Columbia

Mon 30 Nov 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126

Relative orbifold DonaldsonThomas theory and local gerby curves

MATH 126
Mon 30 Nov 2015, 3:00pm4:00pm
Abstract
In this talk I will introduce the generalization of relative DonaldsonThomas theory to 3dimensional smooth DeligneMumford stacks. We adopt Jun Li’s construction of expanded pairs and degenerations and prove an orbifold DT degeneration formula. I’ll also talk about the application in the case of local gerby curves, and its relationship to the work of OkounkovPandharipande and MaulikOblomkov.
hide

Mathematics, UBC

Mon 30 Nov 2015, 3:00pm
Harmonic Analysis Seminar
MATX 1102

Diophantine equations and discrete restriction theory

MATX 1102
Mon 30 Nov 2015, 3:00pm4:30pm
Abstract
In this twopart talk, we discuss a Fourieranalytic approach to solve translationinvariant systems of polynomial equations, when the variables lie in a dense subset of the integers. In the first part, we explain how discrete estimates in restriction theory come into play in this problem. In the second part, we show how to obtain weak restriction estimates by Bourgain's discrete version of the TomasStein argument.
hide

University of Connecticut/University of TexasSan Antonio

Tue 1 Dec 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012

Saddle Solutions of AllenCahn Equation on the Plane.

ESB2012
Tue 1 Dec 2015, 3:30pm4:30pm
Abstract
AllenCahn equation arises in the mathematical study of phase transition. Despite it's seemingly simple appearance, It has displayed very rich structure of solutions and involved with deep mathematics. In this talk, I will discuss the existence, symmetry and classification of saddle solutions of AllenCahn equation on the plane. In particular, I will describe the variational characterization of these solutions as a mountain pass solutions.
hide

UBC Math and PIMS

Wed 2 Dec 2015, 3:00pm
Probability Seminar
ESB 2012

A characterization of Liouville property

ESB 2012
Wed 2 Dec 2015, 3:00pm4:00pm
Abstract
Poisson boundary provides an integral representation of all bounded harmonic functions. We say that a Markov chain satisfies the Liouville property if all bounded harmonic functions are constant, that is the Poisson boundary is trivial.
The first part of the talk is a gentle introduction to Poisson boundary. Then I will state a new condition that is equivalent to the Liouville property and provide a proof of this equivalence. This talk is based on an ongoing work and will be selfcontained.
hide

Mainz

Fri 4 Dec 2015, 3:00pm
Department Colloquium
MATX 1100

Counting curves  complex and tropical

MATX 1100
Fri 4 Dec 2015, 3:00pm4:00pm
Abstract
A curve is called rational if it can be parametrized by rational functions. Counting the number of rational curves in the plane that contain a given number of points has been an old and interesting problem. The degree of a curve is the degree of a polynomial equation defining it. We all know that there is only one curve of degree one through any given pair of points in the plane because this is just a straight line. The answer to similar questions for higher degrees quickly becomes more difficult and interesting. To simplify the problem, one may map a curve in the complex twospace to the real twospace by applying a componentwise absolute value and logarithm. The resulting object is for good reasons called an amoeba  I will show some pictures. The amoeba retracts to its spine which is a much simpler convexgeometric object that is also called a tropical curve. Such can be counted essentially by hand. A proof that the resulting counts coincide with the original problem goes via a recent theory of logarithmic GromovWitten invariants.
hide

Note for Attendees
Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.