Richard Hain
Professor of Mathematics
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, mixed zeta values, and their elliptic generalizations, which occur as periods of fundamental groups of moduli spaces of curves.
My primary collaborators are Francis Brown of Oxford University and Makoto Matsumoto of Hiroshima University.
Current Appointments & Affiliations
 Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1991
Contact Information
 107 Physics Bldg, Durham, NC 27708
 Box 90320, Durham, NC 277080320
 hain@math.duke.edu (919) 6602819
 My (old) departmental web page
 Publications on Google Scholar
 Publications on arXiv.org
 Publications via MathSciNet
 The Cost of Knowledge
 Background

Education, Training, & Certifications
 Ph.D., University of Illinois, UrbanaChampaign 1980
 M.Sc., Australian National University (Australia) 1977
 B.Sc. (hons), University of Sydney (Australia) 1976

Previous Appointments & Affiliations
 Managing Editor of the Duke Mathematical Journal, Mathematics, Trinity College of Arts & Sciences 2018  2022
 Chair, Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2004  2006
 Chair, Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 1999  2002
 Visiting Professor, Mathematics, Trinity College of Arts & Sciences 1990
 Recognition

Awards & Honors
 Research

Selected Grants
 Universal Teichmuller Motives awarded by National Science Foundation 2014  2020
 Park City Mathematics Institute awarded by Princeton University 2011  2015
 Applications of Topology to Arithmetic and Algebraic Geometry awarded by National Science Foundation 2010  2013
 Topology and motives associated to moduli spaces of curves awarded by National Science Foundation 2007  2011
 Hodge Theory, Galois Theory and the Topology of Moduli Spaces awarded by National Science Foundation 2004  2007
 Integrable Systems and Calibrated Geometry awarded by National Science Foundation 2006
 The Third DMJ/IMRN Conference awarded by National Science Foundation 2004  2005
 The Topology, Geometry and Arithmetic of Moduli Spaces of Curves awarded by National Science Foundation 2001  2004
 Modular Forms and Topology awarded by National Science Foundation 1998  2002
 The Second DMJ/IMRN Conference awarded by National Science Foundation 2001  2002
 Modular Forms and Topology awarded by National Science Foundation 1998  1999
 Mathematical Sciences: Representations of Braid and Mapping Class Groups awarded by National Science Foundation 1995  1998
 Representation of Braid and Mapping Class Groups awarded by National Science Foundation 1995  1997
 Representations of Braid and Mapping Class Groups awarded by National Science Foundation 1995  1997
 Mathematical Sciences: Topology and Geometry of Algebraic Varieties awarded by National Science Foundation 1992  1995
 Publications & Artistic Works

Selected Publications

Books

Farb, B., R. Hain, and E. Looijenga, eds. Moduli Spaces of Riemann Surfaces. Vol. 20. American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 2013.

Chern, S. . S., L. Fu, and R. Hain, eds. Contemporary Trends in Algebraic Geometry and Algebraic Topology. Vol. 5. World Scientific Publishing Co., Inc., River Edge, NJ, 2002. https://doi.org/10.1142/9789812777416.Full Text

Bödigheimer, C. . F., and R. Hain, eds. Mapping Class Groups and Moduli Spaces of Riemann Surfaces. Vol. 150. American Mathematical Society, Providence, RI, 1993. https://doi.org/10.1090/conm/150.Full Text

Hain, R. M. Iterated Integrals and Homotopy Periods. Providence, RI: American Mathematical Society, 1984. https://doi.org/10.1090/memo/0291.Full Text


Academic Articles

Cox, David, Hélène Esnault, Richard Hain, Michael Harris, Lizhen Ji, MasaHiko Saito, and Leslie Saper. “Remembering Steve Zucker.” Edited by David Cox, Michael Harris, and Lizhen Ji. Notices of the American Mathematical Society 68, no. 7 (August 2, 2021): 1156–72.

Hain, R. “Hodge theory of the Turaev cobracket and the KashiwaraVergne problem.” Journal of the European Mathematical Society 23, no. 12 (January 1, 2021): 3889–3933. https://doi.org/10.4171/JEMS/1088.Full Text Open Access Copy

Hain, R. “Johnson homomorphisms.” Ems Surveys in Mathematical Sciences 7, no. 1 (January 1, 2021): 33–116. https://doi.org/10.4171/EMSS/36.Full Text

Hain, Richard. “Hodge theory of the Goldman bracket.” Geometry &Amp; Topology 24, no. 4 (November 10, 2020): 1841–1906. https://doi.org/10.2140/gt.2020.24.1841.Full Text Open Access Copy

Hain, R., and M. Matsumoto. “Universal Mixed Elliptic Motives.” Journal of the Institute of Mathematics of Jussieu 19, no. 3 (May 1, 2020): 663–766. https://doi.org/10.1017/S1474748018000130.Full Text

Hain, R. “Notes on the Universal Elliptic KZB Equation.” Pure and Applied Mathematics Quarterly 12, no. 2 (January 30, 2020).Open Access Copy Link to Item

Hain, R. “Notes on the universal elliptic KZB connection.” Pure and Applied Mathematics Quarterly 16, no. 2 (January 1, 2020): 229–312. https://doi.org/10.4310/PAMQ.2020.v16.n2.a2.Full Text

Brown, F., and R. Hain. “Algebraic de Rham theory for weakly holomorphic modular forms of level one.” Algebra and Number Theory 12, no. 3 (January 1, 2018): 723–50. https://doi.org/10.2140/ant.2018.12.723.Full Text

Arapura, D., A. Dimca, and R. Hain. “On the fundamental groups of normal varieties.” Communications in Contemporary Mathematics 18, no. 4 (August 1, 2016). https://doi.org/10.1142/S0219199715500650.Full Text

Hain, Richard. “Genus 3 mapping class groups are not Kähler.” Journal of Topology 8, no. 1 (March 2015): 213–46. https://doi.org/10.1112/jtopol/jtu020.Full Text

Dimca, A., R. Hain, and S. Papadima. “The abelianization of the Johnson kernel.” Journal of the European Mathematical Society 16, no. 4 (January 1, 2014): 805–22. https://doi.org/10.4171/JEMS/447.Full Text Open Access Copy

Hain, R. “Remarks on nonabelian cohomology of proalgebraic groups.” Journal of Algebraic Geometry 22, no. 3 (June 18, 2013): 581–98. https://doi.org/10.1090/S105639112013005986.Full Text

Hain, R. “Rational points of universal curves.” Journal of the American Mathematical Society 24, no. 3 (July 1, 2011): 709–69. https://doi.org/10.1090/S089403472011006930.Full Text Open Access Copy

Hain, Richard, and Makoto Matsumoto. “Relative proℓ completions of mapping class groups.” Journal of Algebra 321, no. 11 (June 2009): 3335–74. https://doi.org/10.1016/j.jalgebra.2009.02.014.Full Text

Hain, R., and M. Matsumoto. “Galois actions on fundamental groups of curves and the cycle.” Journal of the Institute of Mathematics of Jussieu 4, no. 3 (January 1, 2005): 363–403. https://doi.org/10.1017/S1474748005000095.Full Text

Kim, M., and R. M. Hain. “The HyodoKato theorem for rational homotopy types.” Mathematical Research Letters 12, no. 2–3 (January 1, 2005): 155–69. https://doi.org/10.4310/mrl.2005.v12.n2.a2.Full Text Open Access Copy

Kim, Minhyong, and Richard M. Hain. “A De Rham–Witt approach to crystalline rational homotopy theory.” Compositio Mathematica 140, no. 05 (September 2004): 1245–76. https://doi.org/10.1112/s0010437x04000442.Full Text Open Access Copy

Hain, R., and D. Reed. “On the arakelov geometry of moduli spaces of curves.” Journal of Differential Geometry 67, no. 2 (January 1, 2004): 195–228. https://doi.org/10.4310/jdg/1102536200.Full Text

Hain, R., and M. Matsumoto. “Weighted completion of galois groups and galois actions on the fundamental group of ℙ^{1} {0, 1, ∞}.” Compositio Mathematica 139, no. 2 (November 1, 2003): 119–67. https://doi.org/10.1023/B:COMP.0000005077.42732.93.Full Text

Hain, R. “The rational cohomology ring of the moduli space of abelian 3folds.” Mathematical Research Letters 9, no. 4 (2002): 473–91.

Hain, Richard, and David Reed. “Geometric proofs of some results of Morita.” Journal of Algebraic Geometry 10 (2001): 199–217.

Hain, R. M. “The Hodge De Rham theory of relative Malcev completion.” Annales Scientifiques De L’Ecole Normale Superieure 31, no. 1 (1998): 47–92.

Hain, R. “Infinitesimal presentations of the Torelli groups.” Journal of the American Mathematical Society 10, no. 3 (1997): 597–651.

Elizondo, E Javier, and Richard M. Hain. “Chow varieties of abelian varieties.” Sociedad Matemática Mexicana. Boletí N. Tercera Serie 2 (1996): 95–99.

Hain, Richard M. “The existence of higher logarithms.” Compositio Mathematica 100 (1996): 247–76.

Hain, Richard M., and Jun Yang. “Real Grassmann polylogarithms and Chern classes.” Mathematische Annalen 304 (1996): 157–201. https://doi.org/10.1007/BF01446290.Full Text

Hain, Richard M. “Nilmanifolds as links of isolated singularities.” Compositio Mathematica 84 (1992): 91–99.

Hain, R. M., and R. MacPherson. “Higher Logarithms.” Illinois Journal of Mathematics 34 (1990): 392–475.

Hain, R., and P. Tondeur. “The Life and Work of Kuo Tsai Chen.” Illinois Journal of Mathematics 34 (1990): 175–90.

Hain, Richard. “Biextensions and heights associated to curves of odd genus.” Duke Mathematical Journal 61 (1990): 859–98. https://doi.org/10.1215/S0012709490061332.Full Text

Durfee, A. H., and R. M. Hain. “Mixed Hodge Structures on the Homotopy of Links.” Mathematische Annalen 280 (1988): 69–83. https://doi.org/10.1007/BF01474182.Full Text

Hain, R. M. “The de rham homotopy theory of complex algebraic varieties I.” K Theory 1, no. 3 (1987): 271–324. https://doi.org/10.1007/BF00533825.Full Text

Hain, R. M., and S. Zucker. “Unipotent variations of mixed Hodge structure.” Inventiones Mathematicae 88, no. 1 (1987): 83–124. https://doi.org/10.1007/BF01405093.Full Text

Hain, Richard M. “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 1 (1987): 481–97. https://doi.org/10.1007/BF00536980.Full Text

HAIN, R. M. “CORRECTION.” Topology 25, no. 4 (1986): 585–86.Link to Item

Hain, R. M. “On a Generalization of Hilbert’s 21st Problem.” Annales Scientifiques De L’École Normale Supérieure. Quatrième Série 19 (1986): 609–27.

Hain, R. M. “On the Indecomposable Elements of the Bar Construction.” Proceedings of the American Mathematical Society 98 (1986): 312–16. https://doi.org/10.2307/2045704.Full Text

Hain, R. M. “On the indecomposable elements of the bar construction.” Proceedings of the American Mathematical Society 98, no. 2 (January 1, 1986): 312–16. https://doi.org/10.1090/S00029939198608540395.Full Text

Hain, Richard M. “Mixed Hodge structures on homotopy groups.” American Mathematical Society. Bulletin. New Series 14 (1986): 111–14. https://doi.org/10.1090/S027309791986154108.Full Text

Hain, Richard M. “Iterated integrals, intersection theory and link groups.” Topology. an International Journal of Mathematics 24 (1985): 45–66. https://doi.org/10.1016/00409383(85)900448.Full Text

Duchamp, T., and R. M. Hain. “Primitive Elements in Rings of Holomorphic Functions.” Journal Für Die Reine Und Angewandte Mathematik. [Crelle’S Journal] 346 (1984): 199–220. https://doi.org/10.1515/crll.1984.346.199.Full Text

HAIN, R. M. “ITERATED INTEGRALS AND HOMOTOPY PERIODS.” Memoirs of the American Mathematical Society 47, no. 291 (January 1, 1984): 1–98.Link to Item

Hain, R. M. “Twisting Cochains and Duality Between Minimal Algebras and Minimal Lie Algebras.” Transactions of the American Mathematical Society 277 (1983): 397–411. https://doi.org/10.2307/1999363.Full Text

Hain, Richard M. “A characterization of smooth functions defined on a Banach space.” Proceedings of the American Mathematical Society 77, no. 1 (1979): 63–67. https://doi.org/10.1090/s00029939197905396328.Full Text

Eades, P., and R. M. Hain. “On Circulant Weighing Matrices.” Ars Combinatoria 2 (1976): 265–84.


Book Sections

Hain, R. “DeligneBeilinson Cohomology of Affine Groups.” In Hodge Theory and $L^2$Analysis, edited by L. Ji. International Press, 2017.Link to Item

Hain, R. “The Hodgede Rham theory of modular groups.” In Recent Advances in Hodge Theory: Period Domains, Algebraic Cycles, and Arithmetic, 422–514, 2016. https://doi.org/10.1017/9781316387887.019.Full Text

Hain, R. “Normal Functions and the Geometry of Moduli Spaces of Curves.” In Handbook of Moduli, edited by G. Farkas and I. Morrison, 1:527–78. Somerville, MA: International Press, 2013.

Hain, R. “Lectures on Moduli Spaces of Elliptic Curves.” In Transformation Groups and Moduli Spaces of Curves: Advanced Lectures in Mathematics, edited by L. Ji and S. T. Yau, 16:95–166. Beijing: Higher Education Press, 2010.

Hain, R. “Relative Weight Filtrations on Completions of Mapping Class Groups.” In Groups of Diffeomorphisms: Advanced Studies in Pure Mathematics, 52:309–68. Mathematical Society of Japan, 2008.

Hain, R. “Finiteness and Torelli Spaces.” In Problems on Mapping Class Groups and Related Topics, edited by B. Farb, 74:57–70. Providence, RI: Amererican Mathematics Societty, 2006. https://doi.org/10.1090/pspum/074/2264131.Full Text

Hain, R. “Periods of Limit Mixed Hodge Structures.” In CDM 2002: Current Developments in Mathematics in Honor of Wilfried Schmid & George Lusztig, edited by D. Jerison, G. Lustig, B. Mazur, T. Mrowka, W. Schmid, R. Stanley, and S. T. Yau, 113–33. Somerville, MA: International Press, 2003.

Hain, R., and M. Matsumoto. “Tannakian Fundamental Groups Associated to Galois Groups.” In Galois Groups and Fundamental Groups, edited by L. Schneps, 41:183–216. Cambridge: Cambridge Univ. Press, 2003.

Hain, R. “Iterated Integrals and Algebraic Cycles: Examples and Prospects.” In Contemporary Tends in Algebraic Geometry and Algebraic Topology, 5:55–118. River Edge, NJ: World Scientific Publishing, 2002. https://doi.org/10.1142/9789812777416_0004.Full Text

Hain, R., and P. Tondeur. “The Life and Work of KuoTsai Chen [ MR1046561 (91b:01072)].” In Contemporary Trends in Algebraic Geometry and Algebraic Topology (Tianjin, 2000), 5:251–66. World Sci. Publ., River Edge, NJ, 2002. https://doi.org/10.1142/9789812777416_0012.Full Text

Dupont, J., R. Hain, and S. Zucker. “Regulators and Characteristic Classes of Flat Bundles.” In The Arithmetic and Geometry of Algebraic Cycles (Banff, AB, 1998), 24:47–92. Providence, RI: American Mathematical Society, 2000.

Hain, R. “Moduli of Riemann Surfaces, Transcendental Aspects, Moduli Spaces.” In ALgebraic Geometry, edited by L. Gottsche, 1:293–353. Trieste: Abdus Salam Int. Cent. Theoret. Phys., 2000.

Hain, R. “Locally Symmetric Families of Curves and Jacobians.” In Moduli of Curves and Abelian Varieties, edited by C. Faber and E. Looijenga, 91–108. Braunschweig: Friedr. Vieweg, 1999.

Freedman, M., R. Hain, and P. Teichner. “Betti Number Estimates for Nilpotent Groups.” In Fields Medallists’ Lectures, edited by P. Atiyah and P. Iagolnitzer, 5:413–34. River Edge, NJ: World Science, 1997. https://doi.org/10.1142/9789812385215_0045.Full Text

Hain, R., and E. Looijenga. “Mapping Class Groups and Moduli Spaces of Curves.” In Algebraic Geometry—Santa Cruz 1995, 62:97–142. Providence, RI: American Mathematical Society, 1997.

Hain, R. M. “Torelli Groups and Geometry of Moduli Spaces of Curves.” In Current Topics in Complex Algebraic Geometry, edited by C. H. Clements and J. Kollar, 28:97–143. Cambridge: Cambridge Univ. Press, 1995.

Hain, R. M. “Classical Polylogarithms, Motives.” In Motives (Seattle, WA, 1991), 55:3–42. Providence, RI: American Mathematical Society, 1994.

Hain, R. M. “Completions of Mapping Class Groups and the Cycle CC.” In Mapping Class Groups and Moduli Spaces of Riemann Surfaces (Göttingen, 1991/Seattle, WA, 1991), 150:75–105. American Mathematical Society, 1993. https://doi.org/10.1090/conm/150/01287.Full Text

Hain, R. M. “Algebraic Cycles and Variations of Mixed Hodge Structure, Complex Geometry and Lie Theory.” In Complex Geometry and Lie Theory (Sundance, UT, 1989), 53:175–221. Providence, RI: American Mathematical Society, 1991. https://doi.org/10.1090/pspum/053/1141202.Full Text

Hain, R. M., and R. MacPherson. “Introduction to Higher Logarithms.” In Properties of Polylogarithms, edited by L. Lewin, 37:337–53. Providence, RI: American Mathematical Societ, 1991. https://doi.org/10.1090/surv/037/15.Full Text

Carlson, J. A., and R. M. Hain. “Extensions of Variations of Mixed Hodge Structure,” 39–65. Theorie de Hodge, 1987.

Hain, R. M. “The Geometry of the Mixed Hodge Structure on the Fundamental Group.” In Algebraic Geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 46:247–82. Providence, RI: American Mathematical Society, 1987.


Conference Papers

Hain, R. M. “Iterated Integrals and Mixed Hodge Structures on Homotopy Groups.” In Proceedings of the U.S. Spain Workshop, 1246:75–83. Berlin: SpringerVerlag, 1987. https://doi.org/10.1007/BFb0077530.Full Text

Hain, R. M. “Higher Albanese Manifolds.” In Proceedings of the U.S. Spain Workshop, Vol. 1246. Berlin: SpringerVerlag, 1987. https://doi.org/10.1007/BFb0077531.Full Text

Hain, R. M., and S. Zucker. “Truncations of Mixed Hodge Complexes.” In Proceedings of the U.S. Spain Workshop, Vol. 1246. SpringVerlag, 1987. https://doi.org/10.1007/BFb0077533.Full Text

Hain, R. M., and S. Zucker. “A Guide to Unipotent Variations of Mixed Hodge Structure.” In Proceedings of the U.S. Spain Workshop, Vol. 1246. Berlin: SpringerVerlag, 1987. https://doi.org/10.1007/BFb0077532.Full Text


Theses and Dissertations

Hain, R. M. “Iterated Integrals, Minimal Models and Rational Homotopy Theory,” 1980.


Preprints

Hain, Richard. “Mapping Class Groups of Simply Connected Kähler Manifolds,” April 3, 2023.Link to Item

Hain, Richard. “Hecke Actions on Loops and Periods of Iterated Shimura Integrals,” February 28, 2023.Link to Item


 Teaching & Mentoring

Recent Courses
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 Modular inverters. Algebra, Topology and the GrothendieckTeichmüller group. SwissMAP Research Station (Switzerland). August 2022 2022
 Weighted completion of Galois groups and rational points. Rational Points and Galois Representations. University of Pittsburgh. May 2021 2021
 A Guide to Variations of Mixed Hodge Structure: Generalities and Examples. Recent Developments in Hodge Theory. University of Miami. April 2021 2021
 Hecke operators and iterated integrals of modular forms. Galois Theory of Periods Seminar. Oxford University. November 2020 2020
 Johnson Homomorphisms, the GoldmanTuraev Lie bialgebra and GRT. Patterns in Cohomology of Moduli Spaces. Clay Mathematics Institute. October 1, 2019 2019
 Mixed elliptic motives. Masterclass: Elliptic Motives. KTH Royal Institute of Technology and University of Stockholm. May 20, 2019  May 24, 2019 2019
 The Johnson homomorphism and its generalizations. Séminaire "Groupes de Lie et espaces des modules". University of Geneva. April 5, 2019 2019
 Path torsors of moduli spaces of curves. Modular forms, periods and scattering amplitudes. Institute for Theoretical Studies. April 2019 2019
 Hodge Theory and the Goldman–Turaev Lie Bialgebra. Algebra seminar. University of Oregon. October 16, 2018 2018
 Completions of Mapping Class Groups. Mathematics Department Colloquium. University of Oregon. October 15, 2018 2018
 Hodge theory and the GoldmanTuraev Lie bialgebra. Workshop on Poisson geometry of moduli spaces, associators and quantum field theory. Simons Center. May 2018 2018
 Modular inverters. Workshop: Periods and Regulators. University of Bonn. January 2018 2018
 Multiple modular motives II. Periods in Number Theory, Algebraic Geometry and Physics. University of Bonn. January 2018 2018
 Ihara Curves. Workshop: Johnson homomorphisms and related topics. University of Tokyo. August 2017 2017
 Johnson homomorphisms, stable and unstable. Topology seminar. University of Tokyo. August 2017 2017
 Introduction to mixed modular motives. Local zeta functions and the arithmetic of moduli spaces: A conference in memory of JunIchi Igusa. Johns Hopkins University. March 2017 2017
 Motives and derivations of free Lie algebras. Hot Topics: Galois Theory of Periods and Applications. Mathematical Sciences Research Institute. March 2017 2017
 Introduction to Unipotent and Relative Unipotent Completion. Algebraic geometry seminar. Purdue University. October 2016 2016
 Motivic Structures on Mapping Class Groups. ALGECOM14. Purdue University. October 2016 2016
 Completions of path torsors of moduli spaces of curves (4 lectures). GRT, MZVs and associators workshop. Les Diablerets, Switzerland. August 2016 2016
 Galois actions on unipotent fundamental groups of curves. Topology of Complex Algebraic Varieties. CIRM, Luminy, France. May 2016 2016
 Mixed motives associated to elliptic curves. Moduli Spaces in Geometry. CIRM, Luminy, France. October 2015 2015
 Mixed motives associated to classical modular forms. Algebraic Geometry 2015. American Mathematical Society. July 2015 2015
 Rational Points of Universal Curves. Algebra seminar. Colorado State University. April 2015 2015
 Rational Points of Universal Curves. Algebra seminar. University of Pennsylvania. March 16, 2015 2015
 A Torelli Odyssey. Teichmüller Modular Groups. University of Chicago. March 2015 2015
 Normal functions and the geometry of moduli spaces of curves. Institute for Advanced Study, Princeton. January 2015 2015
 The Hodge theory of SL_2(Z) and Pollack's relations between derivations. Workshop on Multiple Zeta Values, Modular Forms and Elliptic Motives II. ICMAT, Madrid. December 2014 2014
 The Hodgede Rham theory of modular groups. Conference on Hodge Theory and L^2cohomology. Johns Hopkins University. November 2014 2014
 The Hodgede Rham theory of modular groups. Workshop on Periods. Institute for Advanced Study, Princeton. October 2014 2014
 Can a mapping class group ever be a Kähler group?. Algebra seminar. University of Sydney. September 12, 2014 2014
 Introduction to universal mixed elliptic motives. Motives conference. Hiroshima University. September 5, 2014 2014
 Universal mixed elliptic motives. minicourse. Institut des Hautes Études Scientifiques. May 2014 2014
 Motivic structures on completions of modular groups. Fundamental Groups in Arithmetic and Algebraic Geometry. Di Giorgi Center, Pisa, Italy. December 20, 2013 2013
 Modular forms and multiple zeta values, Texas Geometry and Topology Conference. October 13, 2013 2013
 The Hodge theory of relative completions of modular groups, Recent Advances in Hodge Theory. June 14, 2013 2013
 Hodge Theory and Iterated Integrals, Summer School, Recent Advances in Hodge Theory. June 13, 2013 2013
 The Beauville splitting of the Chow groups of a the jacobian of a general curve, Algebra Seminar. May 17, 2013 2013
 Higher Genus Polylogarithms, Workshop on GrothendieckTeichmüller Theory and Multiple Zeta Values. April 10, 2013 2013
 Infinitesimal presentations of mapping class groups, Colloquium. February 28, 2013 2013
 The Beauville splitting of the Chow groups of a general jacobian, Algebra, Geometry and Physics seminar. February 27, 2013 2013
 Scissors Congruence, NAM MathFest. November 8, 2012 2012
 Mapping class groups and rational points of algebraic curves, Algebraic Geometry and Number Theory seminar. November 7, 2012 2012
 Colloquium, Mapping class groups and rational points of algebraic curves. October 19, 2012 2012
 Morse theory and the topology of moduli spaces of curves. June 8, 2012 2012
 Morse theory and mapping class groups in low genus, Colloquium. May 29, 2012 2012
 The Torelli group in genus 3, Max Dehn Seminar. February 16, 2012 2012
 The Torelli group in genus 3, Geometry/Topoogy seminar. September 23, 2011 2011
 Universal mixed ellliptic motives. May 24, 2011 2011
 Topology and Arithmetic, Colloquium. May 19, 2011 2011
 On a problem of Eliashberg, Seminaire Algèbre, Topologie et Géométrie. May 10, 2011 2011
 Universal mixed ellliptic motives. May 6, 2011 2011
 Topology and arithmetic, Colloquium. February 24, 2011 2011
 Topology and arithmetic, Max Dehn Seminar. February 11, 2011 2011
 Universal mixed elliptic motives. June 9, 2010 2010
 On the section conjecture for universal curves over function fields, Algebra Seminar. May 28, 2010 2010
 On the section conjecture for curves over universal function fields. April 30, 2010 2010
 On the section conjecture for universal curves over function fields. July 29, 2009 2009
 On the Section Conjecture for universal curves over function fields, Number Theory Seminar. June 24, 2009 2009
 On the Section Conjecture for universal curves over function fields. June 19, 2009 2009
 Hodge and Galois theory of fundamental groups of algebraic varieties, (2 talks) Fundamental Groups in Algebraic Geometry. May 25, 2009 2009
 Groupes de Teichmüller et espaces de modules de courbes, Séminaire Passepartout. May 20, 2009 2009
 Elliptic curves and multiple zeta numbers, UNSWSydney joint Colloquium, University of New South Wales, Australia. November 14, 2008 2008
 Algebraic completions of discrete and profinite groups, Algebra Seminar, University of Sydney. November 6, 2008 2008
 Elliptic curves and multiple zeta numbers, Colloquium. September 23, 2008 2008
 An introduction to moduli of curves through elliptic curves (4 lectures). July 1, 2008 2008
 Elliptic motives and multiple zeta values, Séminaire de géométrie algébrique RennesNantesParis. April 3, 2008 2008
 Hyperelliptic Torelli groups, MaxPlanck Institut, Bonn, Germany. January 9, 2008 2008

Service to the Profession
 Coorganizer (with F. Brown, C. Dupont, V. Vologodsky) of Hot Topis workshop:. Galois Theory of Periods and Applications. MSRI, Berkeley. March 27, 2017  March 31, 2017 2017
 Program committee (with Valery Alexeev, and François Loeser) for conference:. Local zeta functions and the arithmetic of moduli spaces: A conference in memory of JunIchi Igusa. Johns Hopkins University. March 22, 2017  March 26, 2017 2017
 American Mathematical Society, Colloquium Lecture Committee. American Mathematical Society. February 2016  January 2019 2016  2019
 NSF site visit, American Institute of Mathematics. National Science Foundation. May 17, 2015  May 19, 2015 2015
 Distinguished Public Service Award Committee. American Mathematical Society. February 2015  January 2020 2015  2020
 (coorganizer with J. Burgos (Madrid), K. EbrahimiFard (Madrid), H. Gangl (Durham, UK), J. Kramer (Berlin), O. Patashnick (Bristol, UK), L. Scneps (Paris)). Workshop on Multiple Zeta Values, Modular Forms and Elliptic Motives II. ICMAT, Madrid, Spain. December 1, 2014  December 5, 2014 2014
 Organizer (coorganizers Benson Farb and Eduard Looijenga). Moduli Spaces of Riemann Surfaces. IAS/Park City Mathematics Institute. July 3, 2011  July 23, 2011 2011
 Coorganizer (with Herbert Gangl). Multiple zeta values, modular forms and elliptic motives. Heilbronn Institute, University of Bristol, UK. May 2, 2011  May 6, 2011 2011
 American Mathematical Society, Committee on Publications. February 2010  January 1, 2013 2010  2013
 Member : Council of the American Mathematical Society. February 2010  January 1, 2013 2010  2013
 Director : IAS Park City Mathematics Institute. September 2009  September 2014 2009  2014
 American Mathematical Society: Advisory Board for Employment Committee. February 2009  January 31, 2011 2009  2011

Service to Duke
 Assistant managing editor. Duke Mathematical Journal. July 2022  June 2023 2022  2023
 Managing editor. Duke Mathematical Journal. July 2019  June 2022 2019  2022
 Managing coeditor. Duke Mathematical Journal. July 2018  June 2019 2018  2019
 Organizer. Fourth Duke Mathematical Journal Conference. Duke University. April 26, 2018  April 29, 2018 2018
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