Introduction to geometric complexity theory

Prof. Dr. Markus Bläser, Dr. Christian Ikenmeyer


Course description

Geometric complexity theory is an ambitious program initiated in 2001 by Mulmuley and Sohoni towards solving the famous P vs NP problem. The idea is to use algebraic geometry and representation theory to prove complexity lower bounds for explicit problems. There has been a significant amount of research activity in this direction during the last few years and connections to tensor rank and matrix multiplication have been drawn.

In this course we will give short introductions to algebraic complexity theory, to basic algebraic geometry, and to classical representation theory. The goal is to give a first introduction to geometric complexity theory and cover some of the recent results.

Time and date

Summer semester 2017,




There will be oral exams at the end of the semenster (several dates are available).


There will be weekly assignments. You need to obtain half of the points to be admitted to the exam. Minor typos in homework 2 and 7 fixed and a typo in homework 12 fixed.

Lecture Notes

We will keep updating the lecture notes.


The lecture's topics span a wide range of areas in mathematics. A list of books that is reserved for your studies at the library can be found here: Literature