Number/Representation Theory Seminar

More information on these seminars can be found at the following link: http://www.math.toronto.edu/~smorra/

Details

Class invariants in genus 2

by Eyal Goren | McGill
Time: 14:10 — 15:00  (Wednesday, Mar. 17, 2010)
Location: BA6183, Bahen Center, 40 St George St
Abstract:
The main technique to construct class invariants, namely a set of distinguished elements in class fields of a given CM field, is by evaluating modular functions at CM points corresponding to that field. The case of quadratic imaginary fields is classical and well understood; it draws on the existence of modular units and good reduction for CM elliptic curves. The case of quartic fields is much less understood, but has recently seen some new results. Similar to the case of elliptic curves, the reduction of abelian surfaces with CM, and special divisors on the moduli space, play a key role. In this talk, I will report on recent work with Kristin Lauter that provides information about the prime factorization of certain class invariants (first studied by the speaker with DeShalit) and bounds the denominators of the so-called absolute Igusa invariants of genus 2 curves with CM. As will be explained, this last fact has applications to cryptography.

Dates in this series

· Friday, Jan. 15, 2010: SPECIAL COLLOQUIUM -- Modular representations of p-adic groups  (Florian Herzig )
· Wednesday, Jan. 20, 2010: On the Plancherel formula for spherical varieties over p-adic fields (Yiannis Sakellaridis)
· Wednesday, Jan. 27, 2010: Vanishing theorems for torsion automorphic sheaves (Kai-Wen Lan)
· Wednesday, Feb. 10, 2010: Local theory for special cycles on the Shimura variety of GU(1,2) (Ulrich Terstiege)
· Wednesday, Feb. 24, 2010: The Geometric Weil Representation (Shamgar Gurevich)
· Wednesday, Mar. 10, 2010: Brinkmanship in the Semi-Linear Sieve (John Friedlander)
· Wednesday, Mar. 17, 2010: Class invariants in genus 2 (Eyal Goren)
· Wednesday, Mar. 24, 2010: The number of points on curves over finite fields (Alina Bucur)
· Wednesday, Apr. 14, 2010: Gelfand pairs and identities for automorphic periods (Andre Reznikov)
· Wednesday, Sep. 22, 2010: On Eisenstein series and the cohomology of arithmetic groups (Joachim Schwermer)
· Wednesday, Sep. 22, 2010: Organizational Meeting ()
· Wednesday, Sep. 29, 2010: Quantum affine algebras, canonical bases and q-deformation of arithmetical functions (Henry Kim)
· Wednesday, Oct. 06, 2010: Arithmetic cycles on Picard modular varieties (Stephen Kudla)
· Wednesday, Oct. 20, 2010: Frobenius rigidity (Ying Zong)
· Wednesday, Oct. 27, 2010: An Erdos-Kac theorem for multiplicative order (Leo Goldmakher)
· Wednesday, Nov. 03, 2010: Ngo's proof of the fundamental Lemma (Joel Kamnitzer)
· Wednesday, Nov. 17, 2010: The Siegel-Weil formula for classical groups (Shunsuke Yamana)
· Wednesday, Nov. 24, 2010: The $L^2$ restriction of a $GL(3)$ Maass form to $GL(2)$ (Xiaoqing Li)
· Wednesday, Dec. 01, 2010: Pairs of polynomials over $\mathbb{Q}$ taking infinitely many common values (Ben Weiss)
· Wednesday, Dec. 08, 2010: The combinatorics of local models for Shimura varieties (Brian Smithling)
· Wednesday, Jan. 19, 2011: The Congruence Subgroup Kernel and the Fundamental Group of the Reductive Borel-Serre Compactification (John Scherk)
· Wednesday, Jan. 26, 2011: Nekovar duality over p-adic Lie extensions of global fields (Meng Fai Lim)
· Wednesday, Jan. 26, 2011: Organizational Meeting ()
· Wednesday, Feb. 02, 2011: Values of Green functions at CM points (Stephen Kudla)
· Wednesday, Feb. 09, 2011: Classification of Representations (James Arthur)
· Wednesday, Feb. 16, 2011: Monodromy Exercise (Ying Zong)
· Wednesday, Mar. 02, 2011: Post-critically finite polynomials (Patrick Ingram)
· Wednesday, Mar. 16, 2011: TBA (TBA)
· Wednesday, Mar. 23, 2011: Nilpotence join theorem for Lie algebras (Hamid Usefi)
· Wednesday, Mar. 30, 2011: Some results about Arthur's packets in the real case, and a topological application (Laurent Clozel)
· Wednesday, Apr. 06, 2011: A geometric variant of Titchmarsh divisor problem (Amir Akbary)
· Wednesday, Apr. 06, 2011: Zeros of a Family of Approximations of the Riemann Zeta-Function (Steve Gonek)
· Thursday, Aug. 04, 2011: On the dual BGG resolution (Gerald Gotsbacher)
· Wednesday, Sep. 14, 2011: Lower bounds on odd order character sums (Leo Goldmakher)
· Wednesday, Sep. 21, 2011: Galois representations associated to cusp forms over CM fields (Chung Pang Mok)
· Wednesday, Sep. 28, 2011: A going-up lemma (Ying Zong)
· Wednesday, Oct. 05, 2011: Growth of logarithmic derivatives of Dirichlet L-functions (Mariam Mourtada)
· Wednesday, Oct. 12, 2011: The distribution of CM points attached to ideal classes of fixed order in the class group (Bob Hough)
· Wednesday, Oct. 19, 2011: Admissible embedding of L-groups and essentially tame local Langlands correspondence (Geo Kamfai Tam)
· Wednesday, Oct. 26, 2011: Simple zeros of Maass L-functions (Peter Jaehyun Cho)
· Wednesday, Nov. 02, 2011: Construction of relatively supercuspidal representations (Fiona Murnaghan)
· Wednesday, Nov. 09, 2011: A new proof of a theorem of Nishioka (Michael Coons)
· Wednesday, Nov. 16, 2011: Some Rapoport-Zink spaces for unitary groups (Stephen Kudla)
· Wednesday, Nov. 23, 2011: Weights in a generalisation of Serre's conjecture for U(3) (Florian Herzig)
· Wednesday, Nov. 30, 2011: Geometric structure in the representation theory of reductive p-adic groups (Paul Baum)
· Wednesday, Jan. 18, 2012: Weyl sums for quadratic roots (John Friedlander)
· Wednesday, Jan. 25, 2012: Automorphic Representations of Orthogonal and Symplectic Groups (James Arthur)
· Wednesday, Feb. 01, 2012: Local rigidity of biextensions (Ying Zong)
· Wednesday, Feb. 08, 2012: PhD thesis presentation: L-functions and Number Theory (Peter Jaehyun Cho)
· Wednesday, Feb. 15, 2012: Special cycles on Shimura curves and the Shimura lift (Siddarth Sankaran)
· Wednesday, Feb. 29, 2012: Lower bounds for Galois orbits and the Andre-Oort Conjecture (Jacob Tsimerman)
· Wednesday, Mar. 07, 2012: The local Langlands correspondence: from real to p-adic groups (Moshe Adrian)
· Wednesday, Mar. 21, 2012: Bounds for the least quadratic non-residue, values of $L$-functions at $s=1$ and related problems (Youness Lamzouri)
· Wednesday, Mar. 28, 2012: p-adic periods and motivic cohomology (Wieslawa Niziol)
· Wednesday, Apr. 04, 2012: Independence of p-adic Galois representations over finitely generated fields (Gebhard Boeckle)
· Wednesday, Sep. 19, 2012: Cohomology of p-adic analytic groups and generalized multiplicity theorems for the p-modular Local Langlands program (Stefano Morra)
· Wednesday, Sep. 26, 2012: Endoscopic classification for quasi-split unitary groups (Chung Pang Mok)
· Wednesday, Oct. 03, 2012: Splitting of abelian varieties, elliptic Dynkin pairs (Ying Zong)
· Wednesday, Oct. 10, 2012: Waring's problem, translation-invariant systems, and rational curves on hypersurfaces (Trevor Wooley)
· Wednesday, Oct. 24, 2012: Variations on a theorem of Tate  (Stefan Patrikis)
· Wednesday, Oct. 31, 2012: On the variation of the p-rank of the Selmer group of an abelian variety in an infinite p-Hilbert class field tower (Meng Fai Lim)
· Wednesday, Nov. 07, 2012: Automorphic Correction of Kac-Moody algebras  (Henry Kim)
· Wednesday, Nov. 14, 2012: No session (due to internal departmental council) (--)
· Wednesday, Nov. 21, 2012: Endoscopic lift to the Siegel paramodular threefold related to Klein cubic threefold (Takuya Yamauchi)
· Wednesday, Nov. 28, 2012: The Weil Representation, the Theta Correspondence and Periods of Automorphic Forms (Patrick Walls)
· Wednesday, Jan. 09, 2013: Ramanujan and Prime Numbers (Kumar Murty)
· Wednesday, Jan. 16, 2013: The Spin of Prime Ideals (John Friedlander)
· Wednesday, Jan. 23, 2013: CM Periods and L-functions (Kumar Murty)
· Wednesday, Jan. 30, 2013: An alternative description of Drinfeld space and applications (Stephen Kudla)
· Wednesday, Feb. 06, 2013: Igusa integrals and volume asymptotics in analytic and adelic geometry (joint work with A. Chambert-Loir) (Yuri Tschinkel)
· Wednesday, Feb. 13, 2013: Standard and nonstandard comparisons of relative trace formulas (Yiannis Sakellaridis)