15:00 – Sylvie Paycha (Potsdam): The Wodzicki residue; a useful analytic tool for geometric purposes
The Wodzicki residue is a useful analytic tool to capture geometric information. Using the inverse Mellin transform, one can express the singular part as well as the constant term of the heat-kernel expansion on a closed manifold in terms of Wodzicki residues. This extends to two rather different geometric frameworks; the noncommutative torus on the one hand and Hilbert modules on the other. We revisit Atiyah’s L^2-index theorem by means of the (extended) Wodzicki residue and inspired by Connes et al., define scalar curvature on the noncommutative two torus as an (extended) Wodzicki residue. Based on joint work with Sara Azzali, Cyril Lévy and Carolina Neira-Jimenez.
16:30 – Jordan Stoyanov (Newcastle/Ljubljana): Probability Distributions and Their Moment Determinacy
We deal with probability distributions, one-dimensional or multi-dimensional, whose all positive integer order moments are finite. Either such a distribution is uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). Thus the topic of the talk is in the classical moment problem. Besides recalling briefly the well-known conditions by Cramer, Carleman and Krein, the emphasis will be on some new developments obtained over the last years. Some of the following specific topics will be presented in more details:
(a) New Hardy’s criterion for uniqueness.
(b) Criteria based on the rate of growth of moments.
(c) Stieltjes classes for M-indeterminate distributions. Index of dissimilarity.
(d) Multidimensional moment problem.
(e) Nonlinear transformations of random data and their moment (in)determinacy.
(f) M-determinacy of distributions of stochastic processes defined by SDEs.
There will be new and well-referenced results, hints for their proof, and illustrations by examples and counterexamples. Some facts are not so well-known and even look shocking. Intriguing open questions and conjectures will be outlined.