Mathematics Dept.
  Events
Harvard University
Thu 20 Aug 2015, 2:30pm
Algebraic Geometry Seminar
PIMS, Room 4127
Tiling, SYZ and modular forms
PIMS, Room 4127
Thu 20 Aug 2015, 2:30pm-3:30pm

Abstract

 I will introduce a class of Calabi-Yau manifolds associated to the polytope tilings. Their mirrors provide new insights in the toric mirror symmetry, and are also closely related to certain modular forms. This is a joint work with Siu-Cheong Lau. 

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Columbia University
Thu 20 Aug 2015, 4:00pm
Algebraic Geometry Seminar
PIMS, room 4127
The universal implosion and the multiplicative Horn problem
PIMS, room 4127
Thu 20 Aug 2015, 4:00pm-5:00pm

Abstract

 The multiplicative Horn problem asks what constraints the eigenvalues of two n x n unitary matrices place on the eigenvalues of their product.  The solution of this problem, due to Belkale, Kumar, Woodward, and others, expresses these constraints as a convex polyhedron in 3n dimensions and describes the facets of this polyhedron more or less explicitly. I will explain how the vertices of the polyhedron may instead be described in terms of fixed points of a torus action on a symplectic stratified space, constructed as a quotient of the so-called universal group-valued implosion.
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George Bluman
UBC Math
Fri 21 Aug 2015, 2:30pm
Symmetries and Differential Equations Seminar
Math 125
Mappings I
Math 125
Fri 21 Aug 2015, 2:30pm-3:30pm

Abstract

It will be shown that from the symmetries or conservation law multipliers of a nonlinear PDE system one can determine systematically whether it can be mapped invertibly to some linear PDE system. We show to find systematically such a mapping when one exists.

It will also be shown that from the symmetries of a linear PDE system with variable coefficients, one can determine systematically whether it can be mapped invertibly to some linear PDE system with constant coefficients. We show how to find systematically such a mapping when one exists.  This leads to the solution of the problem posed by Kolmogorov on when can a diffusion process be mapped into a Wiener process.

These results will be extended systematically to noninvertible mappings
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George Bluman
UBC Math
Thu 27 Aug 2015, 2:30pm
Symmetries and Differential Equations Seminar
Math 125
Mappings II
Math 125
Thu 27 Aug 2015, 2:30pm-3:30pm

Abstract

Mappings II: 

It will be shown that from the symmetries of a linear PDE system with variable coefficients, one can determine systematically whether it can be mapped invertibly to some linear PDE system with constant coefficients. We show how to find systematically such a mapping when one exists.  This leads to the solution of the problem posed by Kolmogorov on when can a diffusion process be mapped into a Wiener process.

It will also be shown that from the conservation law multipliers of a nonlinear PDE system one can determine systematically whether it can be mapped invertibly to some linear PDE system. We show to find systematically such a mapping when one exists.

These results will be extended systematically to noninvertible mappings.
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