glimpse of homotopy type theory, a new field of mathematics at the intersection of algebraic topology and mathematical logic, and we explain Vladimir V…