Math @ Duke
Richard M Hain, Professor
- Contact Info:
|Office Location: ||107 Physics|
|Office Phone: ||(919) 660-2819, (919) 660-2800 |
|Email Address: |
- Office Hours:
- 3:00 to 4:30 Mondays and Wednesdays, or by appointment
- 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
My primary collaborator is Makoto Matsumoto of Hiroshima University.
- Areas of Interest:
- Curriculum Vitae
- Current Ph.D. Students
- Postdocs Mentored
- Recent Publications
- D. Arapura, A. Dimca, R. Hain, On the fundamental groups of normal varieties
(Submitted, December, 2014) [arXiv:1412.1483]
- Richard Hain, Genus 3 Mapping Class Groups are not Kähler,
Journal of Topology
(Accepted, June, 2014), ISSN 1753-8416 [arXiv:1305.2052], [jtopol.jtu020.short]
- Richard Hain, The Hodge-de Rham theory of modular groups
(Submitted, March, 2014) [arXiv:1403.6443]
- Alexandru Dimca, Richard Hain, Stefan Papadima, The abelianization of the Johnson kernel,
Journal of the European Mathematical Society, vol. 16 no. 4
pp. 805-822 [arXiv:1101.1392], [show_abstract.php]
- Richard Hain, Notes on the Universal Elliptic KZB Equation
(Preprint, September, 2013) [arXiv:1309.0580]
- Recent Grant Support
- Applications of Topology to Arithmetic and Algebraic Geometry, National Science Foundation, DMS-1005675, 2010/07-2013/06.
IAS/Park City Mathematics Institute
Recent and Future Conferences and Talks
- 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
- Moduli Spaces in Geometry, CIRM, Luminy, France, October 26-30 2015.
- Workshop on Multiple Zeta Values, Modular Forms
and Elliptic Motives, II, ICMAT, Madrid, December 1-5, 2014.
- Course on Universal Mixed Elliptic Motives at IHES, Paris, May, 2014.(web page)
Fundamental groups in arithmetic and algebraic geometry, De Giorgi Center, Pisa, Italy, December 16-20, 2013.
- Texas Geometry and Topology Conference, Texas A&M University, October 11-13, 2013.
- Recent advances in Hodge theory, Pacific Institute for the Mathematical Sciences, Vancouver BC, June 10-20, 2013.
- Heights and moduli spaces, Lorentz Center, Leiden, Netherlands, June 10-14, 2013.
- Grothendieck-Teichmüller theory
and Multiple Zeta Values, Newton Institute, Cambridge, UK, April 8-12, 2013.
- Workshop on the Topology of Varieties, Luminy, France, June 4-8, 2012.
- Moduli Spaces of Riemann Surfaces, IAS/Park City Mathematics Institute, Park City, UT, July-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.
Duke University, Box 90320
Durham, NC 27708-0320