Curriculum Vitae

Richard Hain

Box 90320, Durham, NC 27708-0320 +1 919 660 2819 (office)
(email)
Education

Ph.D.University of Illinois, Urbana-Champaign1980
M.Sc.Australian National University (Australia)1977
B.Sc. (hons)University of Sydney (Australia)1976
Areas of Research

Topology of Algebraic Varieties, Hodge Theory, and Moduli of Curves

Areas of Interest

topology
algebraic geometry
arithmetic geometry

Professional Experience / Employment History

Duke University
Chair, Mathematics, 2004-2006
Chair, Mathematics, 1999-2002
Professor, Mathematics, 1991-present
University of Washington
Professor, Mathematics, 1990-92
Associate Professor, Mathematics, 1987-90
Assistant Professor, Mathematics, 1985-87
Acting Assistant Professor, Mathematics, 1980-83
SUNY, Buffalo
Assistant Professor, Mathematics, 1984-85
Visiting Positions
Professeur Invité, Université de Nice, May, 2009
Member, Mathematical Sciences Research Institute, February - March, 2009
Visiting Professor, Sydney University, October - December, 2008
Professeur Invité, Université de Nice, May-June, 2003
University of Sydney, February-March, 2003
Harvard University, September-November, 2002
Visiting Professor, Universität Essen, Germany, April-June 1995
Member, Institut des Hautes Études Scientifiques, France, February-April 1995
Professeur Invité, Institut Henri Poincaré, Paris, February-April 1995
Member, Institute for Advanced Study, Princeton, Fall semester, 1994
Visiting Professor, University of Sydney, Australia, September, 1993
Visiting Professor, University of Utrecht, The Netherlands, May, 1992
Visiting Professor, Aarhus University, Denmark, July, 1991
Visiting Professor, Duke University, September-December 1990
Member, Institut des Hautes Études Scientifiques, France, September, 1989
Max-Planck Institut für Mathematik, Bonn, October-December 1987
Member, Institut des Hautes Études Scientifiques, France, July-September, 1987
Member, Institute for Advanced Study, Princeton, 1985-86
Visiting Assistant Professor, University of Utah, 1983-84
Awards, Honors, and Distinctions

School of Mathematics/Members, Institute for Advanced Study
Fellow, American Mathematical Society
Fellowship, Japan Society for the Promotion of Science, May, 1998
Frontiers in Mathematics Lectures, Texas A&M University, March, 1997
Research Fellowship, American Mathematical Society, 1987-88
Centennial Fellowship, American Mathematical Society
Postgraduate Travelling Scholarship, University of Sydney, 1978-1980
University Medal, Pure Mathematics, University of Sydney, April, 1976
Recent Grant Support

Conferences Organized

Organizer, The Fourth Duke Mathematical Journal Conference, April 26-29, 2018  
Co-organizer (with Francis Brown et al), Hot Topics Workshop: Galois Theory of Periods and Applications, March 27-31, 2017  
Program committee, Local zeta functions and the arithmetic of moduli spaces: A conference in memory of Jun-Ichi Igusa, March 22-26, 2017  
(co-organizer with J. Burgos (Madrid), K. Ebrahimi-Fard (Madrid), H. Gangl (Durham, UK), J. Kramer (Berlin), O. Patashnick (Bristol, UK), L. Scneps (P, (co-organizer with J. Burgos (Madrid), K. Ebrahimi-Fard (Madrid), H. Gangl (Durham, UK), J. Kramer (Berlin), O. Patashnick (Bristol, UK), L. Scneps (P, December 1-5, 2014  
Organizer (co-organizers Benson Farb and Eduard Looijenga), Organizer (co-organizers Benson Farb and Eduard Looijenga). Moduli Spaces of Riemann Surfaces. IAS/Park City Mathematics Institute. July 03, 2011 - Ju, July 3-23, 2011  
Co-organizer (with Herbert Gangl), Co-organizer (with Herbert Gangl). Multiple zeta values, modular forms and elliptic motives. Heilbronn Institute, University of Bristol, UK. May 02, 2, 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  
Professional Service

Dept Officer
Director of Graduate Studies, Mathematics, Duke University, 1993-94 and 1995-96  
Math Community Services
American Mathematical Society, Distinguished Public Service Award Committee, February, 2015 - January, 2020  
Distinguished Public Service Award Committee, Distinguished Public Service Award Committee. American Mathematical Society. February, 2015 - January, 2020, 2015-20  
American Mathematical Society, Colloquium Lecture Committee, American Mathematical Society, Colloquium Lecture Committee. American Mathematical Society. February, 2016 - January, 2019, February, 2016 - January, 2019  
Co-organizer (with F. Brown, C. Dupont, V. Vologodsky) of Hot Topis workshop:, Co-organizer (with F. Brown, C. Dupont, V. Vologodsky) of Hot Topis workshop:. Galois Theory of Periods and Applications. MSRI, Berkeley. March 27, 20, March 2017  
Program committee (with Valery Alexeev, and François Loeser) for conference:, Program committee (with Valery Alexeev, and François Loeser) for conference:. Local zeta functions and the arithmetic of moduli spaces: A conference i, March 2017  
NSF site visit, American Institute of Mathematics, NSF site visit, American Institute of Mathematics. National Science Foundation. May 17, 2015 - May 19, 2015, May 17-19, 2015  
Director : IAS Park City Mathematics Institute, Director : IAS Park City Mathematics Institute. September, 2009 - September, 2014, September, 2009 - September, 2014  
American Mathematical Society, Committee on Publications, American Mathematical Society, Committee on Publications. February, 2010 - January 01, 2013, February, 2010 - January, 2013  
American Mathematical Society, Committee on Publications, February, 2010 - January, 2013  
Member : Council of the American Mathematical Society, Member : Council of the American Mathematical Society. February, 2010 - January 01, 2013, 2010-13  
American Mathematical Society: Advisory Board for Employment Committee, American Mathematical Society: Advisory Board for Employment Committee. February, 2009 - January 31, 2011, February, 2009 - January, 2011  
AMS committee to select speakers for national meetings (chair in 2005-06), 2003 - 2006  
AMS Nominating Committee, 2003-2005  
Committee to choose the Joint AMS-MAA speakers for January 2005 meeting, 2004 - 2005  
Alumni Visiting Committee, University of Illinois, Urbana-Champaign, October, 2003  
AMS Southeastern Section Program Committee (Chair in 2000-2001), 1999 - 2001  
AMS Centennial Fellowship Committee, 1991 - 1993  
Univ Services
Assistant managing editor, Assistant managing editor. Duke Mathematical Journal. July, 2022 - June, 2023, 2022-23  
Managing editor, Managing editor. Duke Mathematical Journal. July, 2019 - June, 2022, 2019-22  
Managing co-editor, Managing co-editor. Duke Mathematical Journal. July, 2018 - June, 2019, 2018-19  
Organizer, Organizer. Fourth Duke Mathematical Journal Conference. Duke University. April 26, 2018 - April 29, 2018, April 2018  
Selected Recent Invited Talks

Is the Goldman-Turaev Lie Bialgebra Motivic?, (virtual), 8 January 2024  
Mapping class groups of simply connected algebraic manifolds, (virtual), 2 November 2023  
Hodge Correlators, the Goldman-Turaev Lie Bialgebra and Johnson Homomorphisms, Les Diablerets, Switzerland, 1 September 2023  
Mapping class groups of simply connected algebraic manifolds, Dijon, 1 September 2023  
Polylogs: prehistory and future directions, University of Maryland, 1 September 2023  
Hecke Actions on Loops and Periods of Iterated Shimura Integrals, Florida, 1 February 2023  
Modular inverters, (virtual), 1 August 2022  
Weighted completion of Galois groups and rational points, (virtual), 1 May 2021  
A Guide to Variations of Mixed Hodge Structure: Generalities and Examples, (virtual), 1 April 2021  
Hecke operators and iterated integrals of modular forms, (virtual), 1 November 2020  
Johnson Homomorphisms, the Goldman--Turaev Lie bialgebra and GRT, Oxford University, 1 October 2019  
The Johnson homomorphism and its generalizations, Switzerland, 5 April 2019  
Path torsors of moduli spaces of curves, ETH Zurich, 1 April 2019  
Hodge Theory and the Goldman–Turaev Lie Bialgebra, Eugene, 16 October 2018  
Completions of Mapping Class Groups, Eugene, 15 October 2018  
Modular inverters, Hausdorff Institute of Mathematics, 1 January 2018  
Multiple modular motives II, Hausdorff Institute of Mathematics, 1 January 2018  
Ihara Curves, Department of Mathematics, 1 August 2017  
Johnson homomorphisms, stable and unstable, Japan, 1 August 2017  
Introduction to mixed modular motives, Baltimore, 1 March 2017  
Motives and derivations of free Lie algebras, Berkeley, CA, 1 March 2017  
Motivic Structures on Mapping Class Groups, ALGECOM-14, Purdue University, October 23, 2016  
Introduction to Unipotent and Relative Unipotent Completion, Algebraic geometry seminar, Purdue University, October 20, 2016  
Introduction to Unipotent and Relative Unipotent Completion, Purdue University, 1 October 2016  
Motivic Structures on Mapping Class Groups, Purdue University, 1 October 2016  
Completions of path torsors of moduli spaces of curves, GRT, MZVs and associators, Les Diablerets, Switzerland, August 27, 2016  
Completions of path torsors of moduli spaces of curves (4 lectures), Les Diablerets, Switzerland, 1 August 2016  
Galois actions on unipotent fundamental groups of curves, Topology of Complex Algebraic Varieties, CIRM, Luminy, France, May 30, 2016  
Galois actions on unipotent fundamental groups of curves, CIRM, Luminy, France, 1 May 2016  
Mixed motives associated to elliptic curves, CIRM, Luminy, France, October 27, 2015  
Mixed motives associated to elliptic curves, CIRM, Luminy, France, 1 October 2015  
Mixed motives associated to classical modular forms , Algebraic Geometry 2015, University of Utah, July 27, 2015  
Mixed motives associated to classical modular forms, University of Utah, 1 July 2015  
Rational Points of Universal Curves, Colorado State University, April 23, 2015  
Rational Points of Universal Curves, Colorado State University, 1 April 2015  
A Torelli Odyssey, Teichmüller Modular Groups, University of Chicago, March 22, 2015  
Rational Points of Universal Curves, University of Pennsylvania, March 16, 2015  
A Torelli Odyssey, University of Chicago, 1 March 2015  
Normal functions and the geometry of moduli spaces of curves, Institute for Advanced Study, Princeton, January 14, 2015  
Normal functions and the geometry of moduli spaces of curves, Institute for Advanced Study, Princeton, 1 January 2015  
The Hodge theory of SL2(Z) and Pollack's relations between derivations, Workshop on Multiple Zeta Values, Modular Forms and Elliptic Motives II, ICMAT, Madrid, December, 2014  
The Hodge theory of SL_2(Z) and Pollack's relations between derivations, ICMAT, Madrid, 1 December 2014  
The Hodge-de Rham theory of modular groups, Johns Hopkins University, November, 2014  
The Hodge-de Rham theory of modular groups, Institute for Advanced Study, Princeton, October, 2014  
Can a mapping class group ever be a Kähler group?, University of Sydney, September 12, 2014  
Introduction to universal mixed elliptic motives, Hiroshima University, September 05, 2014  
Universal mixed elliptic motives, Bures-sur-Yvette, France, May, 2014  
Motivic structures on completions of modular groups, Di Giorgi Center, Pisa, Italy, December 20, 2013  
Modular forms and multiple zeta values, Texas Geometry and Topology Conference, Texas A&M University, October 13, 2013  
The Hodge theory of relative completions of modular groups, Recent Advances in Hodge Theory, University of British Columbia, Vancouver, BC, June 14, 2013  
The Beauville splitting of the Chow groups of a the jacobian of a general curve, Algebra Seminar, University of Sydney, May 17, 2013  
Higher Genus Polylogarithms, Workshop on Grothendieck-Teichmüller Theory and Multiple Zeta Values, Newton Institute, Cambridge, UK, April 10, 2013  
Infinitesimal presentations of mapping class groups, Colloquium, SUNY Stony Brook, February 28, 2013  
The Beauville splitting of the Chow groups of a general jacobian, Algebra, Geometry and Physics seminar, SUNY Stony Brook, February 27, 2013  
Scissors Congruence, NAM MathFest, Morgan State University, Baltimore MD, November 8, 2012  
Mapping class groups and rational points of algebraic curves, Algebraic Geometry and Number Theory seminar, Johns Hopkins University, November 7, 2012  
Colloquium, Mapping class groups and rational points of algebraic curves, University of Illinois, Chicago, October 19, 2012  
Morse theory and the topology of moduli spaces of curves, Centre International de Rencontres Mathématiques, Luminy, France, June 8, 2012  
Morse theory and mapping class groups in low genus, Colloquium, Université de Nice, May 29, 2012  
The Torelli group in genus 3, Max Dehn Seminar, University of Utah, February 16, 2012  
The Torelli group in genus 3, Geometry/Topoogy seminar, University of Chicago, September 23, 2011  
Universal mixed ellliptic motives, Lorentz Center, University of Leiden, The Netherlands, May 24, 2011  
Topology and Arithmetic, Colloquium, Universiteit Utrecht, May 19, 2011  
On a problem of Eliashberg, Seminaire Algèbre, Topologie et Géométrie, Université de Nice, France, May 10, 2011  
Universal mixed ellliptic motives, Heilbronn Institute, Bristol University, UK, May 6, 2011  
Topology and arithmetic, Colloquium, Rice University, February 24, 2011  
Topology and arithmetic, Max Dehn Seminar, University of Utah, February 11, 2011  
Universal mixed elliptic motives, Number Theory Seminar, University of Tokyo, June 09, 2010  
On the section conjecture for curves over universal function fields, Institut Henri Poincaré, Paris, April 30, 2010  
On the section conjecture for universal curves over function fields, Newton Institute, Cambridge, UK, July 29, 2009  
On the Section Conjecture for universal curves over function fields, Number Theory Seminar, Tokyo University, June 24, 2009  
On the Section Conjecture for universal curves over function fields, Number Theory Seminar, Hiroshima University, June 19, 2009  
Hodge and Galois theory of fundamental groups of algebraic varieties, (2 talks) Fundamental Groups in Algebraic Geometry, Université de Nice, May 25 and 26, 2009  
Groupes de Teichmüller et espaces de modules de courbes, Séminaire Passe-partout, Université de Nice, May 20, 2009  
Elliptic curves and multiple zeta numbers, UNSW-Sydney joint Colloquium, University of New South Wales, Australia, November 14, 2008  
Elliptic curves and multiple zeta numbers, Colloquium, University of Michigan, Ann Arbor, September 23, 2008  
An introduction to moduli of curves through elliptic curves (4 lectures), Zhejiang University, Hangzhou, China, July, 2008  
Elliptic motives and multiple zeta values, Séminaire de géométrie algébrique Rennes-Nantes-Paris, Institut des Hautes Etudes Scientifiques, Paris, April 3, 2008  
Hyperelliptic Torelli groups, Max-Planck Institut, Bonn, Germany, January 9, 2008  
Modular forms and derivations of the free Lie algebra of rank 2, Geometry and Lie Theory Conference, University of Sydney, Australia, July 12, 2007  
Elliptic motives, Hodge Theory, Kaehler Manifolds, and Homogeneous Spaces, University of Utah, May 26, 2007  
Universal Teichmuller and elliptic motives, Motives, Related Topics, Applications, Hiroshima University, Japan, March 08, 2007  
Higher Albanese manifolds, Banff International Research Station, February, 2007  
Hyperelliptic Motives, 2005 Summer Research Institute in Algebraic Geometry, University of Washington, Seattle, August 12, 2005  
Algebraic cycles and cohomology of hyperelliptic mapping class groups, Geometry Seminar, Université de Nice, May 25, 2005  
An introduction to Chen's Iterated Integrals, K.-T. Chen Celebration, University of Illinois, April 14, 2005  
Iterated integrals, Hodge theory, and fundamental groups, Arizona Winter School 2005, Alburqueque, NM, March 12-16, 2005  
On the symplectic cohomology of hyperelliptic mapping class groups, International Research Institute on Moduli Spaces and Arithmetic Geometry, Kyoto University, September 8--15, 2004  
Cohomology of mapping class groups and the geometry and arithmetic of curves, Colloquium, University of Toronto, March 25, 2004  
Cycle classes associated to familes of degree 0 divisors on curves, Geometry seminar, Stanford, February 17, 2004  
Torelli Groups and Enumerative Geometry of Moduli of Curves Parts I and II, Geometry Lectures, University of Chicago, December 5 and 8, 2003  
The symplectic cohomology of the genus 2 mapping class groups, Geometry seminar, University of Chicago, November 6, 2003  
Le cycle algébrique Cx - Cx- dans la jacobienne de C et l'action des groupes de Galois sur &pi1(C,x), Séminaire Géométrie algébrique, Université de Nice, June, 2003  
Galois actions on fundamental groups of curves and the cycle C-C-, Journée Groupes Fondamentaux et Polylogs, Université Paris VI, June 19, 2003  
Intégrales itérées et le théorème de de Rham pour le groupe fondamental, Séminaire Passe-Partout, Université de Nice, June 18, 2003  
Galois actions on fundamental groups of curves and the cycle C - C-, Cortona, Italy, June, 2003  
Some geometry and arithmetic of hyperelliptic mapping class groups, Topology Seminar, Tokyo University, December 10, 2002  
Periods of limit mixed Hodge structures, Current Developments in Mathematics Conference, Harvard-MIT, November 16, 2002  
Galois actions on fundamental groups of curves and the cycle C-C-, Number Theory Seminar, Harvard, November 6, 2002  
Galois actions on fundamental groups of curves and the cycle C-C-, Geometry Seminar, Brown University, October 30, 2002  
The cycle C-C-, positivity of normal functions and Moriwaki's inequality , Harvard-MIT Algebraic Geometry Seminar, October 15, 2002  
The rational cohomology ring of the moduli space of principally polarized abelian 3-folds, Topology Seminar, MIT,, September 30, 2002  
Iterated Integrals and Motives, Workshop on Non-Abelian Hodge Theory, MSRI, April 1, 2002  
The rational cohomology of Sp3(Z), Workshop on the Topology of Moduli Spaces, Stanford University, August 16, 2001  
Differential forms and combinatorial group theory, Colloquium, Australian National University, June 28, 2001  
A Hodge analogue of the Galois Lie algebra, Workshop on Hodge theory, Galois theory, moduli and arithmetic geometry, Kyoto University, May 21-24, 2001  
The story of C-C-, Colloquium, University of Chicago, 13 April 2001  
Constructions of Natural Teichmuller Modular Forms, JAMI Conference, Johns Hopkins University, March 24, 2001  
The story of C - C-, Colloquium, University of Arizona, March 22, 2001  
Chen's iterated integrals: key examples and future directions, Nankai University, Tianjin, China, October 9, 2000  
On the action of the absolute Galois group on the fundamental group of the thrice punctured projective line, Aspects of Algebraic Geometry and Commutative Algebra, Texas A&M, May 18-20, 2000, 18 May 2000  
Relative completion of arithmetic mapping class groups, Galois Actions and Geometry Workshop, MSRI, Berkeley, CA., 14 October 1999  
Moduli spaces of curves: transcendental and Hodge theoretic aspects (4 lecutres), ICTP, Trieste, Italy, July and August, 1999  
Moriwaki's Inequality and Generalizations, Midwest Algebraic Geometry Conference, Northwestern University, 31 October 1998  
On the Arakelov geometry of moduli spaces of curves, ICM Satellite Conference: Algebraic and Arithmetic Geometry, Essen, Germany, 4 August 1998  
Colloquium, RIMS, Kyoto University, 24 May 1998  
Colloquium, Tokyo Metropolitan University, 20 May 1998  
Topology Seminar, Tokyo University, 16 May 1998  
Moduli Workshop, Tokyo University, 14 May 1998  
Brandeis-Harvard-MIT-Northeastern Colloquium, Northeastern University, 10 March 1998  
Algebra seminar, Princeton University, 12 February 1998  
Special Seminar, University of Chicago, 11 November 1997  
Howard Garland's 60th Birthday Conference, Yale University, 1 November 1997  
AMS Invited Hour Address, Memphis, TN, 22 March 1997  
Frontiers in Mathematics Lectures, Texas A&M University, March, 1997  
Doctoral Theses Directed

Eric Hopper, Cyclotomic and Elliptic Polylogarithms and Motivic Extensions of Q by Q(m), (2017 - 2021)  
Xin Xiong, Hodge Theory and String Topology, (2017 - 2021)  
Ma Luo, Algebraic De Rham Theory for Completions of Fundamental Groups of Moduli Spaces of Elliptic Curves, (2014 - 2018)  
Anil Venkatesh, Triple Products of Eisenstein Series, (2009 - 2015)  
Kevin Kordek, Theta functions and the structure of Torelli groups in low genus, (March, 2011 - April, 2015)  
Tatsunari Watanabe, Rational points of universal curves in positive characteristic, (August, 2010 - April, 2015)  
Joseph A. Spivey, Twisted cohomology of hyperelliptic mapping class groups, (2008)  
Anthony J. Narkawicz, Cohomology jumping loci and the relative Malcev completion, (2007)  
Kevin Knudson, The Homology of Linear Groups over Laurent Polynomial Rings, (1996)  
Alexandre Kabanov, The Second Homology of the Moduli Space of Riemann Surfaces with Twisted Coefficents, (1995)  
Vincent Moulton, Vector Braids, (1994)  
Jun Yang, Algebraic K-groups of Number Fields and the Hain-MacPherson Trilogarithm, (1991)  
Dale Lear, Extensions of normal functions and asymptotics of the height pairing, (1990)  

Publications

Books

  1. Benson Farb, Richard Hain, Eduard Looijenga, Moduli Spaces of Riemann Surfaces, IAS/Park City Mathematics Series, edited by Farb, B; Hain, R; Looijenga, E, vol. 20 (2013), pp. x+356 pages, American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, ISBN 978-0-8218-9887-1
  2. Shiing-Shen Chern, Lei Fu, and Richard M. Hain, Contemporary Trends in Algebraic Geometry and Algebraic Topology, edited by Chern, S-S; Fu, L; Hain, R, vol. 5 (2002), pp. viii+266 pages, World Scientific Publishing Co., Inc., River Edge, NJ, ISBN 981-02-4954-3
  3. Carl-Friedrich Bodigheimer and Richard M. Hain (editors), Mapping Class Groups and Moduli Spaces of Riemann Surfaces, edited by Bödigheimer, C-F; Hain, R, vol. 150 (1993), pp. xx+372-xx+372, American Mathematical Society, Providence, RI, ISBN 0-8218-5167-5
  4. Hain, RM, Iterated Integrals and Homotopy Periods, vol. 47 (1984), pp. iv-98, American Mathematical Society

Papers Published

  1. Cox, D; Esnault, H; Hain, R; Harris, M; Ji, L; Saito, M-H; Saper, L, Remembering Steve Zucker, edited by Cox, D; Harris, M; Ji, L, Notices of the American Mathematical Society, vol. 68 no. 7 (August, 2021), pp. 1156-1172, American Mathematical Society
  2. Hain, R, Hodge theory of the Turaev cobracket and the Kashiwara-Vergne problem, Journal of the European Mathematical Society, vol. 23 no. 12 (January, 2021), pp. 3889-3933
  3. Hain, R, Johnson homomorphisms, EMS Surveys in Mathematical Sciences, vol. 7 no. 1 (January, 2021), pp. 33-116
  4. Hain, R, Hodge theory of the Goldman bracket, Geometry & Topology, vol. 24 no. 4 (November, 2020), pp. 1841-1906, Mathematical Sciences Publishers
  5. Hain, R; Matsumoto, M, Universal Mixed Elliptic Motives, Journal of the Institute of Mathematics of Jussieu, vol. 19 no. 3 (May, 2020), pp. 663-766
  6. Hain, R, Notes on the Universal Elliptic KZB Equation, Pure and Applied Mathematics Quarterly, vol. 12 no. 2 (January, 2020), International Press
  7. Hain, R, Notes on the universal elliptic KZB connection, Pure and Applied Mathematics Quarterly, vol. 16 no. 2 (January, 2020), pp. 229-312
  8. Brown, F; Hain, R, Algebraic de Rham theory for weakly holomorphic modular forms of level one, Algebra and Number Theory, vol. 12 no. 3 (January, 2018), pp. 723-750
  9. Hain, R, Deligne-Beilinson Cohomology of Affine Groups, in Hodge Theory and $L^2$-analysis, edited by Ji, L (2017), International Press, ISBN 9781571463517
  10. Arapura, D; Dimca, A; Hain, R, On the fundamental groups of normal varieties, Communications in Contemporary Mathematics, vol. 18 no. 4 (August, 2016), pp. 1550065-1550065, ISSN 0219-1997
  11. 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 (February, 2016), pp. 422-514, Cambridge University Press, ISBN 9781107546295
  12. Hain, R, Genus 3 mapping class groups are not Kähler, Journal of Topology, vol. 8 no. 1 (March, 2015), pp. 213-246, Wiley, ISSN 1753-8416
  13. Dimca, A; Hain, R; Papadima, S, The abelianization of the Johnson kernel, Journal of the European Mathematical Society, vol. 16 no. 4 (January, 2014), pp. 805-822, ISSN 1435-9855
  14. Hain, R, Remarks on non-abelian cohomology of proalgebraic groups, Journal of Algebraic Geometry, vol. 22 no. 3 (June, 2013), pp. 581-598, American Mathematical Society (AMS), ISSN 1056-3911
  15. Hain, R, Normal Functions and the Geometry of Moduli Spaces of Curves, in Handbook of Moduli, edited by Farkas, G; Morrison, I, vol. 1 (2013), pp. 527-578, International Press, ISBN 9781571462572
  16. Hain, R, Rational points of universal curves, Journal of the American Mathematical Society, vol. 24 no. 3 , pp. 709-769, American Mathematical Society (AMS), ISSN 0894-0347
  17. Hain, R, Lectures on Moduli Spaces of Elliptic Curves, in Transformation Groups and Moduli Spaces of Curves: Advanced Lectures in Mathematics, Advanced Lectures in Mathematics, edited by Ji, L; Yau, ST, vol. 16 no. 16 (2010), pp. 95-166, Higher Education Press, Beijing, ISBN 978-7-04-029842-0
  18. Hain, R; Matsumoto, M, Relative pro-ℓ completions of mapping class groups, Journal of Algebra, vol. 321 no. 11 (June, 2009), pp. 3335-3374, Elsevier BV, ISSN 0021-8693
  19. Hain, R, Relative Weight Filtrations on Completions of Mapping Class Groups, in Groups of Diffeomorphisms: Advanced Studies in Pure Mathematics, Advanced Studies in Pure Mathematics, vol. 52 (2008), pp. 309-368, Mathematical Society of Japan
  20. Hain, R, Finiteness and Torelli Spaces, in Problems on Mapping Class Groups and Related Topics, Proc. Symp. Pure Math. 74, edited by Farb, B, vol. 74 (2006), pp. 57-70, Amererican Mathematics Societty, ISBN 9780821838389
  21. Kim, M; Hain, RM, The Hyodo-Kato theorem for rational homotopy types, Mathematical Research Letters, vol. 12 no. 2-3 (January, 2005), pp. 155-169, ISSN 1073-2780
  22. Hain, R; Matsumoto, M, Galois actions on fundamental groups of curves and the cycle, Journal of the Institute of Mathematics of Jussieu, vol. 4 no. 3 (January, 2005), pp. 363-403, Cambridge University Press (CUP): STM Journals, ISSN 1475-3030
  23. Kim, M; Hain, RM, A De Rham–Witt approach to crystalline rational homotopy theory, Compositio Mathematica, vol. 140 no. 05 (September, 2004), pp. 1245-1276, Wiley, ISSN 0010-437X
  24. Hain, R; Reed, D, On the arakelov geometry of moduli spaces of curves, Journal of Differential Geometry, vol. 67 no. 2 (Summer, 2004), pp. 195-228, ISSN 0022-040X
  25. Hain, R; Matsumoto, M, Weighted completion of galois groups and galois actions on the fundamental group of ℙ1 -{0, 1, ∞}, Compositio Mathematica, vol. 139 no. 2 (November, 2003), pp. 119-167, ISSN 0010-437X
  26. Hain, R, Periods of Limit Mixed Hodge Structures, in CDM 2002: Current Developments in Mathematics in Honor of Wilfried Schmid & George Lusztig, edited by Jerison, D; Lustig, G; Mazur, B; Mrowka, T; Schmid, W; Stanley, R; Yau, ST (2003), pp. 113-133, International Press
  27. Hain, R; Matsumoto, M, Tannakian Fundamental Groups Associated to Galois Groups, in Galois Groups and Fundamental Groups, edited by Schneps, L, vol. 41 (2003), pp. 183-216, Cambridge Univ. Press
  28. Hain, R; Tondeur, P, The Life and Work of Kuo-Tsai Chen [ MR1046561 (91b:01072)], in Contemporary trends in algebraic geometry and algebraic topology (Tianjin, 2000), vol. 5 (2002), pp. 251-266, World Sci. Publ., River Edge, NJ, ISBN 9789810249540
  29. Hain, R, Iterated Integrals and Algebraic Cycles: Examples and Prospects, in Contemporary Tends in Algebraic Geometry and Algebraic Topology, vol. 5 (2002), pp. 55-118, World Scientific Publishing, ISBN 9789810249540
  30. Hain, R, The rational cohomology ring of the moduli space of abelian 3-folds, Mathematical Research Letters, vol. 9 no. 4 (2002), pp. 473-491
  31. Hain, R; Reed, D, Geometric proofs of some results of Morita, Journal of Algebraic Geometry, vol. 10 no. 2 (2001), pp. 199-217
  32. Dupont, J; Hain, R; Zucker, S, Regulators and Characteristic Classes of Flat Bundles, in The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), vol. 24 (2000), pp. 47-92, American Mathematical Society
  33. Hain, R, Moduli of Riemann Surfaces, Transcendental Aspects, Moduli Spaces, in ALgebraic Geometry, edited by Gottsche, L, vol. 1 (2000), pp. 293-353, Abdus Salam Int. Cent. Theoret. Phys., ISBN 92-95003-00-4
  34. Hain, R, Locally Symmetric Families of Curves and Jacobians, in Moduli of Curves and Abelian Varieties, edited by Faber, C; Looijenga, E (1999), pp. 91-108, Friedr. Vieweg
  35. Hain, RM, The Hodge De Rham theory of relative Malcev completion, Annales Scientifiques de l'Ecole Normale Superieure, vol. 31 no. 1 (1998), pp. 47-92
  36. Freedman, M; Hain, R; Teichner, P, Betti Number Estimates for Nilpotent Groups, in Fields Medallists’ Lectures, edited by Atiyah, ; Iagolnitzer,, vol. 5 (1997), pp. 413-434, World Science, ISBN 9789810231026
  37. Hain, R; Looijenga, E, Mapping Class Groups and Moduli Spaces of Curves, in Algebraic geometry—Santa Cruz 1995, vol. 62 (1997), pp. 97-142, American Mathematical Society
  38. Hain, R, Infinitesimal presentations of the Torelli groups, Journal of the American Mathematical Society, vol. 10 no. 3 (1997), pp. 597-651
  39. Hain, RM, The existence of higher logarithms, Compositio Mathematica, vol. 100 no. 3 (1996), pp. 247-276, ISSN 0010-437X
  40. Hain, RM; Yang, J, Real Grassmann polylogarithms and Chern classes, Mathematische Annalen, vol. 304 no. 1 (1996), pp. 157-201
  41. Elizondo, EJ; Hain, RM, Chow varieties of abelian varieties, Sociedad Matemática Mexicana. Boletí n. Tercera Serie, vol. 2 no. 2 (1996), pp. 95-99
  42. Hain, RM, Torelli Groups and Geometry of Moduli Spaces of Curves, in Current Topics in Complex Algebraic Geometry, edited by Clements, CH; Kollar, J, vol. 28 (1995), pp. 97-143, Cambridge Univ. Press
  43. Hain, RM, Classical Polylogarithms, Motives, in Motives (Seattle, WA, 1991), vol. 55 (1994), pp. 3-42, American Mathematical Society
  44. Hain, RM, Completions of Mapping Class Groups and the Cycle C-C, in Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991), vol. 150 (1993), pp. 75-105, American Mathematical Society, ISSN 0271-4132
  45. Hain, RM, Nil-manifolds as links of isolated singularities, Compositio Mathematica, vol. 84 no. 1 (1992), pp. 91-99, KLUWER ACADEMIC PUBL, ISSN 0010-437X
  46. Hain, RM, Algebraic Cycles and Variations of Mixed Hodge Structure, Complex Geometry and Lie Theory, in Complex geometry and Lie theory (Sundance, UT, 1989), vol. 53 (1991), pp. 175-221, American Mathematical Society, ISBN 9780821814925
  47. Hain, RM; MacPherson, R, Introduction to Higher Logarithms, in Properties of Polylogarithms, edited by Lewin, L, vol. 37 (1991), pp. 337-353, American Mathematical Societ, ISBN 9780821816349
  48. Hain, RM; MacPherson, R, Higher Logarithms, Illinois Journal of Mathematics, vol. 34 no. 2 (1990), pp. 392-475, ISSN 0019-2082
  49. Hain, R; Tondeur, P, The Life and Work of Kuo Tsai Chen, Illinois Journal of Mathematics, vol. 34 no. 2 (1990), pp. 175-190, Duke University Press, ISSN 0019-2082
  50. Hain, R, Biextensions and heights associated to curves of odd genus, Duke Mathematical Journal, vol. 61 no. 3 (1990), pp. 859-898, ISSN 0012-7094
  51. Durfee, AH; Hain, RM, Mixed Hodge Structures on the Homotopy of Links, Mathematische Annalen, vol. 280 (1988), pp. 69-83, ISSN 0025-5831
  52. Hain, RM; Zucker, S, A Guide to Unipotent Variations of Mixed Hodge Structure, Proceedings of the U.S. Spain Workshop, vol. 1246 (1987), pp. 92-106, Springer-Verlag
  53. Hain, RM, Higher Albanese Manifolds, Proceedings of the U.S. Spain Workshop, vol. 1246 (1987), pp. 84-91, Springer-Verlag
  54. Hain, RM, Iterated Integrals and Mixed Hodge Structures on Homotopy Groups, Proceedings of the U.S. Spain Workshop, vol. 1246 (1987), pp. 75-83, Springer-Verlag
  55. Hain, RM, The Geometry of the Mixed Hodge Structure on the Fundamental Group, in Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), vol. 46 (1987), pp. 247-282, American Mathematical Society
  56. Hain, RM; Zucker, S, Truncations of Mixed Hodge Complexes, Proceedings of the U.S. Spain Workshop, vol. 1246 (1987), pp. 107-114, Spring-Verlag
  57. Carlson, JA; Hain, RM, Extensions of Variations of Mixed Hodge Structure (1987), pp. 39-65, Theorie de Hodge
  58. Hain, RM; Zucker, S, Unipotent variations of mixed Hodge structure, Inventiones Mathematicae, vol. 88 no. 1 (1987), pp. 83-124, ISSN 0020-9910
  59. Hain, RM, The de rham homotopy theory of complex algebraic varieties I, K-Theory, vol. 1 no. 3 (1987), pp. 271-324, ISSN 0920-3036
  60. Hain, RM, The de Rham homotopy theory of complex algebraic varieties. II, $K$-Theory. An Interdisciplinary Journal for the Development, Application, and Influence of $K$-Theory in the Mathematical Sciences, vol. 1 no. 5 (1987), pp. 481-497, ISSN 0920-3036
  61. HAIN, RM, CORRECTION, TOPOLOGY, vol. 25 no. 4 (1986), pp. 585-586, ISSN 0040-9383
  62. Hain, RM, Mixed Hodge structures on homotopy groups, American Mathematical Society. Bulletin. New Series, vol. 14 no. 1 (1986), pp. 111-114, American Mathematical Society (AMS), ISSN 0273-0979
  63. Hain, RM, On the Indecomposable Elements of the Bar Construction, Proceedings of the American Mathematical Society, vol. 98 no. 2 (1986), pp. 312-316, JSTOR, ISSN 0002-9939
  64. Hain, RM, On a Generalization of Hilbert’s 21st Problem, Annales Scientifiques de l’École Normale Supérieure. Quatrième Série, vol. 19 no. 4 (1986), pp. 609-627, Societe Mathematique de France, ISSN 0012-9593
  65. Hain, RM, Iterated integrals, intersection theory and link groups, Topology. An International Journal of Mathematics, vol. 24 no. 1 (1985), pp. 45-66, ISSN 0040-9383
  66. HAIN, RM, ITERATED INTEGRALS AND HOMOTOPY PERIODS, MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 47 no. 291 (January, 1984), pp. 1-98, AMER MATHEMATICAL SOC
  67. Duchamp, T; Hain, RM, Primitive Elements in Rings of Holomorphic Functions, Journal für die Reine und Angewandte Mathematik. [Crelle’s Journal], vol. 346 no. 346 (1984), pp. 199-220, WALTER DE GRUYTER GMBH, ISSN 0075-4102
  68. Hain, RM, Twisting Cochains and Duality Between Minimal Algebras and Minimal Lie Algebras, Transactions of the American Mathematical Society, vol. 277 no. 1 (1983), pp. 397-411, JSTOR, ISSN 0002-9947
  69. Hain, RM, Iterated Integrals, Minimal Models and Rational Homotopy Theory (1980)
  70. Hain, RM, A characterization of smooth functions defined on a Banach space, Proceedings of the American Mathematical Society, vol. 77 no. 1 (1979), pp. 63-67, American Mathematical Society (AMS), ISSN 0002-9939
  71. Eades, P; Hain, RM, On Circulant Weighing Matrices, Ars Combinatoria, vol. 2 (1976), pp. 265-284, ISSN 0381-7032
  72. Richard M. Hain, Moduli of Riemann Surfaces, Transcendental Aspects, Moduli Spaces in Algebraic Geometry, ICTP Lecture Notes 1, L. Gottsche editor, 2000, 293--353
  73. Richard M. Hain, Classical Polylogarithms, Motives, Proc. Symp. Pure Math. 55 part 2 (1994), 3--42
  74. Richard M. Hain, Algebraic cycles and variations of mixed Hodge structure, Complex Geometry and Lie Theory, Proc. Symp. Pure Math, 53, (1991), 175--221
  75. Richard M. Hain, The de Rham homotopy theory of complex algebraic varieties I, Journal of K-Theory 1 (1987), 271--324
  76. Richard M. Hain, The de Rham homotopy theory of complex algebraic varieties II, Journal of K-Theory 1 (1987), 481--497
  77. Peter Eades and Richard M. Hain, On circulant weighting matrices, Ars Combinatoria, 2 (1976), 265--284

Other

  1. R.M. Hain, The de Rham homotopy theory of complex algebraic varieties (unpublished version) (Spring, 1984)

Others

  1. Hain, R, Mapping Class Groups of Simply Connected Kähler Manifolds (April, 2023)
  2. Hain, R, Hecke Actions on Loops and Periods of Iterated Shimura Integrals (February, 2023)

Last modified: 2024/03/28