Invariant theory without groups

Abstract: Given an orthogonal representation of a Lie group $G$ on a Euclidean vector space $V$, Invariant Theory studies the algebra of $G$-invariant polynomials on $V$. This setting can be generalized by replacing the representation $G$ with a foliation $F$ on $V$, with equidistant leaves. In this case, one can study the algebra of polynomials that are constant along these fibers - effectively producing an Invariant Theory, but without groups. In this talk we will discuss a surprising relation between the geometry of the foliation and the corresponding algebra, including recent joint work in progress with Ricardo Mendes and Samuel Lin, showing how to estimate volume and diameter of the quotient $V/F$ using the algebra.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.

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