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Richard M Hain, Professor

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

Teaching (Fall 2015):

Office Hours:

3:00 to 4:30 Mondays and Wednesdays, or by appointment

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

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 Hiroshima University.

Areas of Interest:

algebraic geometry
arithmetic geometry

Curriculum Vitae
Current Ph.D. Students   (Former Students)

Postdocs Mentored

Recent Publications   (More Publications)

  1. Richard Hain, Deligne-Beilinson cohomology of affine groups (Preprint, July, 2015) [arXiv:1507.03144]
  2. D. Arapura, A. Dimca, R. Hain, On the fundamental groups of normal varieties, Communications in Contemporary Mathematics (Accepted, June, 2015) [arXiv:1412.1483]
  3. Richard Hain, Genus 3 Mapping Class Groups are not Kähler, Journal of Topology, vol. 8 no. 1 (2015), pp. 213-246, Oxford University Press, ISSN 1753-8416 [arXiv:1305.2052], [213.abstract]
  4. Richard Hain, The Hodge-de Rham theory of modular groups (Accepted, March, 2014) [arXiv:1403.6443]
  5. Alexandru Dimca, Richard Hain, Stefan Papadima, The abelianization of the Johnson kernel, Journal of the European Mathematical Society, vol. 16 no. 4 (2014), pp. 805-822 [arXiv:1101.1392], [show_abstract.php]
Recent Grant Support

  • Universal Teichmuller Motives, National Science Foundation, DMS-1406420, 2014/08-2017/07.      
  • Applications of Topology to Arithmetic and Algebraic Geometry, National Science Foundation, DMS-1005675, 2010/07-2013/06.      
Conferences Organized

  • Workshop on Multiple Zeta Values, Modular Forms and Elliptic Motives II, (with J. Burgos (Madrid), K. Ebrahimi-Fard (Madrid), H. Gangl (Durham, UK), J. Kramer (Berlin), O. Patashnick (Bristol, UK), L. Scneps (Paris)), December 1-5, 2014  
  • Moduli Spaces of Riemann Surfaces, (with Benson Farb and Eduard Looijenga), July 3-23, 2011  
  • Multiple zeta values, modular forms and elliptic motives, (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  
Recent and Future Conferences and Talks
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320