Mathematics Dept.
  Events
Changfeng Gui
University of Connecticut/University of Texas-San Antonio
Tue 1 Dec 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012
Saddle Solutions of Allen-Cahn Equation on the Plane.
ESB2012
Tue 1 Dec 2015, 3:30pm-4:30pm

Abstract

Allen-Cahn 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 Allen-Cahn equation on the plane. In particular, I will describe the variational characterization of these solutions as a mountain pass solutions.
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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, 3:00pm-4:00pm

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 self-contained.
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Mainz
Fri 4 Dec 2015, 3:00pm
Department Colloquium
MATX 1100
Counting curves - complex and tropical
MATX 1100
Fri 4 Dec 2015, 3:00pm-4:00pm

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 two-space to the real two-space by applying a component-wise 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 convex-geometric 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 Gromov-Witten invariants.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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Univ. of Washington
Tue 8 Dec 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 PIMS Lounge
Variable projection and applications
ESB 4133 PIMS Lounge
Tue 8 Dec 2015, 12:30pm-1:30pm

Abstract

Variable projection (VP) gained popularity as a technique for solving nonlinear least squares problems (NNLS) min_{x,y} ||F(x)y - b||^2. The VP approach is an itegrated algorithm in x that `projects out' the variable y at each iteration. The NLLS problem class had a range of applications, and we show that the 'projection' approach generalizes to a very broad setting, retaining the original flavour, with applications to nuisance parameter estimation, kernel learning, and non-smooth optimization. (Editar entrada)

Note for Attendees

Lunch will be provided.
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MIT
Thu 10 Dec 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 PIMS Lounge
An Extended Frank-Wolfe Method, and its Application to Low-Rank Matrix Completion
ESB 4133 PIMS Lounge
Thu 10 Dec 2015, 12:30pm-1:30pm

Abstract

Motivated by the problem of computing low-rank matrix completion solutions, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. We also present computational guarantees for the method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates. We then present computational results for large-scale matrix completion problems that demonstrate significant speed-ups in computing low-rank near-optimal solutions.

Note for Attendees

Lunch will be provided.
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