Lijia Ding (Fudan University, Shanghai China)
Toeplitz operators on higher Cauchy-Riemann spaces over the unit ball
In this talk, we investigate some algebraic properties of Toeplitz operators over higher Cauchy-Riemann spaces C_{\alpha,m} on the unit ball B^d. We first discuss the Berezin transform on higher Cauchy-Riemann spaces. By making use of Berezin transform, we completely characterize (semi-)commuting Toeplitz operators with bounded pluriharmonic symbols over higher Cauchy-Riemann space C_{\alpha,m}. Moreover, when d ≥ 2 we show that compact products of finite Toeplitz operators with a class of bounded pluriharmonic symbols only happen in the trivial case. (This is a joint work with my Ph. D. supervisor prof. Kai Wang.)
18-12-04 Rami Ayoush (Institute of Mathematics of Polish Academy of Sciences)
Martingale approach to Sobolev embedding theorems and Uncertainty Principle
During the talk I will discuss two probabilistic analogs of theorems connected with Sobolev spaces. First concerns the problem of generalizing Hardy-Littlewood-Sobolev inequality: we investigate which subspaces of L_{1} are mapped by Riesz potential I_{\alpha} to L_{\frac{d}{d-\alpha}}. The second analog corresponds to estimates of Hausdorff dimension of vector-valued measures under restrictions on its Fourier transform. It turns out that both problems are dependent on Van Schaftingen's cancelling condition (and its 'higher degree' versions). Joint work with D. Stolyarov and M. Wojciechowski.
The talk is aimed at an audience working in PDEs and harmonic analysis but can interest also probabilists.
18-12-11
Karen Strung
Optimal transport and unitary orbits in C*-algebras
Two areas of mathematics which have received substantial attention in recent years are the theory of optimal transport and the Elliott classification programme for C*-algebras. In this talk, we combine these to address a classical problem of Weyl: when can the distance between unitary orbits of normal operators be computed by spectral data? Here, the settings for our operators are certain well-behaved C*-algebras which arise from Elliott's classification programme.
In the first part of my talk, I will introduce C*-algebras and their classification. In the second part, I will discuss how we combine classification machinery with the theory of optimal transport to find sufficient conditions under which the distance between unitary orbits of two normal elements can be computed by tracial states. This is based on joint work with Jacelon and Vignati.
The first part of the talk is aimed at a general analysis audience, while the second half assumes familiarity with basic functional analysis.