Graduate Student Seminar
Professors: Chantal David and Henri Darmon
Time: Wednesday 3:00-4:00.
Room: Concordia 5th floor.
Syllabus: The graduate student seminar is an
informal seminar which will meet
once a week.
Everyone is welcome to attend,
but the number theory graduate students
and those who are attending the graduate
course 189-726A on algebraic
are strongly encouraged to do so! It is expected
that they will give most of the lectures.
Topics that we can expect to touch upon may include:
- Elliptic curves, L-functions, and the Birch Swinnerton-Dyer
- Modular forms.
- Arithmetic of modular curves.
- Shimura curves and the theory of Cerednik-Drinfeld.
- Iwasawa theory and p-adic L-functions.
- Galois representations attached to modular forms and Fermat's Last Theorem.
Grading Scheme: There will be no assignments. The grade will be
based on in-class participations, and on the lectures given
by the students. It is expected that every student who is registered
in Math 189-726A
will give at least one, and hopefully two, lectures.
To give you an idea of the kind of topics we might cover, here is
Last year's schedule of talks:
- Sept 16: Ignazio Longhi, Introduction to p-adic numbers.
- Sept 23: Ignazio Longhi, Introduction to p-adic numbers, cont'd.
- Sept 30: Malcolm Harper, The Euclidean algorithm in number rings.
- Oct 7: Jack Fearnley , Introduction to elliptic curves.
- Oct 21: Nicolas Arsenault, Class groups of GL(2,p)-extensions.
- Oct 28: Lassina Dembele, The Hasse-Minkowski theorem.
- Nov. 4: Jessica Bridson, Units in real quadratic fields.
- Nov. 11: Yu-Ru Liu, Cubic reciprocity.
- Nov. 18: Francesco Sica, Riemann's Memoir.
- Nov. 25: Wei-Dong Tian, The Kronecker-Weber theorem
- Dec. 2: Dominic Lemelin, The proof of Fermat's Last Theorem (Overview)
- Dec. 9: Dominic Lemelin,
The proof of Fermat's Last Theorem (Cont'd)
- Jan. 22: Jack Fearnley, Curves of genus 1 and Weierstrass
- Jan. 29: Dominic Lemelin, Elliptic curves over C
- Feb. 5: Ignazio Longhi, Tate curves
- Feb. 12: Steve Thiboutot, Galois representations attached to
elliptic curves: an introduction.
- Feb. 19: Nicolas Arsenault, The Weil Pairing.
- Feb. 26: WEEK OFF
- March 5: Odette Barutciski,
Rational torsion points on elliptic curves.
- March 12: Francesco Sica,
- March 19: Lassina Dembele,
Local-global principles for curves of genus one.
- March 26: Dominic Lemelin,
Elliptic curves with complex multiplication.
- April 2: Ignazio Longhi,
Class field theory for function fields of curves over finite fields
- April 9: Nicolas Arsenault,
The Chebotarev density theorem.
- April 16: TBA, TBA
- April 23: TBA, TBA
- April 30: Yu-Ru Liu, The Hasse principle for certain
non-homogenous ternary equations.
- Coming attraction: Steve Thiboutot,
Elliptic curves, Galois representations and the