Omega Tong
Email: onttong at math dot cuhk dot edu dot hk
CV
I am a second year MPhil student at the Chinese University of Hong Kong, under the supervision of Prof. Michael McBREEN.
I am interested in the connection between combinatorics, geometry, representation theory and mathematical physics, with a particular interest in matroid theory. I am currently working on hypertoric varieties and quiver varieties.
Omega Tong
Email: onttong at math dot cuhk dot edu dot hk
CV
I am a second year MPhil student at the Chinese University of Hong Kong, under the supervision of Prof. Michael McBREEN.
I am interested in the connection between combinatorics, geometry, representation theory and mathematical physics, with a particular interest in matroid theory. I am currently working on hypertoric varieties and quiver varieties.
Preprints
Talks and Presentations
- Seminar on Quantum Groups and Quantum Cohomology at CUHK, Fall 2024 - present.
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- The goal of this seminar is to go through the book Quantum Groups and Quantum Cohomology by Davesh Maulik and Andrei Okounkov.
- This book proves a famous conjecture about supersymmetric gauge theory (The Alday-Gaiotto Tachikawa conjecture) using an action of a quantum group (the Yangian) on the cohomology of quiver varieties. Stable envelopes are introduced in order to define this Yangian action.
- Seminar on Quiver varieties, quantum groups and quasi maps at CUHK, Janurary 2024.
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- Studied quantum groups and their Hoft algebra structure by quantizing the Poisson manifolds
- Discussed Drinfeld center, R-matrix, affine quantum groups, and Yangians
- Learned Quiver varieties as a generalization of hypertoric varieties and how quiver varieties can be realized as representations of quantum groups
- Seminar on Supersymmetric gauge theory at CUHK, Fall 2023 - Spring 2024.
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- Learned symplectic reduction by considering symmetries in classical mechanics systems, and its application to toric and hypertoric geometry
- Studied the quantization of classical mechanics as QFT, as well as SUSY QFT and its connection with Morse theory
- Seminar on Coxeter Matroids with Xuhua He, Fall 2022.
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- Defined matroids in terms of the symmetric group, or Coxeter group for the generalization (Matroids have a natural symmetric group action on the set of bases by the Exchange Property)
- Learned Lie Theory from a combinatorics viewpoint by studying Lie-type matroids
- Studied Coxeter Building and its application in constructing Coxeter MatroidsLearned symplectic reduction by considering symmetries in classical mechanics systems, and its application to toric and hypertoric geometry