Abstract: It is a central problem concerning division algebras to determine which finite dimensional division algebras are crossed products, that is, admit a maximal subfield that is Galois over the center. We shall discuss a simple crossed product criterion for tamely ramified valued division algebras, and apply it to describe the location of noncrossed products in the Brauer group of Henselian fields.

Based on joint work with Timo Hanke and Adrian Wadsworth.

Abstract: We will continue the discussion of path induction, and use it to produce further operations on paths, such as applying functions to paths, and the transport between fibers. Then, we will discuss the notions of homotopy between functions and equivalence between types.

Abstract: We will give an introduction to the ideas of the Langlands program, through the classical problems in algebraic number theory, elliptic curves and L-functions.