Mathematics Colloquium
Wednesday, 26 July, 4 pm
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Host: J. K. Verma
Venue: Ramanujan Hall
Speaker: Vaibhav Pandey
Affiliation: Purdue University, West Lafayette, IN, USA
Title: Classical invariant theory
Abstract: Invariant theory has played a key role in the development of modern commutative algebra. The classical invariant theory has a rich history going back at least to the seminal contributions of David Hilbert and Emmy Noether. The beauty of the subject lies in its strong insistence on computations and on the far-reaching consequences of these computations in modern algebra.
In this talk, we will focus on the classical invariant rings---they are the fixed subrings of the natural actions of linear algebraic groups on polynomial rings. Exploring key properties of these rings over rational numbers was a major research program in the late eighteenth century. We will talk about these properties and prove the corresponding ring theoretic properties of these invariant rings over fields of positive characteristic. This is joint work with Mel Hochster, Jack Jeffries, and Anurag Singh.