Waldspurger

Study group on Waldspurger and theta correspondence, II.

Spring, 2011.

Wednesdays, 15:15 -- 17:15 (or later) in AAC06, unless noted otherwise.

Organization/contact: Jeanine Van Order: jeanine.vanorder@epfl.ch.

Aim: The study group is a continuation of the one that started last term (Waldspurger, Fall 2010). The main aim for now is to review background from the theta correspondence to the end of understanding the calculations in Waldspurger, Sur les valeurs de certaines fontions L automorphes en leur centre de symétrie, Compositio 54 (1985) 2, 173 - 242.

some references

LIST OF TALKS:

(1) Philippe MICHEL, 23/03/2011: Overview of theta correspondence.

(2) Philippe MICHEL, 30/03/2011: Overview of theta correspondence, II.

(3) Philippe MICHEL, 06/04/2011: Overview of theta correspondence, III.

(4) Rodolphe RICHARD, 07/04/2011 (14:15, in CM113): Howe duality.

(5) Rodolphe RICHARD, 20/04/2011: Howe duality, II.

(6) Rodolphe RICHARD, 04/05/2011: Howe duality, III.

(7) Jeanine VAN ORDER 11/05/2011: Siegel-Weil formula.

(8) Shanwen WANG, 18/05/2011: Siegel-Weil formula, II.

(9) Jeanine VAN ORDER, 25/05/2011: Extension to similitudes, I.

(10) Dimitar JETCHEV, 01/06/2011: Extension to similitudes, II.

(11) Dimitar JETCHEV, 15/06/2011: Extension to similitudes, III.

(12) Farrell BRUMLEY, 22/06/2011: TBA. 

(13) Farrell BRUMLEY, 06/07/2011: TBA, II.

 

Informal study group on Yuan-Zhang-Zhang.

Summer, 2011.

Wednesdays, 11:00 in MAC3605, unless noted otherwise.

Organization/contact: same as above.

Aim: We seek to understand various topics related to the construction of the so-called geometric kernel function in the recent paper of Yuan-Zhang-Zhang, "Heights of CM points I: Gross-Zagier formula". 

Some references:

[Ca] H. Carayol, Sur la mauvaise réduction des courbes de Shimura, Compositio 59 no. 2 (1986), 151 - 230.  

[Ed] B. Edixhoven, Short introduction to heights and Arakelov theory, in Computational aspects of modular forms and Galois representations, Ed. J.-M. Corveignes and B. Edixhoven, Princeton University Press (2011), 79 - 94.

[Fa] G. Faltings, Calculus on arithmetic surfaces, Annals (2) 119 (1984), 387 - 424.

[GZ] B. Gross and D. Zagier, Heegner points and derivatives of L-series, Inventiones 84 no. 2 (1986), 353 - 378. 

[Ha] R. Hartshorne, Algebraic Geometry, Springer GTM. 

[dJ] R. de Jong, Explicit Arakelov Geometry, PhD thesis, Amsterdam (2004).

[YZ^2] X. Yuan, S.-W. Zhang, and W. Zhang, Heights of CM points I: Gross-Zagier formula (preprint).

[Z] S.-W. Zhang, Heights of CM points I: Gross-Zagier formula for GL_2, Asian J. Math 5 (2005) no. 2, 183 - 190, available at http://www.math.columbia.edu/~szhang/papers/5203.ps

Schedule: 

(1) 10/08/2011: discussion of [Fa]. 

(1) 31/08/2011: background following [Fa] §2,3; Hodge index theorem.