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

• Fall 2012:Math 9: Calculus I
• Fall 2012:Math 17: Calculus II

Links to old course webpages

• Spring 2012:MA 42: Number Theory
• Spring 2012:MA 252: Algebra
• Spring 2012:MA 10: Calculus
• Fall 2011:MA 200: Intermediate Calculus (Physics/Engineering)
• Spring 2011:MA 1560: Number Theory
• Fall 2010:MA 1580: Cryptography
• Fall 2010:MA 0170: Advanced Placement Calculus
• Spring 2010: MA 20: Intermediate Calulus (Physics/Engineering)
• Fall 2009: MA 52: Linear Algebra
• Fall 2009: MA 10: Introductory Calculus II

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

• Abelian surfaces admitting an (l,l)-endomorphism (with K. Lauter, M. Streng)
• Evaluating Igusa functions (with K. Lauter)

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