Teaching

Office hours : Monday 1-2pm and Thursday 1-3pm

see Blackboard on BU Learn.

CMI-HIMR summer school in computational number theory:

Lecture notes (including exercises) are below.

Plan:

1. The Birch and Swinnerton-Dyer conjecture : heuristic, statements and the parity conjecture.

2. Shafarevich-Tate groups : Definition using Principal Homogeneous spaces, Cassels-Tate pairing, order modulo square for Jacobian of curves.

3. Tamagawa numbers of elliptic curves and semistable Jacobians of curves over number fields.

4. Explicit computation of the parity of the rank of (some) semistable Jacobians of genus 2 curves admitting a Richelot isogeny.

For more on the status of the BSD conjecture and numerical evidence, see John Cremona's slides here.

Office hours : by appointment

-New classroom : SCI 115

-There will be no lecture on Tuesday the 5th of March and Tuesday the 7th of March

Office hours : Monday 11-12pm and Wednesday 11-12pm and 3-4pm

1st Midterm : in class on the 27th of September, 20%

2nd Midterm : in class on the 6th of November, 25%

Final exam : 2hours, 18th December, 35%

Weekly quiz : 10%

Weekly homework : 10%

see Blackboard on BU Learn.