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Thursday, November 21, 2013

The commutative algebra of highly symmetric data

Jan Draisma (TUE)

Abstract: In this age of high-dimensional data, many challenging questions take the following shape: can you check whether the data has a certain desired property by checking that property for many, but low-dimensional data fragments? In recent years, such questions have inspired new, exciting research in commutative algebra, especially relevant when the property is highly symmetric and expressible through systems of polynomial equations.I will discuss three concrete questions of this kind that we have settled in the affirmative: Gaussian factor analysis from an algebraic perspective, high-dimensional tensors of bounded rank, and higher secant varieties of Grassmannians. The theory developed for these examples deals with group actions on infinite-dimensional algebraic varieties, and applies in a much wider context. In particular, I will sketch its relation to the fantastic Matroid Minor Theorem due to Geelen, Gerards, and Whittle.

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Location :  Room 611 of the Hans Freudenthal building, formerly known as the Wiskunde/Maths building, (campus De Uithof) Budapestlaan 6, Utrecht.
Date and time : Thursday, November 21, 2013 15:30-16:30. The lecture is preceded by coffee, tea, and cookies from 15.00 to 15.30 hour in the same room.