Representation Theory at the Critical Level
Published in Unpublished., 2024
Lecture notes on Representation Theory at the Critical Level.
Posts by Collection
publications
Profinite Groups
Published in Unpublished., 2024
Expository notes on Profinite Groups and Galois theory.
Differential Forms
Published in Unpublished., 2024
Lecture notes on Differential Forms.
seminars
Geometric Langlands
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In Fall 2023, we are discussing the Geometric Langlands Correspondence.
Monstrous Moonshine
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In Spring 2024, I am organising the Participating Algebra Seminar on Monstrous Moonshine.
Jet Schemes and W-Algebras
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In Spring 2025, we are learning about Jet Schemes and W-Algebras, following Arc Spaces and Vertex Algebras by Tomoyuki Arakawa and Anne Moreau.
talks
Cayley Graphs
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I presented a talk at the Fall 2021 DRP Colloquium on Cayley Graphs. I read the first chapter of Hatcher and prepared a presentation on Cayley Graphs. I worked with Riley Thornton.
Stable Homotopy
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I presented a talk at the Fall 2022 DRP Colloquium on Stable Homotopy. I read from various texts, including Boardman’s Stable Homotopy Theory, Adams’ blue book, and Barnes-Roitzheim’s Foundations of Stable Homotopy Theory. I worked with Ben Szczesny.
Fargues-Fontaine Curve
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I presented a talk at the UCLA Number Theory Participating Seminar on the Fargues-Fontaine Curve. Following Scholze’s Berkeley Notes, I introduced the Fargues-Fontaine curve from three perspectives: as a curve parametrising the untilts of a perfectoid ring, as a special “period ring,” and finally as a diamond, unifying the previous concepts.
Category Theory
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I presented a talk at the UMC Undergraduate Talks on basic category theory. I introduced some basic definitions of categories and functors, and gave some practical examples, such as the chain rule being an aspect of the derivative being a functor and adjoints motivating the construction of free groups.
Split Semisimple Groups
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I presented a talk at the UCLA Participating Algebra Seminar on Split Semisimple Groups. Following Chapter 25 of Knus-Merkurjev-Rost-Tignol’s The Book of Involutions, I introduced the definitions of split semisimple groups and their representations. I constructed root systems and proved that every split semisimple admits a central isogeny from a simply connected group and to an adjoint group, and classified the classical groups (type A, B, C, D) via root systems.
Limits, Colimits, Etc.
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I presented a talk at the UCLA Infinity Categories Seminar on Limits, Colimits, and their Constructions. Following Sections 2.3 and 2.4 of Riehl-Verity’s Elements of Infinity Category Theory, I introduced diagram infinity-categories, defined limits and colimits in the infinity-categorical setting, and proved the preservation of limits by right adjoints.
Tame and Wild Quivers
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I presented a talk at the UCLA Quiver Representations Seminar on Tame and Wild Quivers. Following Chapter 7 of Kirillov’s Quiver Representations and Quiver Varieties, I introduced the definitions of tame and wild quivers, the tame-wild dichotomy (due to Drozd), and introduced the necessary technology to prove a connected quiver is tame iff it is Euclidean: affine Kac-Moody algebras and their root systems, affine Coxeter elements, and defect classification of preprojective/preinjective/regular representations.
McKay Correspondence I
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At the UCLA Summer Quiver Representations Seminar, I started off the seminar by introducing classical McKay Correspondence. Starting from the classification of finite subgroups of SU(2) via spherical polyhedra, I detailed the construction of the McKay quiver and the ADE classification associated to it.
McKay Correspondence II
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At the UCLA Summer Quiver Representations Seminar, I continued from last week by introducing Geometric McKay Correspondence, via the classification of equivariant sheaves on P^1.
Geometric Satake Correspondence I
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At the UCLA Geometric Langlands Seminar, I introduced the Geometric Satake Correspondence by defining Tannakian categories, describing the basics of Tannakian reconstruction, and sketching a (very vague) proof of the correspondence via Mirković-Vilonen’s approach.
Jacquet-Langlands Correspondence
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This was my final project for Math 205B Topics in Number Theory. The course covered L-functions after Tate’s thesis, and I gave my talk on the Jacquet-Langlands correspondence.
Introduction to Monstrous Moonshine
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I organised the UCLA Participating Algebra Seminar in Spring 2024. We discussed Monstrous Moonshine, and I introduced the seminar by giving a broad description of the pieces in Moonshine and how they fit together.
teaching
Olga Radko Endowed Math Circle
Math Circle, UCLA, 2021
I have been teaching at the Olga Radko Endowed Math Circle as a Lead Instructor from Fall 2021-present. I’ve led classes for students aged 11-18 and introduced them to advanced mathematical topics such as group theory, random walks, and combinatorial game theory. I worked on curriculum development, instructor training, and administration alongside my teaching duties.
Math 120
Coaching, Yale University, 2024
I am the TA for Math 120 at Yale this Fall. Together with Pedro Suarez, I run weekly review sessions up until the first midterm.