November 4 (Sat), 2017 (Sat) 10:05--11:05, 14:00--15:00 Graduate School of Mathematical Sciences The University of Tokyo, Tokyo, Japan |

Andrei Okounkov

(Columbia University / Kyoto University)

(Columbia University / Kyoto University)

**Abstract**

My goal in these two lectures is to explain:

1) what are the Donaldson--Thomas counts counting,

2) how are these counts related to other parts of mathematics and mathematical physics,

3) what are the elementary counts, from which all other ones could be, at least in principle, derived,

4) how are the elementary counts described using geometric representation theory.

As this is, realistically, too much ground to cover
in two lectures, I will try to describe what I personally
consider to be the most important points and ideas, hoping
that those who are interested will open the accompanying notes.