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Noncommutative discriminants via Poisson geometry and representation theory

Student-Run Applied & Math Seminar

Speaker: Bach Nguyen, Louisiana State University
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Location: 2112 MSB
Start time: Wed, Dec 13 2017, 12:10PM

The notion of discriminant is an important tool in number theory, algebraic geometry and noncommutative algebra. However, in concrete situations, it is difficult to compute and this has been done for few noncommutative algebras by direct methods. In this talk, we will describe a general method for computing noncommutative discriminants which relates them to representation theory and Poisson geometry. As an application we will provide explicit formulas for the discriminants of the quantum Schubert cell algebras at roots of unity. If time permits, we will also discuss this for the case of quantized coordinate rings of simple algebraic groups and quantized universal enveloping algebras of simple Lie algebras. This is joint work with Kurt Trampel and Milen Yakimov.

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