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 2008/2009

Spring - Math 1540 - Algebra - Time and location to be announced

Spring - Math 1560 - Number Theory - Time and location to be announced

Academic 2007/2008

Fall - Math 1580 - Cryptography - C Hour (MWF 10:00-10:50), Barus & Holley 160

Spring - Math 0420 - Number Theory - G Hour (MWF 2:00-2:50)

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, Spring/Summer 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.
  Errata for Advanced Topics ...
• Rational Points on Elliptic Curves, with John Tate, Springer-Verlag, UTM, 1992
  Errata for Rational Points ...
• Arithmetic Geometry, co-editor with Gary Cornell, Springer-Verlag, 1986.
• The Arithmetic of Elliptic Curves, Springer-Verlag, GTM 106, 1986.

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)

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 References, Links, People (Marc Joye)
• 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