Saturday, February 21, 2015

Stanford University

Room:
Braun Auditorium, Mudd Building (Chemistry Department)

Mirela Ciperiani, University of Texas, Austin

Luis Garcia, Imperial College

Wei Ho, University of Michigan

Daniel Litt, Stanford University

Ken Ono, Emory University

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

10:00-11:00 | Ken Ono |

11:00-11:15 | Coffee Break |

11:15-12:15 |
Wei Ho |

12:15-1:45 |
Lunch |

1:45-2:45 | Luis Garcia |

2:45-3:10 |
Coffee Break |

3:10-4:10 |
Daniel Litt |

4:10-4:30 |
Break |

4:30-5:30 |
Mirela Ciperiani |

6:00 |
Dinner, Reposado Please RSVP to sdasgup2 (at) ucsc (dot) edu |

Work of Kobayashi and Iovita-Pollack describes how local points of supersingular elliptic curves on ramified Z

The Shimura varieties X attached to orthogonal and unitary groups come equipped with a large collection of so-called special cycles. Examples include Heegner divisors on modular curves and Hirzebruch-Zagier cycles on Hilbert modular surfaces. We will review work of Borcherds and Bruinier using regularised theta lifts for the pair (SL

In the last five years, there has been significant theoretical progress on understanding the average rank of all elliptic curves over Q, ordered by height, led by work of Bhargava-Shankar. We will survey these results and the ideas behind them, as well as discuss generalizations in many directions (e.g., to other families of elliptic curves, higher genus curves, and higher-dimensional varieties) and some corollaries of these types of theorems. We will also describe recently collected data on ranks and Selmer groups of elliptic curves (joint work with J. Balakrishnan, N. Kaplan, S. Spicer, W. Stein, and J. Weigandt).

Classical results of Lefschetz and Grothendieck compare the topology of a smooth projective variety X over the complex numbers to that of an ample divisor D on X. For example, if the dimension of X is at least 4, the canonical map from Pic(X) to Pic(D) is an isomorphism, and if the dimension of X is at least 3, the canonical map on etale π

In the early 1970s it was noticed that the prime divisors of the order of the Monster (which was not yet proven to exist), the largest sporadic finite simple group, are the levels appearing in Ogg's classification of hyperelliptic modular curves. Ogg offered a bottle of Jack Daniels for a good explanation of this strange coincidence. Ten years later McKay noticed that 196884=196883+1, where 196884 is the first nontrivial coefficient of the j-function, and 196883 and 1 are the dimensions of the two smallest irreducible representations of the Monster. McKay's observation and Ogg's problem are the first hints of the Conway-Norton Monstrous Moonshine Conjecture, which was proved by Borcherds. In 2010 three Japanese physicists observed that the coefficients of a certain specialization of the K3 elliptic genus could similarly be expressed in terms of the small dimensions of the irreducible representations of the Mathieu group M

Parking is free and plentiful on Roth Way and in the Oval on weekends. Click here for a campus parking map. The Mudd Building is at E7.

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 6:00pm, at Reposado (236 Hamilton Ave, Palo Alto). Please send an email to sdasgup2 at ucsc dot edu if you plan to attend. Graduate students will be partially subsidized at the dinner. We thank the UC Santa Cruz Mathematics Department, the Math Research Center at Stanford University, and the UC Berkeley Mathematics Department for partial financial support.