When is a variety a quotient of a smooth variety by a finite group?
Harvey Mudd College has invited a MathWorks senior engineer team to the Claremont Colleges for a free MATLAB seminar. The seminar is open to all the students and faculty at the Claremont Colleges.
Location: Harvey Mudd College, Sprague Building – Third Floor.
Central to the talk will be the comparison of various notions of Gaussian measures on a topological group $G$.They are introduced as measures on $G$ which are embeddable into continuous one-parameter convolution semigroups or as infinitely divisible measures which by definition admit $n$th roots for every $n$. In this connection the question arises whether any infinitely divisible measure on a topological group $G$ is in fact embeddable.This embedding property holds true for Euclidean spaces and more generally for locally convex vector spaces over the field of real numbers. Since the appearance of the speaker's monograph of 1975 much work has been devoted to solving the embedding problem within the framework of an arbitrary locally compact group, but in full generality the problem is still open. In order to convey at least some ideas on the approach towards the solution of the problem we shall restrict ourselves to Abelian groups and discuss a few nonstandard examples.
We will describe the classical Liapanov's Convexity Theorem and its Functional Analytic Form. We will state a form of a recent extension of the theorem. Some of the tools used in the proof will be mentioned, but we won't give a detailed proof. In addition to recovering the Classical Theorem, the applications will include an extension of the Phelps-Dye Theorem (used to prove that no finite dimensional subspace of $L^1[0,1]$ admits unique best approximations to all $L^1$-functions), and an envy free cake cutting theorem.
Dinner at a local restaurant will follow the concluding lecture.