Spring 2005 Modular Forms RAP



Mondays, 3 pm, 443 Altgeld
Thursdays, 2 pm, 347 Altgeld



University of Illinois Urbana-Champaign

Description:

We will work through much of the new book A First Course in Modular Forms by Fred Diamond and Jerry Shurman. A first goal of reaching Chapter 6 has been set, with an eye toward understanding the relation between modular forms, modular curves, and their jacobians. Talks are intended to be informal, giving a relaxed atmosphere for asking questions.

Roadmap (tentative):

This book can be ordered from the publisher's website, or from Amazon.com, once they get their copies.

Schedule of Talks:

  • Thursday, February 17: Nadia Masri:
    Complex Tori and Elliptic Curves (Chapter 1, sections 3 and 4)

    Reference:
    [1] J. Silverman,
    The Arithmetic of Elliptic Curves,
    Springer, Graduate Texts in Mathematics, 106, (1986), Chapter VI.

  • Monday, February 21: Nadia Masri:
    Complex Tori and Elliptic Curves continued (Chapter 1, sections 3 and 4)

  • Thursday, February 24: Samuel Kadziela:
    Modular Curves and Moduli Spaces (Chapter 1, section 5)

  • Monday, February 28: Tim Kilbourn:
    Modular Curves as Riemann Surfaces, Part I (Chapter 2, sections 1-?)

    Reference:
    [1] G. Shimura,
    Introduction to the Arithmetic Theory of Automorphic Functions
    Princeton University Press, (1971), Chapter 1

  • Thursday, March 3: Tim Kilbourn:
    Modular Curves as Riemann Surfaces, Part II (Chapter 2)

  • Monday, March 7: Scott Ahlgren:
    The Genus of a Modular Curve (Chapter 3, section 1)

  • Thursday, March 10: Stephanie Treneer:
    Automorphic Forms (Chapter 3, section 2)

  • Monday, March 14: Samek Kadziela:
    Meromorphic Differentials (Chapter 3, section 3)

  • Thursday, March 17: NO MEETING

    After the break, we will continue with Chapter 5. When we need the material about divisors in Chapter 6, we will briefly revisit Chapter 3.4.

  • Monday, March 28: Nadia Masri:
    Double Coset Operators (Chapter 5, section 1)

  • Thursday, March 31: Tim Kilbourn:
    The <d> and Tp operators, Part I (Chapter 5, section 2)

  • Monday, April 4: Tim Kilbourn and Scott Ahlgren:
    The <d> and Tp operators, Part II (Chapter 5, section 2)
    The <n> and Tn operators (Chapter 5, section 3)

  • Thursday, April 7: Matt Boylan:
    The Petersson Inner Product (Chapter 5, section 4)

  • Monday, April 11: Matt Boylan and Stephanie Treneer:
    Adjoints of the Hecke Operators (Boylan) (Chapter 5, section 5)
    Oldforms and Newforms and The Main Lemma, Part I (Treneer) (Chapter 5, sections 6 and 7)

  • Thursday, April 14: Nadia Masri:
    The Main Lemma, Part II (Chapter 5, section 7)

  • Monday, April 18: Tim Kilbourn:
    The Main Lemma, Part III

  • Thursday, April 21: Tim Kilbourn:
    Eigenforms (Chapter 5, section 8)

  • Monday, April 25: Nadia Masri:
    L-Series and Functional Equations (Chapter 5, sections 9 and 10)

    We will not meet Thursday, April 28 or Monday, May 2. We will resume with Chapter 6 at some point early in the summer. Thank you for your participation!

    Last updated: April 22, 2005

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