October 18, 2018
Mathematics department to host Oct. 25 lecture
Xuhua He of the University of Maryland, will present the 14th Virginia L. Chatelain Memorial Lecture, titled "The P-Adic Groups and Their Weyl Groups," as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, Oct. 25, in 102 Cardwell Hall.
Lecture abstract: In a 1957 paper, Jacques Tits explained the analogy between the symmetric group Sₙ and the general linear group over a finite field Fq and indicated that Sn should be regarded as the general linear group over F₁, the field of one element. Following Tits' philosophy, we would like to regard the affine Weyl groups as reductive groups over Q₁, the 1-adic field. Although it is still premature to develop the theory of 1-adic fields at the current stage, we do have a fairly good understanding of the conjugacy classes of the affine Weyl groups, together with the length functions on them, and such knowledge allows us to reveal a great part of the structure of the conjugacy classes of p-adic groups. I will explain how this idea may be used in representation theory and in arithmetic geometry.
The math department is a part of K-State's College of Arts and Sciences. To learn more about opportunities in math at K-State, visit the math department website.