## The Workshop on 6D Gauged Theory and Invariants of 4-manifolds on Nov 9-13

**Speaker(s): ** Abhijit Gadde, Bohui Chen, Hiraku Nakajima, Jun Li, Lev Borisov, Pavel Putrov, Sergei Gukov, Weiping Li

**Time: **November 9 - November 13, 2015

**Venue: ** No.77201, Jing Chun Yuan 78, BICMR

The subject of smooth 4-manifolds was a very popular area of mathematics in 80's and 90's due to the invention of Donaldson invariants and Seiberg-Witten invariants. Towards the end of 90's, the subject started to become quiet. It became clear that Donaldson/Seiberg-Witten invariants are not enough to classify smooth 4-manifolds and new invariants are needed. Recently, physicists Gukov from Caltech and his collaborators proposed a new way to construct smooth invariants of 4-manifolds. These invariants are based on recent advance in physics regarding 6D gauged theory and its dimension reduction to 2-dimension. Their proposed invariants are in the form of vertex operator algebra. This is an informal workshop to understand their proposal. The main speakers are a team of physicists leaded by Gukov. The math speakers are mostly experts in Donaldson theory.

**Schedule:**

**Monday, Nov 9**

9-10am: Physics Team: 6D gauged theory and invariants of 4-manifolds

10-11am: Tea break, informal discussion

11-12am: Physics Team: 6D gauged theory and invariants of 4-manifolds

2-3pm: Jun Li (Stanford): An overview of Donaldson theory

3-4pm: Tea break, informal discussion

4-5pm: Lev Borisov (Rutgers): Chiral DeRham complex

**Tuesday, Nov 10**

9-10am: Physics Team: 6D gauged theory and invariants of 4-manifolds

10-11am: Tea break, informal discussion

11-12am: Physics Team: 6D gauged theory and invariants of 4-manifolds

2-3pm: Young-Gen Oh (BICMR Distinguished Lecture): Topological extension of Calabi invariants and its application

3-4pm: Tea break, informal discussion

4-5pm: Wei-Ping Li (HKUST): Euler characteristic of Donaldson moduli space

**Wednesday, Nov 11**

9-10am: Physics Team: 6D gauged theory and invariants of 4-manifolds

10-11am: Tea break, informal discussion

11-12am: Physics Team: 6D gauged theory and invariants of 4-manifolds

2-3pm: Physics Team: 6D gauged theory and invariants of 4-manifolds

3-4pm: Tea break, informal discussion

4-5pm: Bohui Chen (Sichuan University): A smooth compactification of Donaldson moduli space

**Thursday, Nov 12 **

9-10am: Physics Team: 6D gauged theory and invariants of 4-manifolds

10-11am: Tea break, informal discussion

11-12: Discussion

2-3pm: Physics Team: 6D gauged theory and invariants of 4-manifolds

3-4pm: Tea break, informal discussion

4-5pm: Discussion

9-10am: Nakajima (Kyoto): Mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories

10-11am: Tea break, informal discussion

11-12: Discussion