# Tensors in Computer Science

## Prof. Dr. Markus Bläser

## Prof. Dr. Frank-Olaf Schreyer

### Time & Date

If a matrix is a square filled with numbers, then a higher-order tensor is an n-dimensional cube filled with numbers.
Recent years have seen a dramatic rise of interest by computer scientists in the mathematics of higher-order tensors.
The notion of matrix rank can be generalized to higher-order tensors.
While matrix rank can be efficiently computed by, say, Gaussian eliminination, computing the rank of a tensor
of order 3 is NP-hard. The question of the complexity of matrix multiplication can be formulated
as the question of the rank of a certain tensor.
We will mainly focus on applications in complexity theory and quantum computation. In particular,
it is very unlikely that we will deal with applications in machine learning.

### Lecturer

**Prof. Dr. Markus Bläser**, Email: mblaeser at cs.uni-saarland...

Office Hours: whenever my office door is open, E 1 3, Room 412**Prof. Dr. Frank-Olaf Schreyer**, Email: schreyer@math...

Office Hours: tba, E2.4, room 425

### Grading

Oral exams in the semester break