Joseph Silverman

About

Joseph H. Silverman is a professor whose academic lineage and mentorship are documented through the Mathematics Genealogy Project. He earned his Ph.D. from Harvard University in 1982 with a dissertation titled "The Neron-Tate Height on Elliptic Curves." His research focus includes arithmetic dynamics, elliptic curves, and number theory, as evidenced by the topics of his numerous Ph.D. students' dissertations at Brown University. These topics range from dynamical Galois representations, algebraic dynamics, and moduli spaces to arithmetic dynamics of rational maps, height functions, and Galois theory. Silverman has advised a significant number of doctoral students, indicating a strong role in advancing research and education in these mathematical areas. His academic genealogy traces back through prominent mathematicians, including John Tate, Jr., Emil Artin, and Carl Friedrich Gauss, highlighting a distinguished scholarly heritage.

Research topics

• Computer Science
• Algorithm
• Mathematics
• Mathematical analysis
• Geometry

Selected publications

• MMSAT: A Scheme for Multimessage Multiuser Signature Aggregation.

  IACR Cryptology ePrint Archive · 2020 · 11 citations

  Publisher

• Orbits on K3 Surfaces of Markoff Type

  Experimental Mathematics · 2023-08-03 · 6 citations

  articleCorresponding

  AbstractLet W⊂P1×P1×P1 be a surface given by the vanishing of a (2, 2, 2)-form. These surfaces admit three involutions coming from the three projections W→P1×P1, so we call them tri-involutive K3 (TIK3) surfaces. By analogy with the classical Markoff equation, we say that W is of Markoff type (MK3) if it is symmetric in its three coordinates and invariant under double sign changes. An MK3 surface admits a group of automorphisms G generated by the three involutions, coordinate permutations, and s…

  PublisherDOI

• The distribution relation and inverse function theorem in arithmetic geometry

  Journal of Number Theory · 2021-04-19 · 3 citations

  articleSenior authorCorresponding
  PublisherDOI

• The size of semigroup orbits modulo primes

  Pacific Journal of Mathematics · 2023-11-03 · 2 citations

  articleOpen accessSenior author

  Let V be a projective variety defined over a number field K , let S be a polarized set of endomorphisms of V all defined over K , and let P ∈ V (K ).For each prime p of K , let m p (S, P) denote the number of points in the orbit of P mod p for the semigroup of maps generated by S.Under suitable hypotheses on S and P, we prove an analytic estimate for m p (S, P) and use it to show that the set of primes for which m p (S, P) grows subexponentially as a function of N K ‫ޑ/‬ p is a set of density ze…

  PublisherOA PDFDOI

• Post-critically finite maps on ℙⁿ for 𝕟≥2 are sparse

  Transactions of the American Mathematical Society · 2022-12-14 · 2 citations

  articleOpen accessSenior author

  Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f colon double-struck upper P Superscript n Baseline right-arrow double-struck upper P Superscript n"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">P</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false"> → </mml:m…

  PublisherOA PDFDOI

Recent grants

• FRG: Collaborative Research: Algebraic Dynamics

  NSF · $142k · 2009–2013

• Investigations in Arithmetic Geometry and Arithmetic Dynamics

  NSF · $195k · 2007–2011

Frequent coauthors

• Samuel G. Armistead

  Brocade (United States)

  95 shared

• Jeffrey Hoffstein

  Providence College

  71 shared

• Jill Pipher

  57 shared

• Mohamad Al‐Sheikhly

  University of Maryland, College Park

  42 shared

• Marc Hindry

  39 shared

• P. Neta

  Material Measurement Laboratory

  30 shared

• Shu Kawaguchi

  30 shared

• John Tate

  Fred Hutch Cancer Center

  27 shared

Labs

• Joseph Silverman Research LabPI

Education

• Ph.D., Number Theory

  Brown University

• M.S.

  Brown University

• B.A.

  Brown University

Similar researchers at Brown University

• Brendan Hassetth-34