Andrew Hamilton (CU Boulder, Astrophysical & Planetary Sciences) The Standard Model and Beyond
Wed, Feb. 19 4pm (MATH 350)
Grad Student Seminar
Sebastian Bozlee (CU Boulder) On the ranks of recurrence matrices
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As first noticed in the 1970s, the charges of fermions follow patterns that allow the Standard Model U(1)xSU(2)xSU(3) to be embedded in Grand Unified groups SU(5) and SU(2)xSU(2)xSU(4), which in turn embed in SO(10), or equivalently in its covering group Spin(10). Spin(10) seems to know about Lorentz transformations: notably, the Dirac pseudoscalar miraculously equals the Spin(10) pseudoscalar. But Spin(10) lacks a time dimension. To accommodate time, 2 dimensions must be adjoined (the complex structure of spinors means that they live naturally in even dimensions). The main result is: The Dirac (Poincare) and SM algebras are commuting subalgebras of the spin algebra associated with the group Spin(11,1) of transformations of spinors in 11+1 spacetime dimensions. Each of the 3 spatial dimensions of 3+1 dimensional spacetime proves to be a 5-brane.
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Suppose you fill in a matrix with the Fibonacci numbers, left-to-right, top-to-bottom. What will its rank be? The answer is surprisingly simple. We will then explore how much this answer extends when the matrix is filled in with other sorts of sequences defined by linear recurrences.