Time: Friday evening, 19:00
Place: Zoom
We are trying to understand the construction of the 3d N=4 Coulomb branch and the symplectic duality between the Coulomb branch and the Higgs branch.
Here is the rough plan for the seminar:
The definition of the Coulomb branch.
Case study: ADE quiver gauge Coulomb branch and its quantisation.
Noncommutative crepant resolution of the Coulomb branch.
Category O for the Coulomb branch and the KLRW algebra.
Category O for the Nakajima varieties.
Symplectic resolution for the Coulomb branch.
1. Braverman, A., Finkelberg, M., & Nakajima, H. (2016). Towards a mathematical definition of Coulomb branches of $3 $-dimensional $\mathcal N= 4$ gauge theories, II. arXiv preprint arXiv:1601.03586.
2. ZHOU, Y. (2020). SLICES IN THE THICK AFFINE GRASSMANNIAN AND THEIR QUANTIZATIONS.
3. Kamnitzer J, Webster B, Weekes A, et al. Yangians and quantizations of slices in the affine Grassmannian[J]. Algebra & Number Theory, 2014, 8(4): 857-893.
4. Kamnitzer J, Tingley P, Webster B, et al. On category O for affine Grassmannian slices and categorified tensor products[J]. Proceedings of the London Mathematical Society, 2019, 119(5): 1179-1233.
5. Kodera, R., & Nakajima, H. (2018, June). Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras. In Proc. Symp. Pure Math (Vol. 98, p. 49).
6. Braverman, A. Coulomb branches of 3d N= 4 quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes), ArXiv e-prints (2016). arXiv preprint arXiv:1604.03625.
7. Webster B. On generalized category $$\mathcal {O} $$ O for a quiver variety[J]. Mathematische Annalen, 2017, 368(1): 483-536.
8. Braverman, A., Finkelberg, M., & Nakajima, H. (2018). Line bundles over Coulomb branches. arXiv preprint arXiv:1805.11826.
9. Webster, B. (2019). Coherent sheaves and quantum Coulomb branches I: tilting bundles from integrable systems. arXiv preprint arXiv:1905.04623.
2022/3/18 Tianqing Zhu. Yangians and quantizations of slices in the affine grassmannian.
2022/3/25 Keke Zhang. Definition of the Coulomb branch, examples of quiver gauage theories.
2022/3/31 Tianqing Zhu. Quiver ADE type Coulomb branch.
2022/4/8 Tianqing Zhu. Quantised Coulomb branch.
2022/4/15 Keke Zhang. Noncommutative resolution of the Coulomb branch.
2022/5/22 Tianqing Zhu. Introduction to the KLRW algebra.
2022/5/27 Tianqing Zhu. KLRW Yangians and Yangians.