Expositions
This page collects seminar notes, reading reports prepared for courses, and independent expositions (which were mostly written in my freshman and sophomore years, focusing on some simple algebraic facts or problems).
Some of these writing were originally in Chinese if there is Chinese version available. The English version for these notes were translated and organized by Chatgpt and I haven’t had time to check them.
Seminar Notes
Basics on Symplectic Variety and Lagrangian Fibrations
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Holomorphic Anomaly Equation in Two Polarizations
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This is the notes for my talk in Mirror Symmetry Seminar, organized by Prof. Emanuel Scheidegger in 2026 spring semester. The topic for that semester is to discuss about the paper Quantum Background Independence in String Theory by E. Witten and other consequencet results under his understanding of HAE through the viewpoint of background independence.
I talked about sections 5.1 and 5.2 in the paper Attractors and The Holomorphic Anomaly by E. Verlinde, carrying out concrete calculations of HAE in holomorphic and real polarizations and correcting some error signs in Verlinde’s original paper.Speical Kähler Geometry
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This is the notes for my talk in Mirror Symmetry Seminar, organized by Prof. Emanuel Scheidegger in 2025 fall semester. The topic for that semester is to discuss about the paper BCOV Ring and Holomorphic Anomaly Equation by S. Hosono.
I talked about sections 2-5 and 2-6, adding more mathematical background on special Kähler Geometry which are not discussed in detail in Hosono’s paper.Construction of Hyperbolic Surfaces and Dense Geodesics
English PDF Chinese version · coming soon
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This is the notes for my talk in Undergraduate Geometry Seminar organized by Xiang Ma in 2024 spring semester, in which we read the book Geometry of Surfaces by J.Stillwell.
I talked about section 5.4-5.5 in the seminar, which are about dense geodesics on punctured sphere and construction of hyperbolic surfaces by polygon gluing.Reading Reports
Poisson Deformation of del Pezzo Surfaces
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UChicago Math REU 2026, advised by Victor Ginzburg
Write a brief introduction here.
Deligne’s 5 Decompositions
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Course: COURSE NAME HERE
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Hilbert 90 for K2
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Course: COURSE NAME HERE
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GAGA Theorem
English PDF Chinese version · coming soon
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Course: COURSE NAME HERE
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Geometric Littlewood-Richardson Rule
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Course: COURSE NAME HERE
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Quantum Schubert Polynomial
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Course: COURSE NAME HERE
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Independent Expositions
Equivalence between Flat, Projective and Locally Free Modules
English PDF Chinese version · coming soon
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Calculation of Two Galois Group
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Hua Lo Keng Theorems
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A Double Covering of SO(4)
English PDF Chinese version · coming soon
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