# On the set of specializations of a Galois cover

`2019-06-19 10:30:00``2019-06-19 11:30:00``On the set of specializations of a Galois cover``One of the most successful approaches to the inverse Galois problem over Q is via specialization of polynomials f(t,X) in two (or more) variables, or equivalently, specialization of Galois covers of the projective line. The fundamental underlying result, Hilbert's irreducibility theorem, ensures that this specialization process preserves the Galois group "most of the time". In this talk, I will review a series of recent results under the following general question: Which kinds of "strong" versions of the inverse Galois problem can, or cannot be expected to be solved via a specialization approach as above? Such strong versions include famous problems such as "Grunwald problems", "Malle's conjecture" on the distribution of Galois groups, and the "Q-admissibility conjecture" about G-crossed product division algebras. (This being a survey talk, I will try to make it accessible for a broad audience.)``Third floor seminar room (room 201, building 216)``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`One of the most successful approaches to the inverse Galois problem over Q is via specialization of polynomials f(t,X) in two (or more) variables, or equivalently, specialization of Galois covers of the projective line. The fundamental underlying result, Hilbert's irreducibility theorem, ensures that this specialization process preserves the Galois group "most of the time".

In this talk, I will review a series of recent results under the following general question: Which kinds of "strong" versions of the inverse Galois problem can, or cannot be expected to be solved via a specialization approach as above?

Such strong versions include famous problems such as "Grunwald problems", "Malle's conjecture" on the distribution of Galois groups, and the "Q-admissibility conjecture" about G-crossed product division algebras. (This being a survey talk, I will try to make it accessible for a broad audience.)

Last Updated Date : 19/05/2019