Saturday, December 7, 2013

University of California, Santa Cruz

Room: McHenry Library, room 1240

Ashay Burungale, University of California, Los Angeles

Hilaf Hasson, Stanford University

Mark Kisin, Harvard University

Claus Sorensen, University of California, San Diego

John Voight, Dartmouth College/University of California, Berkeley

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

10:00-11:00 | Claus Sorensen |

11:00-11:15 | Coffee Break |

11:15-12:15 |
Mark Kisin |

12:15-1:45 |
Lunch |

1:45-2:45 | Hilaf Hasson |

2:45-3:10 |
Coffee Break |

3:10-4:10 |
Ashay Burungale |

4:10-4:30 |
Break |

4:30-5:30 |
John Voight |

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

All talks will be in the ground floor of McHenry Library at UCSC, room 1240. Refreshments (including the morning coffee)
will be in room 1257.

Let ℓ and p be distinct odd primes unramified in an imaginary quadratic extension K/Q. We outline the proof of the non-triviality of the p-adic formal group logarithm of Heegner points associated to the Rankin-Selberg convolution of an elliptic modular form and a theta series over the Z

By Riemann's Existence Theorem, every finite group G is realizable as the group of deck transformations of a generically etale cover of the projective line over Q. The question of which number fields a given cover descends to (together with the Galois action) has been an active area of research, and is closely related to the Inverse Galois Problem. In this talk, instead of starting with the cover over Q, and trying to find fields over which the group action is defined, I will tackle a question in the reverse direction. Namely, given a model of the cover as a map (i.e., the action may not be defined for this model) over a number field K, what are the minimal field extensions of K over which the action of this model becomes defined? The answer reveals a relationship between this question, the behavior of rational points on models over K, and the behavior of specializations of models over K where the action is defined.

The Grothendieck p-curvature conjecture says that an algebraic differential equation has a full set of solutions if it has a full set of solution modulo p for almost all primes p. I will explain the conjecture, and survey the methods which have been used to prove some cases of it.

We will take a global point of view, and motivate the Breuil-Schneider conjecture; an ersatz p-adic local Langlands correspondence for GL(n). We will sketch how to prove it in the Steinberg case, via automorphic forms on U(n). At the end, we hope to hint at local-global compatibility, and explain how and when the p-adic local Langlands correspondence for GL(2) occurs in the completed cohomology of U(2). (The latter is joint work with P. Chojecki.)

We give an explicit presentation for the ring of modular forms for a Fuchsian group with cofinite area, depending on the signature of the group. Our work can be seen as a generalization of the classical theorem of Petri: we give a presentation for the canonical ring of a stacky curve. This is joint work with David Zureick-Brown.

The closest parking is at the Hahn parking lot. Parking is free and no permit is required on Saturdays, as long as you park in a legal parking space and do not block emergency access, or park in spaces that are posted and reserved for special use. There is a foot bridge that connects the Hahn parking lot to McHenry Library. If you click on this map and zoom out one level, the bridge is indicated by a dotted line. Halfway through the bridge, there is a path that leads to the left, but you want to ignore this path and continue straight until the end of the bridge. After crossing the bridge, make a sharp left slightly downhill to enter the building at the first level. (The main entrance is actually on the second level, so if you enter at the main entrance you will have to take the elevator down one level.)

Here are printable maps: McHenry Library, and more specifically how to get to Hahn parking lot and walk to McHenry.

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 Ristorante Avanti. 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.