Notre Dame
Motivic Milnor Fiber Seminar
Spring 2012
(11am on Thursdays in 258 Hurley)
About the seminar: We will be reading the paper
"Monodromy and the Lefschetz fixed point formula" by Hrushovski and
Loeser, arxiv:1111.1954. The paper uses motivic integration and
cohomology of Berkovich spaces to give a geometric proof of a Lefschetz
type formula for a Monodromy operator.
Date |
Time/Place |
Speaker |
Title |
Feb 9 |
usual |
Nero Budur |
|
Feb 16 |
usual |
Nero Budur |
|
Mar 16 |
1pm HH125 |
Moshe Kamensky |
|
Apr 10 |
2pm HH125 |
Moshe Kamensky |
- continuation - |
Apr 12 |
12pm H258 |
Moshe Kamensky |
|
Apr 19 |
12pm H258 |
Moshe Kamensky |
|
Apr 25 |
12pm H258 |
Moshe Kamensky |
Abstracts of talks:
Feb 9: Nero Budur. Milnor Fibers
Abstract: We will survey some of the uses of the Milnor fibers, connections with
other fields, and introduce the main objects of this seminar, the
motivic Milnor fibers. I will then explain the relation of the motivic
Milnor fibre to the Monodromy conjecture.
Feb 16: Nero Budur. Minor Fibers II
Abstract: We will finish the proof of Denef-Loeser that the m-th Leschetz number of the Milnor monodromy equals the Euler characteristic of the m-th contact variety. We will finally explain the relation of the motivic Milnor fibre to the Monodromy conjecture.
Mar 16: Moshe Kamensky: Integration in valued fields
Abstract: I will give an overview of the main statement of motivic integration, as
provided by the paper ``Integration in valued fields'', by Hrushovski
and Kazhdan (arXiv:math/0510133). The central point is understanding the
definable sets in the (first order) theory of algebraically closed
valued fields. No model theory will be assumed.
Apr 12: Moshe Kamensky: Integration in valued fields III
Abstract: I will discuss in more details the definable sets in ACVF, and we will give a precise formulation of the results of Hrushovski and Kazhdan. I will also discuss some variants that appear in the paper of Hrushovski and Loeser.
Apr 19: Moshe Kamensky: Integration in valued fields IV
Abstract: I will continue reviewing the main results of Hrushovski--Kazhdan, with the goal of covering the material in section 2 of Hrushovski--Loeser.
Apr 24: Moshe Kamensky: An overview of the proof of the main theorem.
Abstract: I will survey the geometric proof of the formula connecting the action of the monodormy operation on the cohomology of the Milnor fiber with the geometry of the truncated arc spaces associated to the Milnor fiber. If time permits, I will conclude the definition of the motivic Euler characteristic.
For problems with this page, email Nero Budur.