笔记
我在哥伦比亚大学、马萨诸塞大学、波士顿学院和 Simons 中心的课程与讨论班上整理的笔记，均为 PDF。
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Summer 2026
Log GLSM and related topics
These are notes from the summer school "Log GLSM and advances in enumerative geometry" at Sichuan University, Meishan campus in July 2026.
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Jan 2025
Higher genus GW theory
What does it take to prove enumerative mirror symmetry for the quintic 3-fold in higher genus? Find out more about recent breakthroughs here.
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Spring 2024
Blowup formula in GW theory
How do GW invariants change under birational transformations? Learn about Iritani's work on the subject here.
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Summer 2023
Simons Summer Math Workshop 2023
Covers log GW theory in both the algebraic and symplectic settings, topological recursion and the spin GW/Hurwitz correspondence, and Givental-Teleman reconstruction of semisimple CohFTs.
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Summer 2022
Integrability, enumerative geometry, quantization
Covers enumerative geometry (GW/Hurwitz, GW/DT, quantum K-theory) and (quantum) integrable systems (KdV, W-constraints, etc).
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Spring 2026
Good moduli spaces, positivity, and rationality
When does an Artin stack admit a "reasonable" moduli space and when does this moduli space have nice properties (for example being (quasi-)projective, rational, etc)?
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Spring 2026
Geometric rep theory and universal centralizers
Covers the geometry of complex semisimple Lie groups (Springer theory, wonderful/toroidal compactifications) before moving on to universal centralizers (and their geometry, mirror symmetry, etc).
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Fall 2021
Moduli spaces and hyperkähler manifolds
Covers hyperkähler manifolds, their geometry, some constructions, and moduli spaces of sheaves on K3 surfaces.
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Spring 2021
Minimal Model Program
Ever wondered how to classify algebraic varieties up to birational equivalence? The MMP is the answer! Covers the basics of the MMP and the MMP in dimension 3.
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Spring 2021
Class field theory
Covers local and global class field theory, including the proofs of the main theorems and some applications.
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Spring 2021
Algebraic topology II
Covers spectral sequences and applications to homotopy groups of spheres, characteristic classes, K-theory, and the Atiyah-Singer index theorem.
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2023-24
The Count of Instantons
On the mathematics (representation theory, geometry, probability theory) and physics (gauge theory) of instanton counting. Notes partially taken by Davis Lazowski.
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Fall 2020
Commutative algebra
Covers the first part of Matsumura's Commutative Algebra with a focus on dimension theory.
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Spring 2022
Informal enumerative geometry seminar
Covers a variety of topics in enumerative geometry, including GW theory, DT theory, and quantum K-theory and its relationship to geometric representation theory.
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Spring 2022
Hyperbolicity
When is a variety hyperbolic? How many rational points does it have? How many rational curves lie on it? Find out here!
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Spring 2022
D-modules and localization
What is a D-module and how do they appear in representation theory? Learn about the Beilinson-Bernstein localization theorem and the Kazhdan-Lusztig conjectures.
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Fall 2021
Hodge theory
Covers the proof of the existence of mixed Hodge structures for smooth varieties and some applications.
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Fall 2021
Deformation theory
Covers how to deform schemes and sheaves, plus the moduli of stable curves and of coherent sheaves.
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Fall 2021
DAHA and knot homology
What on earth is a double affine Hecke algebra? How does it relate to more familiar mathematics? Find out here!
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Fall 2021
Category O
Covers the basic theory of category O for semisimple Lie algebras, including the Kazhdan-Lusztig conjectures.
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Spring 2021
Intersection theory
Ever wondered what a Chow ring is? Or how to compute intersection numbers on moduli spaces? Find out here!
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Spring 2021
Schemes
Covers schemes, sheaves, and cohomology, mostly following Hartshorne.
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Spring 2021
Lie groups and representations II
Covers invariant theory, Lie algebra cohomology, the cohomology of flag varieties, root systems, and Kac-Moody Lie algebras.
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Fall 2020
Geometric invariant theory
Covers the basics of reductive GIT and applications to moduli spaces of curves.
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Fall 2020
FGA explained
Ever wondered what Grothendieck meant in FGA? Find out here!
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Fall 2020
Lie groups and representations I
Covers the representation theory and classification of semisimple Lie groups.
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Fall 2020
Algebraic topology I
Covers homotopy groups, homology, cohomology, and Poincaré duality.
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Spring 2020
Singular spaces
What is a singularity? How can we measure how bad it is and study its geometry? Find out here!
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Spring 2020
Symplectic topology
Covers the basics of symplectic manifolds and some results in the topology of symplectic 4-manifolds.
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Fall 2019
Lie Algebras
Covers the basic theory of Lie algebras and the classification and representation theory of semisimple Lie algebras.
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Fall 2019
Manifolds
Covers the basic theory of smooth manifolds, differential forms, and de Rham cohomology.
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Spring 2019
Varieties
Covers the basic theory of algebraic varieties, including dimension, tangent spaces, and divisors.
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Spring 2019
Algebra II
Covers the basic theory of algebraic varieties, including dimension, tangent spaces, and divisors.
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Spring 2019
Analysis II
Covers Hilbert and Banach spaces, convergence and compactness in infinite dimensions, and Fourier theory.
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Fall 2018
Representation theory
Covers the representation theory of finite groups, Springer theory in type A, and the representation theory and classification of SLn.
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Fall 2018
Analysis I
Covers measure theory, the Lebesgue integral, differentiation, and abstract measure theory.
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Spring 2018
Complex analysis
Covers the basic theory of holomorphic functions, elliptic functions, and the Riemann mapping theorem.