Bay Area Algebraic Number Theory and Arithmetic Geometry Day 6

Saturday, April 6, 2013
University of California, Berkeley
Location: Evans Hall. Morning coffee/bagels: room 732, Talks: room 740, Coffee Breaks: room 1015.
Conference Poster


Speakers:

Bryden Cais, University of Arizona
Mahesh Kakde, King's College, London
Akshay Venkatesh, Stanford University
Kevin Ventullo, University of California, Los Angeles
Hwajong Yoo, University of California, Berkeley


Schedule:

9:30-10:00 Coffee/Bagels
10:00-11:00 Mahesh Kakde
11:00-11:30 Coffee Break
11:30-12:30
Akshay Venkatesh
12:30-2:00
Lunch
2:00-3:00 Kevin Ventullo
3:00-3:30
Coffee Break
3:30-4:30
Hwajong Yoo
4:30-5:00
Break
5:00-6:00
Bryden Cais
6:45
Dinner at RBK
Please RSVP to sdasgup2 (at) ucsc (dot) edu





Titles and Abstracts:

Bryden Cais, "Iwasawa theory of the Igusa tower"
We briefly review Iwasawa's theorems on the growth of the p-part of class groups in the p-cyclotomic extension of Q. We then introduce a function field analogue originally studied by Mazur and Wiles, and raise (and partially answer) a new and interesting question in this setting that has no analogue in the classical situation.

Mahesh Kakde, "Congruences in non-commutative Iwasawa theory"
I will describe a formulation of main conjecture in (non-commutative) Iwasawa theory. This formulation uses K1 of Iwasawa algebras and certain related rings. I will explicitly describe these K1 groups.

Akshay Venkatesh, "Functoriality and the Brauer homomorphism"
Let G be a semisimple group over a number field, and let H=fix(f) be the fixed group for an automorphism f of G that has prime order p. I'll discuss the relationship between mod p automorphic forms on H and on G. Joint work with David Treumann.

Kevin Ventullo, "The rank one abelian Gross-Stark conjecture"
Let F be a number field and chi a character of F. Stark's conjecture predicts a relationship between the leading term of the archimedean L-function of chi at s=0 and the determinant of a regulator map defined on the units of F tensored with C. When F is totally real and chi is totally odd, Gross formulated a p-adic analogue of this conjecture. In this talk, I will explain both of these conjectures, and some recent work which unconditionally proves Gross' conjecture in the rank one case. If there is time, I will explain some applications of the techniques used to the Iwasawa Main Conjecture, and possibly make some remarks on the higher rank case.

Hwajong Yoo, "Modularity of reducible mod ℓ representations and congruence subgroup property"
This lecture concerns reducible two-dimensional mod ℓ representations that arise from newforms. If a newform of weight 2, trivial character and square-free level N yields a reducible mod ℓ representation, the semisimplification of this representation will be 1⊕χ where χ is the mod ℓ cyclotomic character. The natural question is to describe the set of square free levels N for which there exist a newform of weight two for Γ0(N) that gives rise to 1⊕χ. After providing some background, I will explain how the well known conjecture about the congruence subgroup property of S-arithmetic groups sheds light on the question.


Parking:

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.

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.


Registration:

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. Note that an RSVP to this email address is required if you plan to attend the dinner afterwards (see below).


Dinner:

There will be a dinner following the conference at 6:45pm at Revival Bar and Kitchen in downtown Berkeley. Please RSVP to sdasgup2 (at) ucsc (dot) edu. There is a limit of 20 people for the dinner, and slots will be reserved in the order that RSVPs are received.