PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan, Mihran Papikian, Ae Ja Yee, Kirsten Eisentraeger.

Title:Labeled trees, divisorial valuations at infinity, and the two-dimensional Jacobian Conjecture
Seminar:Algebra and Number Theory Seminar
Speaker:Alex Borisov, Binghamton University
Abstract:
Starting from a projective plane and performing several blowups of points at infinity, one can get various smooth compactifications of the affine plane. Each irreducible component of the complement of the affine plane gives a valuation on the field of rational functions in two variables. These valuations are called divisorial valuations, and they play an important role in many geometric approaches to the two-dimensional Jacobian Conjecture. We will introduce two discrete invariants of these valuations, and discuss their significance and limitations for the Jacobian Conjecture. Despite the algebro-geometric motivation, our methods are essentially combinatorial, based on the (dual) intersection graph of curves at infinity.

Room Reservation Information

Room Number:MB106
Date:03 / 17 / 2016
Time:11:15am - 12:05pm