Álvaro Pelayo                                                    

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A theory is more impressive the greater the simplicity of its premises, the more kinds of things it relates, and the more extended its area of applicability.

A. Einstein


This research is currently supported by

  

and the Spanish Ministry of Science.
                                                       

RESEARCH DIRECTIONS

General Areas:
Integrable Systems
Spectral Geometry
Symplectic Geometry
Homotopy Type Theory

Past and Current Collaborators: S. Awodey, L. Charles, J .Coffey, J.J. Duistermaat, A. Figalli, F.G. Gascon, M. Gualtieri, V. Guillemin (as co-editor), L. Kessler, B. Kostant, Y. Le Floch, Y. Lin, R. Mazzeo, D. Peralta, A.R. Pires, L. Polterovich,T. Ratiu, N. Reshetikhin, F. Rezakhanlou, S. Sabatini, B. Schmidt,V. Voevodsky, S. Vũ Ngọc, M. A. Warren, A. Weinstein (as co-editor)

Reports:
Current Research and Future Plans (8 pages)
Outline of Research Plans 2013-2016 (1 page)
Report of work at IAS 12/2010-08/2013 (5 pages)

I work on the following groups of problems:

G1 Hamiltonian Dynamics and Symplectic Geometry

(introduction for IAS Board of Trustees)
Publications in G1

Summary of G1
G2 Spectral Theory and Semiclassical Analysis

(it's related G1, see Tao's answer to Why is symplectic geometry so important in modern PDE? 5/27/12)
Publications in G2

Summary of G2
G3 Group Actions Publications in G3

Summary of G3
G4 Homotopy Type Theory (HoTT) and Univalence

(my goal: to do dynamics using proof-assistants)
Publications in G4

Summary of G4


A More Specific Classification by Topic:




This research has been supported by

  

as well as the Spanish Science Ministry, the Mathematical Sciences Research Institute in Berkeley, the Institute for Advanced Study in Princeton, the Oberwolfach Institute in Germany, and the Spanish National Research Council. Currently active Grants:

Research