Palm equivalence, number rigidity and conditional measures for determinantal point processes

The determinantal point processes arise from many branches of areas such as random matrices, representation theory, random graphs and zeros of holomorphic functions etc. In this talk, I will briefly recall the basic materials in the theory of determinantal point processes and then will discuss some results concerning the Palm equivalence, number rigidity and conditional measures and Olshanski’s problem on this area. The talk will be based on several joint works with Alexander Bufetov, Yoann Dabrowski, Alexander Shamov and Shilei Fan.