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Southern California Number Theory Day 2010

Saturday, May 15, 2010 on the Caltech Campus

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Speakers     Location     Schedule      Abstracts   

Parking     Directions to Caltech
   Dinner    Contact

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Invited Speakers: Ken Ribet (University of California, Berkeley), Mirela Ciperiani (University of Texas, Austin), Cristian Popescu (University of California, San Diego), Matthew Emerton (Northwestern University)

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Location: All talks will be held in the Sloan Building (Department of Math) room 151 on the Caltech campus. Click on campus map to locate Sloan building (we are building number 37).

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There are no fees for the conference (except for dinner),
but in order to plan for refreshments we need to know who is coming. 
Please click here to register

List of registered participants


9:30 - 10:00 - Refreshments

10:00 - 11:00 - Ken Ribet (University of California, Berkeley),
"Modular degrees and congruence numbers for modular abelian varieties over Q"

11:00 - 11:30 - Break

11:30 - 12:30 - Mirela Ciperiani (University of Texas, Austin),
"Tate-Shafarevich groups over Z_p-extensions"

12:30 - 2:30 - Lunch Break

2:30 - 3:30 - Cristian Popescu (University of California, San Diego),
"The arithmetic of Picard 1-motives"

3:30 - 4:00 - Break

4:00 - 5:00 - Matthew Emerton (Northwestern University),
"On the Iwasawa theory of modular forms"

5:30 - Dinner - see below


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Ken Ribet
(University of California, Berkeley)

Modular degrees and congruence numbers for modular abelian varieties over Q

I will discuss joint work with Agashe, Stein and others concerning congruences among modular forms and the geometry of Jacobians of modular curves. One recent elementary, but striking, observation is that modular degrees and congruence numbers must coincide (locally at the relevant primes) whenever "multiplicity one'' theorems hold for the ambient Jacobian variety. Because one has tabulated numerous examples where congruence numbers are larger than modular degrees, we get a host of new instances where multiplicity one fails.




Mirela Ciperiani (University of Texas, Austin)

Tate-Shafarevich groups over Z_p-extensions

Cristian Popescu (University of California, San Diego)

The arithmetic of Picard 1-motives

I will report on my recent joint work with Greither on the Galois module structure of l-adic realizations of Picard 1-motives in positive characteristic and their Iwasawa theoretic analogues in characteristic 0. In the process, I will state and sketch the proof of an equivariant Main Conjecture in Iwasawa theory.

Finally, I will discuss applications of the equivariant Main Conjecture ranging from proofs of refinements of the Brumer-Stark and Coates-Sinnott Conjectures to proofs of particular cases of the Equivariant Tamagawa Number Conjecture of Bloch-Kato and the non-abelian Main Conjecture of Coates-Fukaya-Kato-Sujatha-Venjakob.



Matthew Emerton (Northwestern University)

On the Iwasawa theory of modular forms

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Parking: Parking at Caltech is free on the weekends. Please park in the lot located on California Blvd which can be located on this map.

Directions: Directions to Caltech can be found by following this link. A map of the Pasadena area can be found here.

Dinner: Dinner will be at Saladang Song, a Thai restaurant located at 363 S Fair Oaks Avenue, Pasadena. The restaurant is within walking distance or a short drive from Caltech campus. Cost will be $25 per person ($20 for students), including tax and tip, drinks are extra. Pay at the restaurant. Please click here to register

Contact Organizers: Dinakar Ramakrishnan, Elena Mantovan



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