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02:10 PM - 03:00 PM
939 Evans |
Combinatorics Seminar, Permutohedra, associahedra, and beyond, Alexander Postnikov, MIT
The volume of the permutohedron is given by a multivariate polynomial that has many interesting combinatorial properties. We give 3 different formulas the this polynomial and discuss its relation with the Catalan numbers, the Eulerian numbers, parking functions, binary trees, mixed volumes of hypersimplices, Hall’s marriage theorem, and Weyl’s character formula. We also study a more general class of polytopes that includes permutohedra, Stasheff’s associahedra and cyclohedra, Stanley-Pitman polytopes, graphical zonotopes, and various generalized associahedra that came up in DeConcini-Procesi wonderful arrangements. We describe combinatorial structure of these polytopes and give formulas for their volumes and Erhart polynomials. This talk will be an extended version of the talk given at Stanley’s conference, see slides at http://www.math.mit.edu/~apost/talks.html
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02:10 PM - 03:00 PM
959 Evans |
Quantum Geometry Seminar, Matrix Lipschitz seminorm and compact operator metric spaces, Wei Wu, East China Normal University
On a matrix order unit space, we introduce a matrix version of Lipschitz seminorms on order unit spaces. Many properties still hold in this situation. A compact operator metric space is a matrix order unit space with a matrix Lip-norm on it. They are operator space version of Rieffel’s compact quantum metric spaces. In fact, any ordinary compact metric space and compact quantum metric space can appear as a compact operator metric space. After defining its corresponding Gromov-Hausdorff distance, we will compare these different types of Gromov-Hausdorff distance.
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02:30 PM - 03:30 PM
187 Dwinelle |
Northern California Symplectic Geometry Seminar, Complex, real and tropical curves, Grisha Mikhalkin, University of Toronto
Tropical varieties are limit objects of the so-called amoebas of complex algebraic varieties under a certain deformation of the ambient complex structure. This talk will focus on tropical curves and their applications for a range of classical problems in complex and real algebraic geometry.
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04:00 PM - 05:00 PM
187 Dwinelle |
Northern California Symplectic Geometry Seminar, Existence of Engel structures, Thomas Vogel, University of Munich
We develop a construction of Engel structures based on the decomposition of manifolds into round handles and some results from contact topology. We prove that every parallelizable 4-manifold admits an Engel structure.
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04:15 PM - 05:00 PM
60 Evans |
MSRI-Evans Talks, The characteristic polynomial of a hyperplane arrangement, Richard Stanley, Massachusetts Institute of Technology and MSRI
An arrangement A is (for this talk) a finite set of affine hyperplanes in a vector space over a field K. A fundamental combinatorial invariant of an arrangement is a polynomial X(t) called the *characteristic polynomial* of A.We will discuss some applications of the characteristic polynomial, including the counting of regions of the complement L of the hyperplanes in A when K=R (the real numbers), the computation of the homology of the complement of the hyperplanes in A when K=C (the complex numbers), the partial computation of the Smith normal form of a "distance matrix" associated with A, the computation of the eigenvalues of a certain random walk on the regions of the complement L (when K=R), and the counting of points lying on none of the hyperplanes when K is finite. Some examples of interesting characteristic polynomials will be given, including those that satisfy a "Riemann hypothesis."
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05:30 PM - 07:00 PM
961 Evans |
Informal Student String Theory Seminar, An introduction to the Virasoro algebra from the physics point of view, Qingtao Chen
First the speaker would like to talk about basic concept of CFT(Conformal Field Theory), normal ordering, OPE(Operator Product Expansion).Then we move on to introduce the Virasoro algebra, which can be viewed as a special case of Vertex operator algebra. Finally we compute some examples and determine the central charge of the Fermi Ghost field.
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