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 (Fall 2009):

Teaching (Spring 2010):

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 Hiroshima University.

Current Ph.D. Students  

Postdocs Mentored

Recent Publications

  1. Richard Hain, Makoto Matsumoto, Relative pro-l completions of mapping class groups, J. Algebra, vol. 321 (2009), pp. 3335-3374 [arXiv:0802.0806]
  2. Richard Hain, Relative weight filtrations on completions of mapping class groups, in Groups of Diffeomorphisms, Advanced Studies in Pure Mathematics, vol. 52 (May, 2008), pp. 309--368, Mathematical Society of Japan [arXiv:0802.0814]
  3. Richard Hain, Lectures on Moduli Spaces of Elliptic Curves, Advanced Lectures in Mathematics (Submitted, 2008), International Press, Boston [arXiv:0812.1803]
  4. Richard Hain, Finiteness and Torelli Spaces, in Problems on Mapping Class Groups and Related Topics, Proc. Symp. Pure Math. 74, edited by Benson Farb (September, 2006), pp. 57-70, American Mathematical Society [math.GT/0508541]
  5. Richard M. Hain and Makoto Matsumoto, Galois actions on fundamental groups of curves and the cycle C-C-, J. Inst. Math. Jussieu, vol. 4 (2005), pp. 363-403 [math.NT/0306037]
Recent Grant Support

Conferences Organized

Recent and Future Conferences and Talks .