# Noon lecture

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On 9.5.2013 at 12:20 in S6, there is the following noon lecture:

# On algebraic vector bundles over configuration spaces

## Igor Køí¾

## University of Michigan

## Abstract

A commutative ring R is said to have the Quillen-Suslin property if every finitely generated projective module over R is free. A famous theorem of Quillen and Suslin (solving a question of Serre) states that the ring of polynomials in n variables over a field is Quillen-Suslin. The result was later generalized by Gubeladze, and there are also effective algorithmic versions, which have applications in signal processing. In this talk, I will show that the ring polynomial ring in n variables x_1,...,x_n with all x_i-x_j with i,j different inverted is Quillen-Suslin. This result has an interesting geometric interpretation relevant in mathematical physics. An algorithmic solution remains an interesting open problem.

list of noon lectures ( 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | newer lectures)

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