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Southern California Number Theory Day 2011

Saturday, May 21, 2011 on the Caltech Campus

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Speakers     Location     Schedule      Abstracts     Parking     Directions to Caltech    Dinner    Contact

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Invited Speakers: Thomas Haines (University of Maryland), Niranjan Ramachandran (University of Maryland), Alice Silverberg (UC Irvine), Chandrashekhar Khare (UCLA)

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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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Register for conference


9:30 - 10:00 - Refreshments

10:00 - 11:00 - Thomas Haines (University Of Maryland),
"Endoscopic transfer of the Bernstein center"

11:00 - 11:30 - Break

11:30 - 12:30 - Niranjan Ramachandran(University of Maryland),
"Integral motives and zeta functions"

12:30 - 2:30 - Lunch Break

2:30 - 3:30 - Alice Silverberg (UC Irvine),
"On elliptic curves with an isogeny of degree 7, and related questions"

3:30 - 4:00 - Break

4:00 - 5:00 - Chandrashekhar Khare (UCLA),
"Automorphic forms and Iwasawa theory"

5:30 - Dinner - see below

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Thomas Haines

Thomas Haines (University of Maryland)
Endoscopic transfer of the Bernstein center

The Langlands-Shelstad theory of endoscopy plays a central role in the study of Shimura varieties and the Arthur-Selberg trace formula. The fundamental lemma and a deep consequence, endoscopic transfer, have now been established in works of Ngo, Waldspurger, and Hales. Both of these statements are identities involving orbital integrals of a function f on a p-adic group G and those of certain transfer" functions f^H on related groups H, called endoscopic. This talk will give background on the fundamental lemma, some of its variants, and the roles they played. Then I will describe a conjectural construction of a large class of matching functions in the Bernstein centers of G and H. This conjecture has been verified in some encouraging cases. The functions being transferred arise in connection with Shimura varieties with bad reduction, and some applications to that subject will also be briefly discussed.


Niranjan Ramachandran

Niranjan Ramachandran (University of Maryland)

Integral motives and zeta functions

The talk will be a survey of the joint work with Milne. The existing constructions of motives do not provide an integral category of mixed motives over a finite field. As a result, these constructions do not provide a motivic interpretation of the $p$-part of special values of zeta functions where $p$ is the characteristic. The talk will outline an approach to integral motives via the theory of the de Rham Witt complex.



Alice Silverberg


Alice Silverberg (UC Irvine)
On elliptic curves with an isogeny of degree 7, and related questions

In joint work with Ralph Greenberg and Karl Rubin, we ask when the images of 7-adic representations of elliptic curves over Q with a rational subgroup of order 7 are as large as they can be. This leads to a construction of the family of all elliptic curves with a rational subgroup Galois-isomorphic to a given group of order 7, and also leads to a question about the rational points on a recalcitrant genus 12 curve.



Chandrashekhar Khare


Chandrashekhar Khare (UCLA)
Automorphic forms and Iwasawa theory

The method of Ribet and Wiles constructs unramified extensions of cylotomic extensions of totally real fields using automorphic forms. We will discuss how one one can construct ramified extensions, and the role these extensions play in questions about non-vanishing of p-adic regulators.

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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. Please pay at the restaurant. Register for conference and dinner.

Contact Organizers: Dinakar Ramakrishnan, Matthias Flach, Elena Mantovan



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