1024ºË¹¤³§

Biography

Overview

I am a Senior Lecturer at the 1024ºË¹¤³§, UK. I completed my BSc, MSc (DEA) and PhD at the University of Barcelona, Spain, as well as post-doctoral research in the University de Limoges, France; my teaching and research hitherto were undertaken during non-tenured academic positions in the University of Barcelona for six years.

Membership in Learned Societies

• American Mathematical Society
• European Mathematical Society
• Societat Catalana de Matemàtiques
• Real Sociedad Matemática Española
• Sociedad Española de Matemática Aplicada
• Fellow of the Higher Education Academy

Awards

• Extraordinary Doctorate Award, University of Barcelona, 2008

Research interests

My main research interests are based on chaos and the study of integrability in non-linear dynamical systems, with special emphasis on models derived from applied mathematics and physics - notably N-Body Problems and other systems arising from Celestial Mechanics, and in general Hamiltonians with or without a homogeneous potential. Recent attention is also being paid to systems derived from epidemiological models as well as chaotic models related to Medicine, Physics and Sociology.

Aside from these and other interests currently addressed, recent work also tackles the algebraic structure of higher-order variational equations and the symbolic and numerical computation of Galois (e.g., monodromy and Stokes) matrices for these systems, as well as the true dynamical significance of their projective limit as related to the Galois groupoid. This projective limit is amenable to explicit inference based on the first degrees of the variational systems, but more work needs to be performed in this direction.

The dual version of these infinite variational systems has proven itself very useful to compute formal first integrals as well as describe their sums explicitly in terms of their generic coefficients, and sometimes easily resummable, as shown in recent work for systems hitherto deemed chaotic. More importantly, in the case of the dual variationals the original system need not be Hamiltonian and the first integrals need not be meromorphic, and effective complete integrability replaces proofs of non-integrability. This is my main short-term goal.

All of this is done in preparation for further work aimed at building a constructive categorical link between Algebra and Dynamics, and to characterize chaos and integrability from a general perspective that transcends the Hamiltonian realm.

Current doctoral students

• Emily Bamber

Latest preprints

• , ArXiv

Teaching responsibilities

Current Teaching

• Algebraic Structures and Discrete Mathematics (M20745)
• Topics in Algebra and Geometry (M31448):
  • Category Theory
  • Axiomatic Geometry, Euclidean and hyperbolic geometries
• Mathematical Foundations (M20739), first semester
• Year 3 and 4 Project coordination

Past Teaching (in 1024ºË¹¤³§)

• Introduction to Python (first half of M24200), notes and material
• Introduction to Topology (first half of M314), notes  
• Abstract Algebra (M20727), notes
• Introduction to C++ (MTH399), some material  
• first half of Applied Mathematics (now known as Mechanics and Dynamics M30218)
• Mathematical Principles (ENG410)
• Engineering Analysis 

All of these and other teaching materials can be seen