Mon, Mar 9

Algebra Seminar

Michaela Vancliff, University of Texas at Arlington

Generalizing classical Clifford algebras, graded Clifford algebras and their associated geometry

4:00 PM, 250 Mathematics Building

Graded Clifford algebras are non-commutative graded algebras related to classical Clifford algebras, and certain properties of such an algebra can be deduced from certain commutative geometric data associated to it. In particular, a standard result is that a graded Clifford algebra \(C\) is quadratic and Artin-Schelter regular with Hilbert series equal to that of a polynomial ring if and only if a certain quadric system associated to \(C\) is base-point free. About two decades ago, T. Cassidy and the speaker introduced a generalization of such an algebra, called a graded skew Clifford algebra, and they found that many results concerning graded Clifford algebra shave analogues in the case of graded skew Clifford algebras, provided the appropriate non-commutative geometric data is defined. More recently, T.Cassidy and the speaker defined a "skew" version of classical Clifford algebras, and related such algebras to graded skew Clifford algebras. Indeed,just as (classical) Clifford algebras are the Poincaré-Birkhoff-Witt (PBW) deformations of exterior algebras, skew Clifford algebras may be viewed as \(\mathbb{Z}_2\)-graded PBW deformations of quantum exterior algebras.

Fri, Mar 13

Topology and Geometry Seminar

Melissa Zhang (UC Davis)

Title: TBD

4:00 PM, 122 Mathematics Building

Fri, Apr 10

Applied Mathematics Seminar

Yulong Lu (U Minnesota)

Title: TBD

4:00 PM, Room: TBD

Fri, Apr 10

Topology and Geometry Seminar

Roberta Shapiro (University of Michigan)

TBA

4:00 PM, 122 Mathematics Building

TBA

Wed, Apr 15

Analysis Seminar

Rizwanur Khan, University of Texas at Dallas

TBA

4:00 PM, 250 Mathematics building

TBA