Sheldon Joyner

Department of Mathematics tel: 1-781-736-3068 (office) Brandeis University 1-781-249-0087 (cell) Goldsmith 218, MS 050 email: [email protected] 415 South Street web: http://people.brandeis.edu/~joyner Waltham, MA 02453

Appointments: Brandeis University, Lecturer, 09/2011 - present The University of Western Ontario, Postdoctoral Fellow and Assistant Professor, 07/2008 - 08/2011

Education: Purdue University, Ph.D., 08/2008, Thesis Advisor: Minhyong Kim Thesis Title: Zeta functions as iterated integrals The University of Arizona, Ph.D. program (transferred to Purdue), 08/2000 - 05/2005 Stellenbosch University, M.Sc. cum laude, 08/2000, Advisors: Barry Green and Andries van der Walt Thesis Title: On non-archimedean dynamical systems Stellenbosch University, Hons. B.Sc. cum laude, 12/1998

Areas of specialization: Number Theory and Arithmetic Geometry

Publications and preprints: 1. On a generalization of Chen’s iterated integrals, J. Number Theory, 130 no.2 (2010), 254-288 2. Pullback of parabolic bundles and covers of P1 \{0, 1, ∞}, (with Ajneet Dhillon), Mich. Math. J., 61 no. 1 (2011), 199-224 3. An algebraic version of the Knizhnik-Zamolodchikov equation, Ramanujan J., 28 no. 3 (2012), 361-384 4. On an extension of the universal monodromy representation for P1 \{0, 1, ∞}, submitted 2

Teaching: (Fall 2011 - present: Brandeis University; Fall 2008 - Summer 2011: The University of Western Ontario; 2006 - Spring 2008: Purdue University; 2001 - 2005: The University of Arizona)

Algebra II for graduate students: Spring 2013 (projected) Algebraic geometry for graduate students: Fall 2012 (projected) Multivariable calculus Spring 2013, Fall 2012 (projected) Number theory for graduate students: Spring 2012 Number theory for undergraduates: Spring 2012 Nonstandard analysis reading course: Spring 2012 Algebra I for graduate students: Fall 2011 Abstract algebra for undergraduates: Fall 2011 Calculus II: Summer 2011, Spring 2011, Spring 2004 Finite mathematics: Summer 2010, Spring 2010, Spring 2009, Summer 2009 Introductory analysis (calc without trig) II: Spring 2008, Fall 2007, Fall 2006 Introductory analysis (calc without trig) I: Fall 2008, Spring 2007, Spring 2006, Spring 2003 Riemann surfaces problem sessions: Spring 2005 Differential equations problem sessions: Spring 2005 Calculus I: Fall 2004, Fall 2003 Collegiate algebra: Fall 2002, Spring 2002, Fall 2001

Invited Lectures: (apart from peer seminar talks at home institutions)

Mathematics seminar, The University of Arizona, May 3, 2012: The polylogarithm generating function and the theta functions Workshop on multiple zeta values, modularity and elliptic motives, Heilbronn Institute, University of Bristol May 3, 2011: A quasi-modularity property of the polylogarithm generating function Workshop on arithmetic and geometry of algebraic varieties at The Fields Institute: March 19, 2011: The modular group and the Grothendieck-Teichm¨uller group Arithmetic Geometry seminar, McMaster University: September 23, 2010: On a certain PSL(2,Z) 1-cocycle Colloquium, Willamette University: September 16, 2010: The Riemann zeta function and the complex iterated integrals 3

Algebra seminar, Wesleyan University:

September 10, 2010: On a certain PSL(2, Z) 1-cocycle Colloquium, Wesleyan University: September 9, 2010: The Hopf algebra of complex iterated integrals Workshop on arithmetic and geometry of algebraic varieties at The Fields Institute: March 7, 2010: An algebraic Knizhnik-Zamolodchikov equation Algebra and number theory seminar, University of Rochester: October 27, 2009: Unipotent connections and functional equations of zeta functions Bimonthly Canadian Noncommutative Geometry Workshop at The Fields Institute: October 2, 2009: The geometry of the functional equation of Riemann’s zeta function Special polylogarithm seminar at Institut de mathematiques de Jussieu: May 28, 2009: Complex iterated integrals Workshop on arithmetic and geometry of algebraic varieties at The Fields Institute: March 7, 2009: Zeta functions as iterated integrals Number Theory Workshop at the University of Stellenbosch: June 2005: On Abhyankar’s conjecture Algebra and Number Theory Seminar at the University of Arizona: Spring 2005: Multi-zeta values and their regularizations University of Stellenbosch Mathematics Colloquium: June 2005: Polylogarithms, complex and p-adic August 2000: On p-adic Dynamical Systems Workshop on Arithmetic Geometry, Institute for Experimental Mathematics, Essen, Germany: December 1999: On p-adic Dynamical Systems and Good Reduction

Expository talks for undergraduates: Seminar at Willamette University, September 16, 2010: p-adic L-functions and the Bernoulli numbers Pizza seminar at The University of Western Ontario, September 29, 2009: Solving Rubik’s cube using group theory 4

Academic visits, Conferences and Meetings Attended Pro-unipotent fundamental groups: arithmetic and diophantine aspects, Bellairs Research Institute, Barbados, May 2012 Analytic Aspects of L-functions and Applications to Number Theory, University of Calgary, May 2011 Workshop on multiple zeta values, modularity and elliptic motives, Heilbronn Institute, University of Bristol, May 2011 (Invited speaker) Weekend workshops on algebraic varieties, The Fields Insitute: Mar 2011, Mar 2010, Mar 2009, Nov 2008 One month visit to IHES, Bures-sur-Yvette: Oct 2010 AMS / MAA Joint Meetings San Francisco: Jan 2010 Canadian Noncommutative Geometry Workshop, The Fields Institute: Oct 2009 Special polylogarithm seminar, Institut de mathematiques de Jussieu: May 2009 One week visit to University College London: May 2009 The Seventh Annual Spring Institute on Noncommutative Geometry, (Geometry

over F1, noncommutative geometry, and zeta), Vanderbilt University: May 2009 Arizona Winter School on Transcendance: Mar 2008 AMS / MAA Joint Meetings San Diego: Jan 2008 Arizona Winter School on p-adic Geometry: Mar 2007 Number Theory Workshop, University of Stellenbosch: Jun 2005 Arizona Winter School on Fundamental Groups in Arithmetic: Mar 2005 Workshop on Arithmetic Geometry, Institute for Experimental Mathematics, Essen: Dec 1999

Mathematical Interests: (inter alia) Zeta and L functions; functional equations of zeta functions; theta functions; Iterated integrals; Knizhnik-Zamolodchikov equations; polylogarithm functions; Fundamental Groups in Algebraic Geometry; Grothendieck-Teichmuller theory; Representation theory of affine Lie algebras; Quantum groups; Vertex operator algebras; Coleman integration; Nonstandard analysis 5

Prizes, Awards and Scholarships: Summer 2006: Purdue Research Fellowship 2002: JPG van der Horst prize for the best M.Sc. student in Mathematics at the University of Stellenbosch for the years 2000, 2001 and 2002 2000; 1999: Harry Crossley Scholarship 2000; 1999: Grantholder Bursary through the South African Foundation for Research and Development 1999: Prof Cillie Scholarship 1998: G.B.B. Rubbi prize for Hons. B.Sc. in Mathematics at the University of Stellenbosch 1997: G.B.B. Rubbi prize for Third Year Mathematics at the University of Stellenbosch 1995: Prize for First Year Physics at the University of Stellenbosch

Service: Faculty advisor to freshman students at Brandeis University, Fall 2012 (projected) Referee for article in conference proceedings “Infinite analysis 11”, Spring 2012 Reviewer for Zentralblatt Math, as of October 2010 Reviewer for Math Reviews, as of September 2010

Languages: English: fluent (first language) Spanish: fluent Afrikaans: fluent French: fluent in reading; good listening comprehension; improving in other aspects German: fluent in reading mathematics

References: Prof Minhyong Kim Oxford University [email protected] Prof Richard Hain Duke University [email protected] Prof Tatyana Foth University of Western Ontario [email protected] Prof Matthias Franz (teaching ref) University of Western Ontario [email protected] Prof Masoud Khalkhali University of Western Ontario [email protected] Dr Rita Saerens (teaching ref) Purdue University [email protected] Prof Dinesh Thakur University of Arizona [email protected] Prof Sai Kee Yeung Purdue University [email protected]