Joseph H. Silverman

Office: 202 Kassar House
Phone (direct): (401) 863-1124
Phone (dept office): (401) 863-2708
Fax: (401) 863-9013
Email: joseph_silverman@brown.edu

Mailing Address:

• Mathematics Department
  Box 1917
  Brown University
  Providence, RI 02912 USA

Teaching Schedule: 

Academic 2009/2010

Fall - On Leave - Visiting researcher at Microsoft Research, New England

Spring - Math 1560 - Number Theory - C hour (10:00–10:50am), Location TBA

Spring - Math 420 - Number Theory - D hour (11:00–11:50am), Location TBA

Academic 2008/2009

Spring - Math 1540 - Algebra - C hour (10:00–10:50am), Barus & Holley 160

Spring - Math 1560 - Number Theory - D hour(11:00–11:50am), Barus & Holley 161

Research Interests: Number theory, elliptic curves, arithmetic and Diophantine geometry, number theoretic aspects of dynamical systems, cryptography

Mathematical genealogy and list of Ph.D. students

Selected Publications (For a CV and complete list of publications, Click Here)

Books

• An Introduction to Mathematical Cryptography, with Jill Pipher and Jeffrey Hoffstein, Springer-Verlag, UTM, 2008.
• The Arithmetic of Dynamical Systems, Springer-Verlag, GTM 241, 2007.
• A Friendly Introduction to Number Theory, Prentice Hall, Third Edition 2006.
• Cryptography and Lattices Conference (CaLC 2001), editor, Lecture Notes in Computer Science 2146, Springer-Verlag, 2001.
• Diophantine Geometry: An Introduction, with Marc Hindry, Springer-Verlag, GTM 201, 2000.
• Modular Forms and Fermat's Last Theorem, co-editor with Gary Cornell and Glenn Stevens, Springer-Verlag, 1997.
• Advanced Topics in the Arithmetic of Elliptic Curves, Springer-Verlag, GTM 151, 1995.
  
• Rational Points on Elliptic Curves, with John Tate, Springer-Verlag, UTM, 1992.
  
• Arithmetic Geometry, co-editor with Gary Cornell, Springer-Verlag, 1986.
• The Arithmetic of Elliptic Curves, Springer-Verlag, GTM 106, 1986. Expanded 2nd Edition, 2009.

Selected Preprints and Reprints

Presentations

• The Ubiquity of Elliptic Curves - Version 1, Expanded version of MAA Invited Lecture presented at the Baltimore meeting, January 2003. (Powerpoint)
• The Ubiquity of Elliptic Curves - Version 2, Public Lecture, University College of Dublin, September 2007. (Powerpoint)
• A Number Theorist's Perspective on Dynamical Systems, Frontier Lectures, Texas A & M, April 2005 (PDF)
• An Introduction to Height Functions, Expanded version of lectures presented at MSRI, January 2006. (PDF)
• An Introduction to the Theory of Lattices, Summer School on Computational Number Theory and Applications to Cryptography, University of Wyoming, June/July 2006. (PDF)
• An Introduction to the Theory of Elliptic Curves, Summer School on Computational Number Theory and Applications to Cryptography, University of Wyoming, June/July 2006. (PDF)
• The Arithmetic of Dynamical Systems, Kuwait Lecture, Cambridge University, February 20, 2007. (PDF)
• Independence of Heegner Points, Number Theory Seminar, Cambridge University, February 22, 2007. (PDF)
• p-adic Properties of Elliptic Divisibility Sequences, Number Theory and Computability, ICMS Edinburgh, June 27, 2007. (PDF)
• The Four Faces of Lifting for the Elliptic Curve Discrete Logarithm Problem, 11th Workshop on Elliptic Curve Cryptography, University College Dublin, September 5, 2007. (PDF)
• Dynamics and Canonical Heights on K3 Surfaces with Noncommuting Involutions, Workshop on Rational Points on K3 Surfaces, BIRS, Banff, December 3, 2008. (PDF)
• Specialization Maps and Unlikely Intersections, Journees Arithmetique, St. Etienne, France July 6-10, 2009. (PDF)

Reference Sheets The following reference sheets are being made available as a service to the general mathematical community. They should be printed landscape (i.e., rotated 90 degrees).

Links to Number Theory Sites, Elliptic Curve Sites and Other Sites of Interest

• ABC Conjecture Web Site (Abderrahmane Nitaj)
• Algorithmic Number Theory Links (Noam Elkies)
• ArXiv Number Theory Preprint Server
• ArXiv Algebraic Geometry Preprint Server
• Elliptic Curve Tables (John Cremona)
• Online Version of Cremona's Elliptic Curve Tables
• Lehmer's Conjecture Web Site (Michael Mossinghoff)
• Mathematics Geneaology Project
• Modular Forms Database (William Stein)
• NTRU Cryptographic Systems
• Number Theory Web

Send questions and comments to: jhs@math.brown.edu