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Math @ Duke
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Richard M Hain, Professor
 - Contact Info:
| Office Location: | 107 Physics | | Office Phone: | (919) 660-2819, (919) 660-2800 | | Email Address: |   | Teaching (Spring 2012):
- Office Hours:
- 2:30 to 4:00 Mondays and Wednesdays, or by appointment
- Education:
- Specialties:
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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:
- the topology and related geometry of various moduli spaces, such as the moduli spaces of smooth curves and moduli spaces of principally polarized abelian varieties;
- the study of fundamental groups of algebraic varieties, particularly of moduli spaces whose
fundamental groups are mapping class groups;
- the study of various enriched structures (Hodge structures, Galois actions, and periods) of fundamental groups of algebraic varieties;
- polylogarithms and mixed zeta values which occur
as periods of fundamental groups of moduli spaces of
curves.
My primary collaborator is Makoto Matsumoto of the University of Tokyo.
- Areas of Interest:
- topology
algebraic geometry
arithmetic geometry
- Curriculum Vitae
- Current Ph.D. Students
(Former Students)
- Postdocs Mentored
- Recent Publications
(More Publications)
- Richard Hain, Monodromy of codimension-one sub-families of universal curves,
Duke Math. Journal
(Accepted, November, 2011) [arXiv:1006.3785]
- 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]
- Richard Hain, Rational points of universal curves,
J. Amer. Math. Soc. 24 (2011), 709-769
[arXiv:1001.5008]
- Alexandru Dimca, Richard Hain, Stefan Papadima, The abelianization of the Johnson kernel
(Submitted, January, 2011) [arXiv:1101.1392]
- Richard Hain, Remarks on non-abelian cohomology of proalgebraic groups,
J. Algebraic Geom.
(Accepted, 2011) [arXiv:1009.3662]
- Recent Grant Support
- Applications of Topology to Arithmetic and Algebraic Geometry, National Science Foundation, DMS-1005675, 2010/07-2013/06.
- Park City Mathematics Institute, Princeton University, 7451-2302 & 7451-2310, 2010/04-2011/03.
- Topology and motives associated to moduli spaces of curves, National Science Foundation, DMS-0706955, 2007/08-2010/07.
- Conferences Organized
- Moduli Spaces of Riemann Surfaces, organizer (co-organizers Benson Farb and Eduard Looijenga), July 3-23, 2011
- Multiple zeta values, modular forms and elliptic motives, co-organizer (with Herbert Gangl), May 2-6, 2011
- (with Jonathan Wahl) The Third Duke Mathemtical Journal Conference, April 23-25, 2004
- (with Jonathan Wahl) The Second Duke Mathematical Journal Conference, April 27-29, 2001
- (with Jonathan Wahl) The Duke Math. Journal Conference, May 1-2, 1998
- Torellifest, a conference at Duke, March, 1996
- Mapping Class Groups and Moduli Spaces of Curves, Seattle, August 1991
IAS/Park City Mathematics Institute
Recent and Future Conferences and Talks
- Moduli Spaces of Riemann Surfaces, IAS/Park City Mathematics Institute, Park City, UT, July 3 to 23, 2011.
- Motivic Fundamental Groups,
Lorentz Center, University of Leiden, May 23-27, 2011.
- Multiple zeta values, modular forms and elliptic motives, Heilbronn Institute, University of Bristol, UK, May 3-6, 2011.
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dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
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 Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
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