If we knew what it was we were doing, it would not be called research, would it? Albert Einstein

I'm interested in a range of problems, most of which lie at the border between mathematical physics and theoretical physics. I'm working with Vladimir Zakharov in the fields of integrable systems and general relativity. Currently my research is focused on:

  1. Theory of Relativity: this include a mathematical study of Einstein's field equation, its solutions, their stability, physical implications of the theory of relativity, conservation laws and different anomalies.
  2. Theory of Solitons: the Inverse Scattering Transform, integrable systems and their exact solutions, applications to physics and in particular to general relativity, Hamiltonian structures, the dressing method, consequences of the Belinski-Zakharov transform and gravitational solitons.
  3. Electromagnetism and the problem of Radiation-Reaction: construction of new solutions of radiation-reaction models, studying the limits of validity of electromagnetic theory in high acceleration, establishing a new model for charged particles that includes the particle's self-force.
  4. Mathematical nutrition is a new interdisciplinary field that employes mathematical models to better understand how nutrition and lifestyle affect our health. I cofounded Nutrino precisely for this purpose, with the hope to make humanity's understanding of nutrition more precise.
You can find the slideshows of some of my talks about these topics in the Talks page.