Kenneth Ward

Department of Mathematics and Statistics American University 4400 Massachusetts Avenue NW Washington, D.C. 20016 Phone: (202) 885-3116 Fax: (202) 885-3155 Email: [email protected] url: http://edspace.american.edu/kward/

Nationality: American

Current position

Professorial Lecturer, American University

Research interests

Arithmetic algebraic geometry, game design and play, number theory

Including:

• Geometry of finite fields • Mathematical gaming: Learning, cognition, and structural theory • Hyperbolic and spacetime geometries • Sphere packing • Arithmetic statistics • Representation theory of global fields • Special functions • Algorithmic number theory and cryptography

Appointments held

2015-2018 Professorial Lecturer Department of Mathematics & Statistics, American University 2014-2015 Assistant Professor of Mathematics Advisor to the Associate Provost for the Quantitative Disciplines NYU-ECNU Institute of Mathematical Sciences, New York University Shanghai 2013-2014 Visiting Professor, Mathematics Coordinator NYU-ECNU Institute of Mathematical Sciences, New York University Shanghai 2013 Consultant on Undergraduate Mathematics to the Provost Oﬃce of the Provost, New York University

1 2008-2013 Lecturer, Graduate Assistant Department of Mathematics, Oklahoma State University 2006-2007 Research Assistant Riccardo Levi-Setti, Enrico Fermi Institute, University of Chicago 2004-2006 Graduate Fellow Department of Economics, University of Chicago 2002-2004 Assistant Instructor Paul J. Sally, Jr., Department of Mathematics, University of Chicago 2002-2004 Research Assistant Steven D. Levitt, Department of Economics, University of Chicago 2000-2001 Research Assistant Gary S. Becker, Department of Economics, University of Chicago

Education

2012 PhD in Pure Mathematics, Oklahoma State University 2009 MSc in Pure Mathematics, Oklahoma State University 2004 BA in Mathematics with Honors, University of Chicago 2004 BA in Economics with Honors, University of Chicago

Publications & Productions

2018 But There’s No Proof: A Thoroughly Unjustified Adventure in Logic. In preparation. 2018 Kwel: A Game of Circles and Glei: A Game of Spheres. In development. 2018 “Slices of π.” With Mario Ego-Aguirre. In preparation. 2018 “Arithmetic actions on cyclotomic function fields.” With Aristides Kontogeorgis. In preparation. 2018 “The q-unit circle.” arXiv preprint here. 2018 “Counting roots of hypergeometric series over finite fields.” With Amit Ghosh. Submit- ted to Journal of the London Mathematical Society. arXiv preprint here. 2017 “An explicit triangular integral basis for any separable cubic extension of a function field.” With Sophie Marques. Accepted by European Journal of Mathematics. arXiv preprint here. 2017 “Explicit Galois representations of automorphisms on holomorphic differentials in characteristic p.” Finite Fields and Their Applications, 44: 34-55. 2017 “Cubic fields: A primer.” With Sophie Marques. Accepted by European Journal of Mathematics. arXiv preprint here. 2016 “Holomorphic differentials of certain solvable covers of the projective line over a perfect field.” With Sophie Marques. Accepted by Mathematische Nachrichten. arXiv preprint here. 2015 “The number of roots of polynomials of large degree in a prime field.” With Amit Ghosh. International Mathematics Research Notices, 4: 898-926. 2014 “Values of twisted Artin L-functions.” Archiv der Mathematik 103: pp. 285-290. 2012 “Asymptotics of class number and genus for abelian extensions of an algebraic function

2 ﬁeld.” Journal of Number Theory 132(11): pp. 2491-2498. 2007 “Equilibria in games with auction-like discontinuities.” Carroll Round Proceedings, George- town University 4: pp. 88-111. 2007 “Testing the eﬃciency of markets in the 2002 World Cup.” As research assistant to Steven Levitt. Journal of Prediction Markets 1(3): pp. 255-270. 2004 “Uniqueness of strict dominance reduction in continuous compact games.” Unpublished note. (Economics Working Paper, University of Chicago)

Presentations

2018 “Binomial revolutions: A discreet discrete study of unity,” Integers 2018, Augusta, Georgia 2018 “Reinventing the wheel,” Mathematics & Statistics Colloquium, American University 2018 “The algebraist’s unit circle,” Invited Guest Lecture, CINVESTAV del IPN, Mexico City, Mexico 2017 “Circle packing and spacetime,” Physics Colloquium, American University 2017 “What’s in a circle?”, Mathematics Colloquium, Oklahoma State University 2017 “Open problems and conjectures in cyclotomic theory,” Number Theory Seminar, Ok- lahoma State University 2017 “Fibonacci numbers and the primes,” RISE-DC Invited Lecture, Eastern High School, Washington, D.C. 2016 “Cyclotomy in finite field arithmetic,” Algebra Seminar, University of Pennsylvania 2016 “Factoring curves over finite fields,” Number Theory Seminar, Dartmouth College 2016 “A few open problems in lifting,” Mathematics Seminar, University of Athens, Greece 2016 “K3 surfaces and the hypergeometric connection,” Mathematics & Statistics Seminar, American University 2015 Chair, U.S. National Climate Assessment Panel, American University 2015 “The structure of holomorphic differentials.” Fq12, The 12th International Conference on Finite Fields and Their Applications, Skidmore College 2015 “Explicit Galois representations of automorphisms on holomorphic differentials in characteristic p,” New York Joint Number Theory Seminar, New York City 2014 “Statistics for curves over finite fields,” Probability Seminar, NYU-ECNU Institute of Mathematical Sciences, Shanghai, China 2014 “Holomorphic differentials of cyclotomic function fields,” International Congress of Math- ematicians (ICM 2014), Number Theory Seminar, Seoul, Korea 2013 “Counting roots of polynomials,” Special Seminar, NYU-ECNU Institute of Mathemat- ical Sciences, Shanghai, China 2012 “Polynomials of large degree in a prime field,” Midwest Number Theory Conference, Number Theory Seminar, University of Illinois at Urbana-Champaign 2012 “Counting roots of polynomials of large degree in a prime field,” Number Theory Sem- inar, University of Colorado-Boulder 2011 “Class numbers in function fields: In memory of Manohar Madan,” Number Theory Seminar, Ohio State University 2011 “An asymptotic relation of the class number and genus for abelian extensions of a function field,” Algebra and Number Theory Seminar, University of Arizona

3 2011 “Class numbers and genera of algebraic function ﬁelds,” Number Theory Seminar, Columbia University 2005 “Existence of equilibria in auctions with incomplete information,” Fourth Annual Car- roll Round, Auction Theory Seminar, Georgetown University 2004 “Convexity in Nash equilibria”, Third Annual Carroll Round, John F. Nash, Jr. Lecture (with special introduction by John F. Nash, Jr.), Georgetown University 2004 “Uniqueness of strict dominance reduction in continuous compact games.” Economics Seminar, University of Chicago

Current collaborations

• Approximations of the circle. With Mario Ego-Aguirre (AU). • Modular forms on the q-plane. With Joshua Lansky (AU). • Binomials in positive characteristic. With Aristides Kontogeorgis (U. Athens, Greece) and Jeﬀrey Hakim (AU). • The Euler characteristic of a cubic global ﬁeld. With Sophie Marques (Cape Town, S. Africa).

Grants, honors & awards

2018 Mathematics Summer Scholarship (for research assistant Mario Ego-Aguirre) 2018 Unity 3D Education Development Grant 2016 College of Arts and Sciences Mellon Research Grant, American University 2015-6 Simons Collaborative Grant (for joint work with Amit Ghosh) 2015 College of Arts and Sciences Mellon Research Grant, American University 2014-2015 Arts and Sciences Research Grant, New York University Shanghai 2014 Invited Session Chair, International Congress of Mathematicians (ICM 2014), Seoul 2012 Centennial Scholar, Oklahoma State University · Awarded to 100 graduates of distinction in the history of Oklahoma State University, in honor of the University’s centennial 2011 Distinguished Graduate Fellowship, Graduate College, Oklahoma State University 2011 Jeanne LeCaine Agnew Fellowship, Department of Mathematics, Oklahoma State Uni- versity 2009 E. K. McLachlan Award, Department of Mathematics, Oklahoma State University 2007 John and Caryl Jobe Fellowship, Department of Mathematics, Oklahoma State Univer- sity 2004 Best Paper Award, Third Annual Carroll Round, Georgetown University

4 Teaching & advising

2018-2019 American University · Reimagining Reason · Linear Algebra · Business Statistics 2017-2018 American University · DC Math Circle (co-director, lead instructor) · Mario Ego-Aguirre (advisee); assistant on VR game design · Matt Sutton (advisee); accepted to UCL urban design graduate program · Elizabeth Pancotti (advisee), independent study, analysis and calculus on manifolds; accepted to MIT economics of education program · Foundations of Mathematics · Calculus II · Great Ideas in Mathematics · Basic Statistics 2016-2017 American University · Claire Perkins, independent study, arithmetic groups and modular forms · Great Ideas in Mathematics · Calculus I · Calculus II 2015-2016 American University · Thomas Woermer, Master’s thesis, algorithms in voting theory · Craig Oliver, independent study, graph theory and search trees · Foundations of Mathematics (proof-based methodology for mathematics majors) · Applied Calculus · Applied Precalculus · Great Ideas in Mathematics 2013-2015 New York University Shanghai · Abstract Algebra (honors course) · Ordinary Diﬀerential Equations (recitations only) · Calculus · Great Ideas in Mathematics 2008-2013 Oklahoma State University · Arithmetic Geometry (seminar series for graduate students and faculty) · Mathematical Interest Theory · Diﬀerential Equations · Linear Algebra · Calculus · Precalculus · W.L. Putnam Examination Practice Sessions 2004 University of Chicago · Honors Calculus (Simons summer program for gifted high school students) 2002-2004 NSF SESAME Program, University of Chicago · Number Theory (as assistant to Paul J. Sally, Jr. and John Boller)

5 Conferences and workshops attended

2018 Integers 2018, Augusta, Georgia 2018 Arithmetic Geometry, Number Theory, and Computation, MIT 2017 Blackboard to Bedside: How high-dimensional geometry is transforming the MRI in- dustry, U.S. Senate, Washington, D.C. 2017 TPSE (Transforming Post-Secondary Education in Mathematics), Math Chairs +1, University of Maryland 2017 JAMI 2017, Local zeta functions and the arithmetic of moduli spaces: A conference in memory of Jun-Ichi Igusa, Johns Hopkins University 2016 Super QVNTS: Kummer Classes and Anabelian Geometry, University of Vermont 2015 Fq12, The 12th International Conference on Finite Fields and Their Applications, Skid- more College 2015 Lifting Problems and Galois Theory, BIRS, Banff, Alberta 2015 Arithmetic 2015, Brown University 2015 Arithmetic Differentiation, University of California-Berkeley 2012 Southern California Number Theory Day, University of California-Irvine 2012 Arizona Winter School: Ramification and Geometry, Southwest Center for Arithmetic Geometry, University of Arizona 2011 The Pretentious View of Analytic Number Theory, Mathematics Research Communi- ties, American Mathematical Society, Snowbird, Utah 2011 Workshop on the Arithmetic of Function Fields, Imperial College, London

Committee work & Memberships

2015-2018 External · American Mathematical Society (AMS) · Association for Women in Mathematics (AWM) American University · University-Wide Committee on Active Learning Department of Mathematics & Statistics: · Undergraduate Studies Committee · Summer Research Committee · Public Relations Committee · Q1 & Q2 Committees

Language skills

Foreign language: Fluency in German, reading ﬂuency in French, reading ﬂuency in Russian Computer language: R, C, C++, SAS, SPSS, STATA