Bay Area Algebraic Number Theory and Arithmetic Geometry Day 12

Saturday, April 9, 2016
University of California, Berkeley
Location: Evans Hall. Morning coffee in 732, Lectures in 740, breaks in 1015.


Frank Calegari, University of Chicago
Kestutis Cesnavicius, UC Berkeley
Jaclyn Lang, UCLA
Romyar Sharifi, University of Arizona
Daqing Wan, UC Irvine


9:30-10:00 Coffee/Bagels, Evans 732
10:00-11:00 Romyar Sharifi
11:00-11:15 Coffee Break
Jaclyn Lang
1:45-2:45 Frank Calegari
Coffee Break
Kestutis Cesnavicius
Daqing Wan
Dinner, TBA
Please RSVP to sdasgup2 (at) ucsc (dot) edu

Titles and Abstracts:

Frank Calegari, "Fun with compatible systems"
Given a compatible system of p-adic Galois representations of the Galois group of a number field F for all primes p, information about the Galois representation at one prime should (conjecturally) tell you a lot about the Galois representations at other primes. In practice, this is often quite tricky, even if one knows the Galois representation is of geometric or automorphic origin. We discuss known techniques for passing information between primes (due to Serre and Larsen-Pink), and describe how one can combine these tools with automorphic methods to give new applications, both to automorphy lifting theorems and to the construction of interesting families of Galois representations.

Kestutis Cesnavicius, "The Manin--Stevens constant in the semistable case"
Stevens has conjectured that for every optimal parametrization phi: X_1(n) ---> E of an elliptic curve E over Q of conductor n, the pullback of some Neron differential on E is the differential associated to the normalized new eigenform that corresponds to the isogeny class of E. We address this conjecture under the assumption that E is semistable, the key novelty lying in the 2-primary analysis when n is even.

Jaclyn Lang, "Images of Galois representations associated to Hida families"
We explain a sense in which Galois representations associated to non-CM Hida families have large images. This is analogous to results of Ribet and Momose for Galois representations associated to classical modular forms. In particular, we show how extra twists of the Hida family decrease the size of the image.

Romyar Sharifi, "Modular symbols and the arithmetic of cyclotomic fields"
I will explain how certain aspects of the arithmetic of cyclotomic fields can be seen through the lens of the geometry of modular curves. Roughly speaking, a construction of mine allows one to attach ideal classes in cyclotomic integer rings to geodesics in the complex upper half-plane. Conjecturally, this construction is inverse to another arising from the Galois action on cohomology of modular curves modulo an Eisenstein ideal. I will state what is known and expected in this regard, along with related intriguing constructions.

Daqing Wan, "L-functions for p-adic Representations of Function Fields"
We explore the analytic properties of the L-function attached to a continuous p-adic Galois representation of a global function field of positive characteristic p, especially for those representations coming from algebraic geometry. This includes the possible rationality, p-adic meromorphic continuation and p-adic entireness property for such L-functions (Artin's conjecture), based on recent joint work with Ruochuan Liu.


To park in a campus parking lot, you can purchase a permit from a ticket dispenser located in the lot. Permits should be placed on your dashboard. It costs $12 to park all day, and the dispensers take credit cards. If you have a parking permit of the correct "strength" from another UC campus, you can park for free by displaying your UC permit.

The Berkeley campus has a method to pay for campus parking via mobile phones. To use this service, you can set up an account ahead of time as described on the web page and download the iPhone or Android app ahead of time as well.

A list of parking lots is available here; clicking on the second link "Campus Parking Lots" sends you to a Google map displaying the lots. Scroll down on the left panel until you see the name of the desired parking lot; click on the name and you get a description of the lot and its capacities.

Two recommended parking locations are the Upper Hearst Parking Structure and the Lower Hearst Parking Structure. The easiest solution is to park on level 1 of the Lower Hearst Structure. This structure is on the north side of Hearst Avenue, just south of Euclid. Because Hearst is a divided road, you need to be heading west on Hearst in order to turn into the lot. Walking to Evans Hall from either structure takes less than 5 minutes.


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 China Village Restaurant in Albany. 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.