Richard Hain, Professor

Richard Hain

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 collaborators are Francis Brown of Oxford University and Makoto Matsumoto of Hiroshima University.

Office Location:  107
Office Phone:  (919) 660-2819
Email Address: send me a message
Web Pages:  http://fds.duke.edu/db/aas/math/faculty/hain/
http://www.thecostofknowledge.com/

Teaching (Fall 2017):

Teaching (Spring 2018):

Office Hours:

2:00 to 3:00 MWF, or by appointment
Education:

Ph.D.University of Illinois -- Urbana-Champaign1980
M.Sc.Australian National University (Australia)1977
B.Sc. (hons)University Sydney Australia1976
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.

Areas of Interest:

topology
algebraic geometry
arithmetic geometry

Current Ph.D. Students  

Postdocs Mentored

Undergraduate Research Supervised

Recent Publications   (search)

  1. Arapura, D; Dimca, A; Hain, R, On the fundamental groups of normal varieties, Communications in Contemporary Mathematics, vol. 18 no. 04 (August, 2016), pp. 1550065-1550065, ISSN 0219-1997 [doi]
  2. Hain, R, Notes on the Universal Elliptic KZB Equation, Pure and Applied Mathematics Quarterly, vol. 12 no. 2 (July, 2016), International Press [arXiv:1309.0580], [1309.0580v3]  [abs]
  3. Hain, R, The Hodge-de Rham theory of modular groups, in Recent Advances in Hodge Theory Period Domains, Algebraic Cycles, and Arithmetic, edited by Kerr, M; Pearlstein, G, vol. 427 (January, 2016), pp. 422-514, Cambridge University Press, ISBN 110754629X
  4. Hain, R; Matsumoto, M, Universal Mixed Elliptic Motives (Submitted, December, 2015) [arxiv:1512.03975]  [abs]
  5. Hain, R, Deligne-Beilinson Cohomology of Affine Groups (Submitted, July, 2015) [arXiv:1507.03144]  [abs]
Recent Grant Support

Conferences Organized

Recent and Future Conferences and Talks