Here are the notes to some of my presentations (since Fall 2022)
***************These are unedited and will very likely contain errors*********************
Proof of Tate's Conjecture: II, the Shafarevich Conjecture (May 2025)
UCLA Participating Number Theory Seminar (Organized by Dr. Ziyang Gao)
Proof of Tate's Conjecture: I (April 2025)
UCLA Participating Number Theory Seminar (Organized by Dr. Ziyang Gao)
Class Field Theory for Quadratic Imaginary Fields via CM Elliptic Curves (March 2025)
Final Assignment for UCLA topics course on Class Field Theory (Dr. Romyar Sharifi)
Faltings Height and Theta Height II (Feb 2025)
UCLA Participating Number Theory Seminar (Organized by Dr. Ziyang Gao)
Representation of Finite Lie-Type Groups in Defining Characteristic (Feb 2025)
UCLA Participating Algebra Seminar (Organized by Sam Qunell)
Faltings Height and Theta Height_I (Feb 2025)
UCLA Participating Number Theory Seminar (Organized by Dr. Ziyang Gao)
Absolute Hodge Cycles, Mumford-Tate Groups and Principle A (Feb 2025)
UCLA MATH 207A (Topics in Number Theory, Dr. Don Blasius)
This note contains only parts of what I planned to cover. Will possibly be updated.
A Brief Introduction to the Theory of Heights (Jan 2025)
UCLA Participating Number Theory Seminar (Organized by Dr. Ziyang Gao)
Geometric Satake Equivalence (Dec 2024)
UCLA Participating Algebra Seminar (Organized by Dr. Gurbir Dhillon)
Moduli of Elliptic Curves and Deligne-Mumford Compactification (Nov 2024)
UCLA Participating Number Theory Seminar (Organized by Dr. Kim Tuan Do)
Quasi-coherent Sheaves on Algebraic Stacks (May 2024)
Algebraic Stacks Reading Seminar (Organized by Dr. Danny Krashen) at UPenn.
Vojta's Higher Dimensional Mordell's Conjecture (May 2024)
MATH 7210 (Topics in Diophantine Geometry, Dr. Ching-Li Chai) at UPenn.
Algebraic Stacks--Definitions and Properties (April 2024)
Algebraic Stacks Reading Seminar (Organized by Dr. Danny Krashen) at UPenn.
An Introduction to K3 Surfaces and Preparation for Torelli Theorems (April, 2024)
Algebraic Geometry Research Seminar (Organized by Dr. Ron Donagi) at UPenn.
Descent and Stacks (March, 2024)
Algebraic Stacks Reading Seminar (Organized by Dr. Danny Krashen) at UPenn.
From Arithmetic Langlands to Geometric Langlands (February 2024)
Algebraic Geometry Research Seminar (Organized by Dr. Ron Donagi) at UPenn.
Representability Criteria for Schemes (February 2024)
Algebraic Stacks Reading Seminar (Organized by Dr. Danny Krashen) at UPenn.
The Original Proof of the Nirenberg-Newlander Theorem (December 2023)
MATH 6440 (Partial Differential Equations, Dr. Robert Strain) at UPenn.
The ABC Conjecture over Function Fields (December 2023)
MATH 7020 (Algebraic Function Fields, Dr. Julia Hartmann) at UPenn.
Whitehead's Theorem (September 2023)
MATH 6180 (Algebraic Topology I, Dr. Jonathan Block) at UPenn.
BĂ©zout's Theorem in Algebraic Geometry (December 2022)
Directed Reading Program (Mentor: Elijah Gunther) at UPenn.