Address:
Department of Mathematics - Hill Center
Rutgers, The State University Of New Jersey
110 Frelinghuysen Rd.
Piscataway, NJ 08854-8019
Office:
Hill Center 624, Busch Campus
Email Addresses:
jcmiller at math or my Johns Hopkins email.
Advisor:
Henryk Iwaniec
Research Interests:
Number theory - especially the Weber problem and other class number problems, cyclotomic fields and Zp-extensions, norm-Euclidean domains, the Minkowski conjecture, the principal ideal problem and related lattice problems, class group computation methods, and low-lying zeros of Dirichlet L-functions and Dedekind zeta functions. Recently I have begun to investigate the class groups of ray class fields of imaginary quadratic fields, and the Zp-extensions built out of these. I am also working on problems associated to real quadratic fields, as well as elliptic curves over real quadratic fields.
Publications:
Preprints:
Previous semesters:
Research Talks:
April 23, 2015, ICERM Topical Workshop: Mathematics of Lattices and Cybersecurity, Brown University: "Class numbers of cyclotomic fields."
February 16, 2015, Ph.D. Thesis Defense at Rutgers University: "Class numbers of totally real number fields."
December 5, 2014, RIMS Workshop on Algebraic Number Theory and Related Topics, Kyoto, Japan: "On class numbers of cyclotomic fields and Zp-extensions."
September 16, 2014, Number Theory Seminar at Rutgers: "Class numbers of cyclotomic Zp-extensions."
August 11, 2014, Eleventh Algorithmic Number Theory Symposium (ANTS-XI) in Gyeongju, Korea: "Class numbers of real cyclotomic fields of composite conductor."
July 17, 2014, Kobe University, Kobe, Japan: "Upper bounds on class numbers and applications to cyclotomic fields."
January 16, 2014, Joint Mathematics Meetings AMS Special Session on Analytic Number Theory: "Computing class numbers beyond Odlyzko's bounds: Real cyclotomic fields."
November 22, 2013, Algebra-Number Theory Seminar at University of Maryland: "Upper bounds on class numbers and applications to cyclotomic fields."
October 27, 2013, MAA New Jersey Section: "Computing class numbers beyond Odlyzko's bounds: Real cyclotomic fields."
October 25, 2013, Collaborative Number Theory Seminar at the CUNY Graduate Center: "Calculating class numbers beyond Odlyzko's bounds: Real cyclotomic fields."
October 10, 2013, Dartmouth College: "Breaking Odlyzko's bounds: Class numbers of real cyclotomic fields."
September 24, 2013, Number Theory Seminar at Rutgers: "Breaking Odlyzko's bounds: Class numbers of real cyclotomic fields.."
August 23, 2013, Graduate Student Research Glimpse, Special Pre-enrollment Program in Mathematics at Rutgers: "Class Numbers of Cyclotomic Fields."
August 10, 2013, Waseda University, Tokyo, Japan: "New results on class numbers of real cyclotomic fields of prime conductor and power of 2 conductor."
December 11, 2012, Number Theory Seminar at Rutgers: "Applications of toral automorphisms."
Expository Talks:
March 10, 2015, Financial Mathematics Seminar at Johns Hopkins University: "Cliquet pricing and forward volatility skew."
March 6, 2015, Graduate Pizza Seminar at Rutgers: "The Riemann Zeta Function."
December 11, 2014, Student Number Theory Seminar at Rutgers: "Ranks of elliptic curves."
September 25, 2014, Student Number Theory Seminar at Rutgers: "An introduction to Artin L-functions via examples."
July 16, 2014, Kobe University, Kobe, Japan: "A brief introduction to the Riemann zeta function and other L-functions."
May 2, 2014, Graduate Student Elliptic Curves Seminar at Rutgers: "Elliptic curves of everywhere good reduction."
February 10, 2014, Rutgers Basic Notions and Research Perspectives Seminar at Rutgers: "Class number problems in number theory."
November 20, 2013, Graduate Student Algebraic Geometry Seminar at Rutgers: "Automorphic forms and algebraic groups."
April 5, 2013, Graduate Pizza Seminar at Rutgers: "Who hid my subgroup?"
February 15, 2012, Number Theory Basic Knowledge Seminar at Rutgers: "Cyclotomic Units and Class Groups."
December 6, 2011, Number Theory Basic Knowledge Seminar at Rutgers: "Applications of Gauss Sums."
October 25, 2011, Number Theory Basic Knowledge Seminar at Rutgers: "More on Hecke's Lemma."
March 29, 2011, Number Theory Basic Knowledge Seminar on Homogeneous Spaces at Rutgers: "Laplace-Beltrami Operators."
March 22, 2011, Number Theory Basic Knowledge Seminar on Homogeneous Spaces at Rutgers: "Riemannian manifolds and Laplacians."
February 1, 2011, Number Theory Basic Knowledge Seminar on Homogeneous Spaces at Rutgers: "Galois correspondence for covering spaces."
November 12, 2010, Graduate Pizza Seminar at Rutgers: "Farey sequences."
September 28, 2010, Number Theory Basic Knowledge Seminar at Rutgers: "Stickelberger's Factorization of Gauss Sums."
March 25, 2010, Working Seminar on Rational Points on Surfaces at Rutgers: "Rational points on Cubic Surfaces."
February 15, 2010, Mathematical Finance Career Workshop at Rutgers: "Searching for, Applying to and Getting the Job."
November 3, 2009, Working Seminar on Rational Points on Curves at Rutgers: "Relative Primality and solutions to Axp + Byq = Czr."
Maintained by jcmiller and last modified May 27, 2015.