Past Seminars- Conference

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  • Chandrashekhar Khare
    Sat Oct 27, 2007
    2:30 pm
    I will spend most of the time formulating Serre's conjecture and explaining some of its applications: for instance, it implies Artin's conjecture for 2-dimensional odd complex representations of the absolute Galois group of Q. I will sketch some of the main ideas in the recent proof of the conjecture in joint work with Wintenberger, as completed...
  • Elena Mantovan
    Sat Oct 27, 2007
    11:30 am
    In the case of good reduction, smooth integral models for Shimura varieties of PEL type have been constructed by Faltings and Chai. In my talk I'll describe how their construction can be extended to the cases of bad reduction at unramified primes, and discuss the geometry of the resulting spaces. A useful tool in this context is provided by the...
  • Vinayak Vatsal
    Sat Oct 27, 2007
    10:00 am
    It has been known since Euler that the values of the Riemann zeta function at negative integers are certain rational numbers, namely the Bernoulli numbers Bk. Similarly, the values of Dirichlet L-functions at s=0 are related to class numbers of certain number fields. These are simple instances of a common phenomenon, namely that the values of L-...
  • Sat Oct 27, 2007
    9:30 am
    Southern California Number Theory Day, 10:00-5:00
  • Kirsten Eisenträger
    Sat Oct 14, 2006
    4:00 pm
  • David Solomon
    Sat Oct 14, 2006
    2:30 pm
    Let k be a totally real number field of degree r, S an appropriate finite set of places and L a finite abelian extension of k with group G. If L is also totally real, then, roughly speaking, Stark's conjecture predicts that the r-th derivatives of the L-functions LS(s,\chi) at s = 0 for all characters \chi of G are determined by an equivariant r x...
  • Kannan Soundararajan
    Sat Oct 14, 2006
    11:30 am
    I will discuss solutions to a+b = c where a, b, c are composed entirely of primes from a given finite set S. In joint work with Konyagin, we show the existence of special sets S for which this equation has many solutions. Moreover we show that the equation a+1=c also has many solutions for some sets S. I will also discuss joint work with...