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August 18, 2015
Tuesday, August 18
Noncommutative Geometry
Time: 11:00
Speaker: Shahab Azarfar (Western)
Title: "Selberg Trace Formula"
Room: TBA

Abstract: Consider a closed smooth hyperbolic surface Σ=ΓH. Let k(x,y) be a continuous function which depends only on the hyperbolic distance between x,yH, and has some nice'' decay properties. Using k(x,y), we construct a trace-class integral operator Tk on L2(Σ). The trace of Tk is computed in two different ways using the Lidski's trace formula. The resulting Selberg's trace formula gives a relation between the length of closed geodesics and the eigenvalues of the hyperbolic Laplacian on Σ.

PhD Thesis Defence
Time: 13:30
Speaker: Javad Rastegari Koopaei (Western)
Title: "Fourier inequalities in Lorentz and Lebesgue spaces"
Room: MC 107

Abstract: This talk is on the mapping properties of the Fourier transform between Banach function spaces. These are generalizations of Hausdorff-Young and Pitt's inequalities.

We provide several relations between weight functions, that guarantee the boundedness of the Fourier series coefficients, viewed as a map between weighted Lorentz spaces. As a useful machinery, we briefly introduce the quasi concave functions and generalize a number of known inequalities. Finally, we apply our results to Fourier inequalities in weighted Lebesgue spaces and Lorentz-Zygmund spaces