# Chaire Aisenstadt

Professeur Hiraku Nakajima sera au CRM du 11 au 24 août 2019. Professeur Nakajima donnera une série de trois conférences les 19, 21 et 23 août à la salle 5340, de 10h45 à 11h45 durant les trois jours. La première conférence sera un exposé grand public.

**19 août 2019 - 10h45 à 11h45**

Pavillon André-Aisenstadt, salle 5340

## Première conférence : Introduction to Coulomb branches of 3d N=4 SUSY gauge theories

**Abstract **: Physicists assign a 3d N=4 SUSY gauge
theory to a pair of a complex reductive group and its symplectic
representation. Then they further assign the Coulomb branch, which is
a hyperKaehler manifold possibly with singularities. I will explain
a recent mathematical approarch to its rigorous definition based on
a homology group of a certain infinite dimensional variety.

**21 et 23 août 2019 - 10h45 à 11h45**

Pavillon André-Aisenstadt, salle 5340

## Deuxième et troisième conférences : Bow varieties

**Abstract** : Bow varieties are originally introduced by Cherkis as ADHM
type description of moduli spaces of U(N) instantons on
multi-Taub-NUT spaces. They are isomorphic to Coulomb branches of
quiver gauge theoriities of affine type A, and can be used to realize
integrable highest weight representations of the corresponding affine
Lie algebra, as an example of geometric Satake for Kac-Moody Lie
algebras. I will explain definitions, properties, results on bow
varieties.

## BIOGRAPHIE

Hiraku Nakajima was born in Tokyo, Japan. He received his Ph.D. in 1991 from the University of Tokyo. Nakajima began his academic career as a research assistant at the University of Tokyo. From 1992 to 1995 he was an assistant professor at Tohoku University’s Mathematical Institute. In 1995 he returned to the University of Tokyo, where he served as an assistant professor. In 1997 he moved to Kyoto University and, in 2008, he became professor at Research Institute for Mathematical Sciences. Lastly in 2018, he became professor and principal investigator, at Kavli Institute for the Physics and Mathematics of the Universe in 2018. Nakajima received both the Geometry Prize (1997) and the Spring Prize (2000) from the Mathematical Society of Japan. He was a plenary speaker at the International Congress of Mathematicians (Beijing, 2002). He has also received the 2005 JSPS Prize of the Japan Society for the Promotion of Science, the 2014 Japan Academy Prize, and the Asahi Prize. Nakajima’s research interests include geometry, representation theory, and mathematical physics. He is particularly known for the development of the theory of quiver varieties. Other major accomplishments include his proofs of Nekrasov’s conjecture and the AGT conjecture, both geometric conjectures which originated in physics.