Department of Mathematics

Invariant Theory

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Master and Phd Students
Lecturer Prof. Brent Doran
Room & Time Mon. 8.30-10.00 HG G43 // Wed. 16:15-18:00 ML H 34.3

Starting on Mon, April 29, there will be talks  both on Mondays and Wednesdays.

Description Invariant theory is a classical subject whose history is deeply intertwined with the foundations of algebraic geometry.  In this seminar, we get a view of the subject from its 19th century origins to developments in the 21st century. The core topic will be geometric invariant theory, but aspects of computational invariant theory, and what might be termed arithmetic invariant theory will also be explored. Topics like counter-examples to Hilbert's 14th problem, constructing moduli spaces, and computing stable loci will be included.  A proof of the Verlinde formula, originating in the mathematical physics of string theory, will be a goal for late in the course.  As time permits, we will look at the new paper by Bhargava and Gross on arithmetic considerations and applications of the subject.
Literature Primary:

Mukai, S.  Introduction to invariant theory and moduli


Dolgachev, I. Lectures on invariant theory

Derksen and Kemper, Computational invariant theory

Mumford, Fogarty, Kirwan.  Geometric invariant theory

Bhargava and Gross.  Arithmetic invariant theory (2012, pdf on

Further information
Here is a list of the talks

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