Saturday, April 26, 2014

Stanford University Mathematics Department (Building 380)

Morning coffee/bagels in 2nd floor common room

Talks in room 380-C (in basement)

Henri Darmon, McGill University

Michael Larsen, Indiana University

Michael Magee, University of California, Santa Cruz

Alice Silverberg, University of California, Irvine

Ander Steele, University of Calgary

9:30-10:00 | Coffee/Bagels |

10:00-11:00 | Henri Darmon |

11:00-11:15 | Coffee Break |

11:15-12:15 |
Ander Steele |

12:15-1:45 |
Lunch |

1:45-2:45 | Alice Silverberg |

2:45-3:10 |
Coffee Break |

3:10-4:10 |
Michael Magee |

4:10-4:30 |
Break |

4:30-5:30 |
Michael Larsen |

6:00 |
Dinner, Three Seasons |

Let E be an elliptic curve over

The eigenspaces of the Laplacian on the two dimensional sphere consist of homogeneous polynomials and occur with increasing dimension as the eigenvalue grows. I'll explain how one can remove this high multiplicity by using arithmetic Hecke operators which arise from the Hamilton quaternions. The resulting Hecke eigenfunctions are subject to predictions arising from random function theory and quantum chaos, in particular concerning the topology of their zero sets. I'll discuss what is known in this area and how one can try to study these 'nodal lines'.

I will discuss a number of related conjectures concerning the rational points of varieties (especially curves and abelian varieties) over fields with finitely generated Galois group and present some evidence from algebraic number theory, Diophantine geometry, and additive combinatorics in support of these conjectures.

In joint work with Alexander Abatzoglou, Andrew Sutherland, and Angela Wong, we use elliptic curves with complex multiplication to obtain necessary and sufficient conditions for primality of integers in certain sequences. We give fast deterministic primality proving algorithms for such integers. We use these algorithms to efficiently search for very large primes, and prove the primality of several integers with more than 100,000 decimal digits, including some with over a million bits in their binary representations. We obtain the largest proven prime N for which no significant partial factorization of N-1 or N+1 is known. We also give a general framework, that builds on earlier work of Chudnovsky-Chudnovsky, Gross, and Denomme-Savin.

Let f be an eigenform on Γ

Parking is free and plentiful in the Oval and surrounding lots (on Roth Way and Lausen St) on weekends. Here is a campus map, with the math building (380) labelled "Math Corner."

There is no formal registration, but if you plan to attend, we would appreciate an email to sdasgup2 at ucsc dot edu to
help plan the event, especially if you plan to attend the dinner afterwards.

There will be a dinner following the conference at 6pm at Three Seasons in downtown Palo Alto. Please send an email to sdasgup2 at ucsc dot edu if you plan to attend.