"Mathematical Colloquium" — a seminar of the
Mathematical Center in Akademgorodok and
Sobolev Institute of Mathematics SB RAS, the purpose of which is to give students a general idea of the areas of research carried out by scientists from the Novosibirsk Scientific Center, as well as Russia and the whole world. The emphasis in the reports is placed on the accessibility of the presentation of the material to a wide circle of the mathematical community, and only then on the detailing of the mathematical content.
At the next Colloquium on
September 29 at
4:30 pm Fedor V. Petrov (Doctor of Physical and Mathematical Sciences, Senior Researcher of the Laboratory of Representation Theory and Dynamical Systems of the St. Petersburg branch of Steklov Mathematical Institute RAS, Professor of St. Petersburg State University) will present a talk
"Minimality of tensor expansions". The seminar will be held in
room 220 of the Sobolev Institute of Mathematics SB RAS (Novosibirsk, 4 Acad. Koptyug avenue).
A tensor v from the kth tensor power of a vector space X is called decomposable if it can be written as a tensor sum of k vectors. The smallest number of decomposable tensors whose sum is a given tensor is called its tensor rank.
For k=2, tensors can be identified with matrices. In this case, the tensor rank coincides with the usual matrix rank. There are many equivalent definitions and many efficient ways to calculate the rank of a matrix. For k>2, the concept of tensor rank is much more intricate. To understand from a given expansion of the tensor whether it is minimal is a very difficult task in all respects.
In the course of the report, we will discuss old and new sufficient conditions for the minimality and uniqueness of tensor expansions.
More details can be found on the website of the Mathematical Colloquium
http://sobolevmath.tilda.ws.
