Notes

Presentations and Lectures

  1. Reducedness of quiver varieties (recording). A talk that I gave at Perimeter Institute in February 2022.

  2. Coulomb Branches from Geometry (Lecture 1, Lecture 2 ). Two lectures that I gave at the Learning Seminar on Coulomb Branches at Perimeter Institute in November 2021.

  3. Higgs and Coulomb Branches of 3d N=4 Gauge Theories (pdf). TA session for Joel Kamnitzer's lectures at the IHÉS summer school on Enumerative Geometry, Physics and Representation Theory in July 2021.

  4. "Monopole bubbling" and transversal slice structure in the generalized affine Grassmannian slices (pdf). A talk that I gave at Harbin Institute of Technology in April 2021. Slight modification of my talk at Tsinghua University.

  5. Affine Grassmannian, Orbits, and Slices (pdf). A talk that I gave at Yau Mathematical Sciences Center, Tsinghua University in April 2021. This has almost the same content as my talk at Perimeter Institute, with a bit more details.

  6. Generalized affine Grassmannian slices (slides). Mathematical Physics group meeting, Perimeter Institute for Theoretical Physics, November 2020.

  7. Affine Grassmannian, Slices and Shifted Truncated Yangians (pdf). I gave this lecture in the Geometric Representation Theory Learning Seminar at University of Toronto in April 2020.

  8. Twisted Holography: Example of Bimodules (slides). Quantum Fields and Strings group meeting, Perimeter Institute for Theoretical Physics, April 2020.

  9. Semismall Morphisms (pdf). Affine Pushforward and Smooth Pullback for Perverse Sheaves (pdf). I gave these two lectures in the Perverse Sheaves Learning Seminar at University of Toronto in November 2018.

  10. Topological Holography: Example of the D2-D4 Brane System (slides). Gong Show in the conference on Higher Algebra and Mathematical Physics held at Perimeter Institute for Theoretical Physics in August 2018.

Other Notes

  • Reducedness of Nakajima Quiver Schemes (pdf). This note has been superseded by my paper.

  • Phase Space of Minuscule 't Hooft Operators (pdf). This note extends the results in section 7 of Costello-Gaiotto-Yagi's paper to arbitrary gauge group of ADE type.

  • Another Proof of Givental's Main Lemma (pdf). This proof came out when I was reading Feigin-Finkelberg-Kuznetsov-Mirković's paper on semi-infinite flags.

  • A Note on Quantum ADHM Algebra and Large N Limit (pdf). This note is an expanded version of the appendix A.1 in my joint paper with Jihwan Oh.

  • Remarks on Atiyah's "Instantons in 2d and 4d" (pdf). I wrote this note to fill some gaps in Atiyah's paper "Instantons in 2d and 4d", which helped me to streamline my thought on these instanton stuffs, though the contents in this note is well-known to experts.

  • On the Moduli of Stable N=1 SUSY Curves (pdf). This note fulfills the construction on the compactification of moduli of N=1 SUSY curves proposed in a letter from Deligne to Manin. Afterwards this note was embedded into my joint paper with Sayed F. Moosavian.

  • Proper Flat Unital Magma is Abelian Scheme (pdf). This note generalizes a theorem in Mumford's textbook on Abelian varieties (see appendix to II.4 in Mumford's book).