Past Seminars- Algebra

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  • Maurice Rojas
    Thu Apr 12, 2012
    3:00 pm
    We show how to efficiently count exactly the number of solutions of a system of n polynomials in n variables over certain local fields L, for a new class of polynomials systems. The fields we handle include the reals and the p-adic rationals. The polynomial systems amenable to our methods are made up of certain A-discriminant chambers, and our...
  • Vladimir Baranovsky
    Thu Dec 1, 2011
    1:00 pm
    A very useful technique in homological algebra, is the Basic Peturbation Lemma which tells how cohomology of a complex changes when a differential is perturbed. It has numerous applications in algebra, topology, and computational methods in algebra; some of which will be reviewed in the talk.
  • John Brevik
    Thu Nov 17, 2011
    2:00 pm
    The classical Noether-Lefschets Theorem states that for a sufficiently general surface S in P^3 the only algebraic curves lying on S are the complete intersections. In 2010 we proved an extension of this result to surfaces (and higher dimensional hypersurfaces in P^n) containing a fixed base locus. I will discuss this result and the describe how...
  • Michael Skirvin
    Thu Nov 10, 2011
    2:00 pm
    Springer theory is a branch of geometric representation theory revolving around objects such as the nilpotent cone, flag variety, and Weyl group, and which received significant study in the 70's and 80's. We will give a brief review of Springer theory, while emphasizing parallels between the adjoint quotient map of Lie theory and the Hitchin...
  • Melody Chan
    Thu Oct 27, 2011
    2:00 pm
    A tropical curve is a vertex-weighted metric graph. It is hyperelliptic if it admits an involution whose quotient is a tree. Assuming no prior knowledge of tropical geometry, I will develop the theory of tropical hyperelliptic curves and discuss the relationship with classical algebraic curves and their Berkovich skeletons.
  • Christopher Davis
    Thu Jun 2, 2011
    2:00 pm
    Finding a point on a variety amounts to finding a solution to a system of polynomials. Finding a "rational point" on a variety amounts to finding a solution with coordinates in a fixed base field. (Warning: our base field will not be the field of rational numbers Q.) We will present some theorems about when it is possible to find such a...
  • Grzegorz Banaszak
    Thu May 26, 2011
    2:00 pm