Reinier Bröker
Brown University
Box 1917
151 Thayer Street
Providence, RI 02912
USA
Info and CV
Office: 111
Tel: +1 401-863-5025
E-mail: reinier at math dot brown dot edu
Curriculum Vitae
Teaching
Links to old course webpages
Publications
Explicit CM-theory for level 2-structures on abelian surfaces (with D. Gruenewald, K. Lauter), to appear in Algebra and Number Theory (2011)
Modular polynomials via isogeny volcanoes , to appear in Mathematics of Computation (2011) (with K. Lauter, A. V. Sutherland)
p-adic class invariants , LMS Journal of Computation and Mathematics 14, pp. 108--126 (2011)
An explicit height bound for the classical modular polynomial , Ramanujan Journal of Mathematics 22, pp. 293-313 (2010) (with A. V. Sutherland)
Modular polynomials for genus 2 , LMS Journal of Computation and Mathematics 12, pp. 326-339 (2009) (with K. Lauter)
Constructing supersingular elliptic curves , Journal of Combinatorics and Number Theory 1, Volume 1, Issue 3, pp. 269-273 (2009)
Evaluating large degree isogenies and applications to pairing based cryptography , Pairing 2008, published by Springer-Verlag in Lecture Notes in Computer Science 5209, pp. 100-112 (with D. Charles, K. Lauter)
Computing Hilbert Class Polynomials , Algorithmic Number Theory Symposium VIII, published by Springer-Verlag in Lecture Notes in Computer Science 5011, pp. 282-295 (2008) (with J. Belding, A. Enge, K. Lauter)
Constructing elliptic curves of prime order , Contemporary Mathematics 463, pp. 17-28 (2008) (with P. Stevenhagen)
A p-adic algorithm to compute the Hilbert class polynomial , Mathematics of Computation 77 (2008), pp. 2417-2435
Efficient CM-constructions of elliptic curves over finite fields , Mathematics of Computation 76 (2007), pp. 2161-2179 (with P. Stevenhagen)
Elliptic curves with a given number of points , Algorithmic Number Theory Symposium VI, published by Springer-Verlag in Lecture Notes in Computer Science 3076, pp. 117-131 (2004) (with P. Stevenhagen)
PhD-thesis : Constructing elliptic curves of prescribed order, Universiteit Leiden, 2006
Preprints
Talk notes, selection
Fourier coefficients of Siegel modular forms , talk given at the Algebra Seminar at Brown University, October 2010
Abelian surfaces with extra endomorphisms , talk given at the Five College Number Theory Seminar, December 2009
Computing modular polynomials , talk given at the Maine/Quebec Number Theorey Conference, October 2009
Explicit CM-computations in dimension 2 , talk given at the Algebra Seminar of Boston University, October 2008
Computing Hilbert class polynomials , talk given at ANTS VIII, Banff, May 2008
Modular polynomials for genus 2 , talk given at Number Theory Seminar of the University of Washington, April 2008
p-adic class invariants , talk given at the Quebec-Vermont Number Theory Seminar, February 2007
Constructing elliptic curves for cryptogaphy , talk given at ECC in Toronto, September 2006
Constructing elliptic curves with a given number of points , talk given at the DIAMANT/Eidma symposium, November 2005