Department of

March 2014 April 2014 May 2014 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 1 2 3 4 5 1 2 3 2 3 4 5 6 7 8 6 7 8 9 10 11 12 4 5 6 7 8 9 10 9 10 11 12 13 14 15 13 14 15 16 17 18 19 11 12 13 14 15 16 17 16 17 18 19 20 21 22 20 21 22 23 24 25 26 18 19 20 21 22 23 24 23 24 25 26 27 28 29 27 28 29 30 25 26 27 28 29 30 31 30 31

Wednesday, April 9, 2014

**Abstract:** An interesting topic in modern mathematical physics is the so-called "2d\4d relation" between Liouville conformal blocks (hypergeometric type integrals over contours in CP^1) and instanton counting (sums over fixed points in the moduli space of instantons in C^2). We will tell about a simple way to prove this relation, using a natural q-deformation of the both sides. After the q-deformation, the Liouville integrals acquire poles and can be taken by residues. These residue sums are manifestly the sums that appear in instanton counting.