**The Kolchin Seminar in Differential
Algebra **

**Saturday April 16 ^{th}
2005**

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**Kurusch Ebrahimi-Fard**

Physikalisches Institut
der Universitaet Bonn**Algebraic Birkhoff decomposition in pQFT, and the
diagrammatic Renormalization Group differential equation
**

3:30 - 4:30PM

**Abstract:** Connes-Kreimer uncovered the mathematical structure underlying
renormalization in pQFT in terms of Hopf algebras of Feynman
graphs. The process of renormalization - in short, subtraction
of divergencies in a physical sound way - is captured by an
algebraic Birkhoff decomposition of Feynman rules. We briefly
review these recent findings, and then start to explore the
renormalization group differential equations from a diagrammatic
point of view.

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**Raymond T. Hoobler**

City College (CUNY)**Generators of D-Modules in positive characteristic**

5:00-6:00PM

**Abstract:** Let
and let be a polynomial in .
Then the localization of with respect to , , is a
module over the ring of differential operators,
. If
char()=0, then is a module of finite length over .
This leads to the Bernstein-Sato polynomial
and a
differential operator
such that

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**Coffee and tea will be served beginning at 3:00 PM Room
HW706 **

**Click
here for directions to Hunter College and location of room **