Curriculum Vitae de Philip Boalch

Brief Bio:

I spent 6 years in Cambridge 1991-1997 before moving to Oxford and getting a D. Phil in 1999 with Hitchin.
I was then a post-doc of Dubrovin in SISSA, Trieste, back in the days when it was next to the ICTP, and you
could easily go swim in the Adriatic and then have lunch with Narasimhan and the other mathematicians at ICTP.
Then I spent a year in Strasbourg visiting Biquard before moving to Columbia, New York, as a Ritt assistant
professor with Krichever. I was selected by the CNRS in 2002 and so moved back from the US to Paris in 2003.
My wife is from Newton Mass., my kids have 3 passports and I'm often in Vermont in August.

I'm interested in geometric aspects of nonlinear algebraic differential equations, such as the Painlevé equations,
and their interaction with moduli theory in a broad sense (not necessarily algebraic). I view this subject as a
generalisation of algebraic geometry, where we allow derivatives in the equations. For example the Painlevé
equation y'' = 2y^3+ xy + c is a deformation of the equation for the Jacobi elliptic functions, and contains
extremely rich geometry (this is now understood as a wild nonabelian Hodge deformation). Most of my papers
are an elaboration of my first paper (Adv. Math. 2001) aiming to extend many of the geometric properties known
about representations of surface groups to their natural generalisation, the wild surface groupoids (leading to
moduli spaces of monodromy/Stokes data of meromorphic connections, with many wonderful properties). The
right viewpoint seems to be to generalise the notion of Riemann surface to wild Riemann surface and view
everything as stemming from that.

Many years ago I also explicitly constructed a genus seven algebraic curve canonically attached to the icosahedron
(see also pp.69-70 of these slides, from my two 2006 Cambridge talks: I, II)

Publications

Exposés

Enseignements

Encadrement de thèses

Encadrement de post-docs

Coorganisation des reunions

Prix

Grants