Past Seminars- Algebra

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  • Ralph Greenberg
    Tue May 3, 2016
    2:00 pm
    There is a classical theorem of Iwasawa which concerns certain modules X for the formal power series ring Λ = Zp[[T]] in one variable.  Here p is a prime and Zp is the ring of p-adic integers.  Iwasawa's theorem asserts that X has no nonzero, finite Λ-submodules. We will begin by describing...
  • Kiran Kedlaya
    Tue Apr 12, 2016
    2:00 pm
  • Yuri G. Zarhin
    Tue May 5, 2015
    2:00 pm
    We study the monodromy of a certain class of semistable hyperelliptic curves over the rationals that was introduced by Shigefumi Mori forty years ago (before his Minimal Model Program). Using ideas of Chris Hall, we prove that the corresponding $\ell$-adic monodromy groups are (almost) ``as large as possible". We also discuss an explicit...
  • Herbert Lange
    Fri Feb 20, 2015
    3:30 pm
  • Jeremy Pecharich
    Tue Jun 3, 2014
    1:00 pm
    We will introduce the notion of an operad, which generalize the properties coming from associative algebras or Lie algebras. While the definition of an operad to somewhat complex everything will be done through example so we can get familiar with operads and their vast array of applications. If time permits we will give some applications to...
  • Jie Xia
    Tue May 13, 2014
    2:00 pm
    Shimura varieties are defined over complex numbers and generally have number fields as the field of definition. Motivated by an example constructed by Mumford, we find conditions which guarantee a curve in char. p lifts to a Shimura curve of Hodge type. The conditions are intrinsic in positive characteristics and thus...
  • Michael J. Larsen
    Tue Apr 29, 2014
    2:00 pm
    I will discuss a number of related conjectures concerning the rational points of varieties (especially curves and abelian varieties) over fields with finitely generated Galois group and present some evidence from algebraic numebr theory, Diophantine geometry, and additive combinatorics in support of these conjectures.