Titlebook: Schrödinger Operators, Spectral Analysis and Number Theory; In Memory of Erik Ba Sergio Albeverio,Anindita Balslev,Ricardo Weder Conference

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,On the Spectral Gap for Networks of Beams,e between the first two eigenvalues) for the operator with these conditions is studied. Upper and lower estimates for the spectral gap are obtained, and it is shown that stronger estimates can be obtained for certain classes of graphs. Graph surgery is used as a technique for estimation. A geometric

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Symbolic Calculus for Singular Curve Operators,erators in Topological Quantum Fields Theory (TQFT) are precisely generalized Töplitz operators of this kind and we compute for some of them, and conjecture for the others, their main symbol, determined by the associated classical trace function.

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,On the Generalized Li’s Criterion Equivalent to the Riemann Hypothesis and Its First Applications,o the Riemann Hypothesis. This criterion is the statement that the Riemann hypothesis is equivalent to the non-negativity of the sums over non-trivial Riemann zeroes . . (generalized Li’s coefficients), which are equal to the derivatives . of the Riemann .-function, for some real .> −1/2 (if so, thi

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Trace Maps Under Weak Regularity Assumptions, of the boundary. For . in the whole space . we only assume that the . are Lebesgue measurable. As an application of our trace maps we consider the Dirichlet problem and we prove a coarea formula where the level sets are only assumed to be Lebesgue measurable ..