UCLA Mathnet Login

Number Theory

The UCLA Number Theory group researches topics in the arithmetic theory of modular forms, automorphic forms,  their associated L-functions, both classical and p-adic. The group has 4 permanent faculty: Don Blasius, William Duke, Haruzo Hida, and Chandrashekhar Khare. Each has worked broadly in number theory and settled key conjectures as well as introducing new topics of study. As a case in point, Hida's theory of (ordinary) p-adic families, and the theories to which it gave rise (due to Mazur and Coleman) are now both an independent area of research  of mathematicians worldwide, and a powerful tool for applications, e.g. to  Galois representations and p-adic L-functions. Likewise, Khare, with Wintenberger, proved Serre's Conjecture on modular forms. Since that proof, the extension of the conjecture to automorphic forms has taken hold and stimulated a great deal of research. Duke is a leading analytic number theorist, known for many basic contributions, including the settling, using modular forms, of a well-known equidistribution problem dating back to Gauss. Blasius has made basic contributions to the special values of L-functions, and pioneered, with J. Rogawski, the use of endoscopy in the study of Galois representations.

At any given time, the Number Theory Group has two or more post-docs, and up to 10 graduate students. There is a weekly number theory seminar, and always several ongoing instructional seminars devoted to the study of current research papers or topics, and the presentation of research of group members at all levels. Also, in recent years, a number of students from the group have chosen to complete their degrees in cryptography, under the supervision of affiliated group members Rafail Ostrovsky (joint Computer Science/Mathematics) or Amit Sahai (Computer Science).

Leading UCLA PhD's in number theory include Robert Guralnick and Ken Ono; Chandrasekhar Khare was a student of Hida but received his PhD from Caltech. The majority of PhD's obtain good academic placements and most eventually get tenure at a university.

Faculty Visiting Faculty Graduate Students

Don Blasius

Bill Duke

Haruzo Hida

Chandrashekhar Khare

Romyar Sharifi

Nickolas Andersen

Jukka Keranen

Preston Wake

Casey Fu

Geunho Gim

Joseph Hughes

Sudesh Kalyanswamy

Joshua Lampkins

Jaehoon Lee

Mohammed Zuhair Mullath Mohammed

John Yu

 

 

 

 For more information about the Number Theory group, please consult their website.