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Curriculum Vitae

Richard Hain

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Box 90320, Durham, NC 27708-0320
(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

  • RTG: Linked via L-functions: training versatile researchers across number theory, National Science Foundation, 2023/10-2028/09.      
  • Topics in the topology, geometry and arithmetic of moduli spaces associated to curves, Simons Foundation, 2023/09-2028/08.      
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
Distinguished Public Service Award Committee, Distinguished Public Service Award Committee. American Mathematical Society. February, 2015 - January, 2020, 2015-20  
American Mathematical Society, Distinguished Public Service Award Committee, February, 2015 - January, 2020  
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 Topics workshop, Co-organizer (with F. Brown, C. Dupont, V. Vologodsky) of Hot Topics workshop. Galois Theory of Periods and Applications. Mathematical Sciences Resear, 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  
Member : Council of the American Mathematical Society, Member : Council of the American Mathematical Society. February, 2010 - January 01, 2013, 2010-13  
American Mathematical Society, Committee on Publications, February, 2010 - January, 2013  
American Mathematical Society, Committee on Publications, American Mathematical Society, Committee on Publications. February, 2010 - January 01, 2013, February, 2010 - January, 2013  
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, Duke Mathematical Journal, 2022-23  
Managing editor, Duke Mathematical Journal, 2019-22  
Managing co-editor, Managing co-editor. Duke Mathematical Journal. July, 2018 - June, 2019, 2018-19  
Organizer, Fourth Duke Mathematical Journal Conference, April 2018  
Selected Recent Invited Talks

Mapping class group actions on the homology of configuration spaces, University of Pennsylvania, 27 February 2025  
Relative higher Albanese manifolds over modular curves, University of Edinburgh, 25 November 2024  
Actions of mapping class groups on the homology of configuration spaces, University of Chicago, 17 October 2024  
Torelli groups and the geometry and arithmetic of moduli spaces of curves, Purdue University, 15 October 2024  
What can one say about the loci where the normal function of the Ceresa cycle is constant?, (online), 1 October 2024  
Torelli groups and the geometry and arithmetic of moduli spaces of curves, Chapel Hill, 12 September 2024  
Mapping class groups of simply connected algebraic manifolds, Université de Montpellier, 31 May 2024  
The rank of the normal function of the Ceresa cycle, Brown University, 16 May 2024  
Hecke actions on loops and periods of iterated Shimura integrals, Université de Montpellier, 15 May 2024  
The rank of the normal function of the Ceresa cycle, Université de Montpellier, 14 May 2024  
The Goldman–Turaev Lie bialgebra — is it motivic?, Université de Montpellier, 13 May 2024  
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 [grt-mzvs-and-associators-0]  
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 [html]  
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 [html]  
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 [available here]  
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 [abstract]  
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 [notes]  
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 [available here]  
The Hodge theory of relative completions of modular groups, Recent Advances in Hodge Theory, University of British Columbia, Vancouver, BC, June 14, 2013 [html]  
The Beauville splitting of the Chow groups of a the jacobian of a general curve, Algebra Seminar, University of Sydney, May 17, 2013 [html]  
Higher Genus Polylogarithms, Workshop on Grothendieck-Teichmüller Theory and Multiple Zeta Values, Newton Institute, Cambridge, UK, April 10, 2013 [gdow03]  
Infinitesimal presentations of mapping class groups, Colloquium, SUNY Stony Brook, February 28, 2013 [event.php]  
The Beauville splitting of the Chow groups of a general jacobian, Algebra, Geometry and Physics seminar, SUNY Stony Brook, February 27, 2013 [event.php]  
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 [poster]  
Morse theory and the topology of moduli spaces of curves, Centre International de Rencontres Mathématiques, Luminy, France, June 8, 2012 [htm]  
Morse theory and mapping class groups in low genus, Colloquium, Université de Nice, May 29, 2012 [php]  
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 [info.php3]  
Topology and Arithmetic, Colloquium, Universiteit Utrecht, May 19, 2011 [html]  
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 [index.php]  
Topology and arithmetic, Colloquium, Rice University, February 24, 2011 [html]  
Topology and arithmetic, Max Dehn Seminar, University of Utah, February 11, 2011 [php]  
Universal mixed elliptic motives, Number Theory Seminar, University of Tokyo, June 09, 2010 [html]  
On the section conjecture for curves over universal function fields, Institut Henri Poincaré, Paris, April 30, 2010 [cohomology-algebraic-varieties-hodge-theory-algebraic-cycles-motives]  
On the section conjecture for universal curves over function fields, Newton Institute, Cambridge, UK, July 29, 2009 [html]  
On the Section Conjecture for universal curves over function fields, Number Theory Seminar, Tokyo University, June 24, 2009 [html]  
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 [view_entry.php]  
Elliptic curves and multiple zeta numbers, UNSW-Sydney joint Colloquium, University of New South Wales, Australia, November 14, 2008 [pdf]  
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 [html]  
Elliptic motives and multiple zeta values, Séminaire de géométrie algébrique Rennes-Nantes-Paris, Institut des Hautes Etudes Scientifiques, Paris, April 3, 2008 [pdf]  
Hyperelliptic Torelli groups, Max-Planck Institut, Bonn, Germany, January 9, 2008 [html]  
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 [available here]  
Universal Teichmuller and elliptic motives, Motives, Related Topics, Applications, Hiroshima University, Japan, March 08, 2007 [html]  
Higher Albanese manifolds, Banff International Research Station, February, 2007 [birspages.php]  
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 [html]  
Iterated integrals, Hodge theory, and fundamental groups, Arizona Winter School 2005, Alburqueque, NM, March 12-16, 2005 [html]  
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 [html]  
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 [available here]  
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 [available here]  
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 [ps]  
Relative completion of arithmetic mapping class groups, Galois Actions and Geometry Workshop, MSRI, Berkeley, CA., 14 October 1999 [html]  
Moduli spaces of curves: transcendental and Hodge theoretic aspects (4 lecutres), ICTP, Trieste, Italy, July and August, 1999 [html]  
Moriwaki's Inequality and Generalizations, Midwest Algebraic Geometry Conference, Northwestern University, 31 October 1998 [ps]  
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 [html]  
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 (listed separately)
Last modified: 2025/04/04

 

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