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K-State Today

October 18, 2018

Mathematics department to host Oct. 25 lecture

Submitted by Reta McDermott

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.

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