Abstract:For a smooth projective variety X over C , the global sections of the symmetric algebra of the tangent bundle form a C-algebra S(X) , which has been little studied up to now. I will use a series of examples to show that this algebra is both interesting and difficult to calculate. I'll end with a theorem that bounds its (Krull) dimension in terms of the Kodaira dimension of X . This is ...
Abstract：I will discuss some new bounds on the spectra of Laplacian operators on hyperbolic 3-manifolds. One example of such a bound is that the spectral gap of the Laplace-Beltrami operator on a closed orientable hyperbolic 3-manifold must be less than 47.32, or less than 31.57 if the first Betti number is positive. The bounds are derived using two approaches, both of which employ linear prog...
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