Richard M Hain, Professor

Richard M Hain
Office Location:  107 Physics
Office Phone:  (919) 660-2819, (919) 660-2800
Email Address: send me a message

Teaching (Spring 2012):

Office Hours:

2:30 to 4:00 Mondays and Wednesdays, or by appointment
Education:

Ph.D.University of Illinois, Urbana-Champaign1980
M.Sc.Australian National University1977
B.Sc.(Hons)University of Sydney1976
Specialties:

Algebra
Topology
Geometry
Research Interests: Topology of Algebraic Varieties, Hodge Theory, and Moduli of Curves

I am a topologist whose main interests include the study of the topology of complex algebraic varieties (i.e. spaces that are the set of common zeros of a finite number of complex polynomials). What fascinates me is the interaction between the topology, geometry and arithmetic of varieties defined over subfields of the complex numbers, particularly those defined over number fields. My main tools include differential forms, Hodge theory and Galois theory, in addition to the more traditional tools used by topologists. Topics of current interest to me include:

My primary collaborator is Makoto Matsumoto of the University of Tokyo.

Areas of Interest:

topology
algebraic geometry
arithmetic geometry

Current Ph.D. Students  

Postdocs Mentored

Recent Publications

  1. Richard Hain, Monodromy of codimension-one sub-families of universal curves, Duke Math. Journal (Accepted, November, 2011) [arXiv:1006.3785]
  2. Richard Hain, Normal Functions and the Geometry of Moduli Spaces of Curves, in Handbook of Moduli, edited by Gavril Farkas, Ian Morrison (Accepted, August, 2011) [arXiv:1102.4031]
  3. Richard Hain, Rational points of universal curves, J. Amer. Math. Soc. 24 (2011), 709-769 [arXiv:1001.5008]
  4. Alexandru Dimca, Richard Hain, Stefan Papadima, The abelianization of the Johnson kernel (Submitted, January, 2011) [arXiv:1101.1392]
  5. Richard Hain, Remarks on non-abelian cohomology of proalgebraic groups, J. Algebraic Geom. (Accepted, 2011) [arXiv:1009.3662]
Recent Grant Support

Conferences Organized

IAS/Park City Mathematics Institute Recent and Future Conferences and Talks