Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
We present our solutions to two long standing open problems, one from probability theory formulated by Malyshev in 1970 and another one from a crossroad of geometry and dynamics, going back to Darboux in 1879. The Malyshev problem is of finding effective, explicit necessary and sufficient conditions in the closed form to characterize all random walks in the quarter plane with a finite group of the random walk of order 2n, for all n ≥ 2. Previously known results covered the cases n = 2, 3, and 4. We also describe all n-periodic Darboux transformations for four-bar link problems for all n ≥ 2, thus completely solving the Darboux problem, that he solved for n = 2, and which was recently extended to n = 3. The talk is based on a joint work with Milena Radnovic (arXiv:2512.21976).
In this talk we examine some aspects of the classical-quantum correspondence induced by symplectic maps and metaplectic operators. We first recall the notion of the metaplectic group, the double covering of the symplectic group.
We then extend this construction to the complex setting and define the metaplectic semigroup associated with the semigroup of positive complex symplectic linear maps. In this context, we review the various definitions appearing in the literature, notably those due to M. Brunet and P. Kramer, L. Hörmander, and R. Howe.
We finally establish several properties of the metaplectic semigroup, with particular emphasis on applications to time-frequency analysis and to evolution equations with complex quadratic Hamiltonians.
This talk is based on joint work with G. Giacchi, M. Malagutti, A. Parmeggiani and L. Rodino.
