August 11, 2025: UNSW Mathematics and Statistics postgraduate conference. Classifying algebraic surfaces
Abstract: In this talk I discuss how to (begin to) classify smooth projective varieties over the complex numbers. By considering the graph G whose vertices correspond to surfaces and whose arrows correspond to blow-ups of surfaces, we can study the complete family of surfaces by studying properties of G and its connected components.
April 29, 2025: UNSW pure mathematics seminar (PhD confirmation talk). The Sarkisov Program
Abstract: When pursuing a classification program as broad as the Mori program - the classification of projective varieties up to birational equivalence - it is critical to have a series of guiding strategic schemes by which to approach the classification. For instance, (1) isolate some distinguished representatives to be considered the ‘best’ in each equivalence class, and (2) understand the relationships between the many possible best representatives. Towards scheme (2), in this talk I will give a visual introduction to the Sarkisov program - an elegant algorithm which factorises birational maps between best representatives (when the best representative is not unique) into a series of ‘elementary’ transformations (of which there are exactly 4 types).
March 3, 2025: UNSW Mathematics and Statistics PhD/Masters Seminar. Classifying algebraic curves and surfaces
Abstract: One of the ultimate goals of algebraic geometry is the attempt to classify all geometric objects obtained by systems of polynomials up to some notion of “isomorphism.” In practice, this is too difficult and so we must loosen some conditions to say anything meaningful. In this talk, I will give a very rough outline of what classification theory looks like in the case of algebraic curves and surfaces (over the complex numbers) using the weaker notion of “birational equivalence.” Minimal knowledge is assumed, and all are welcome!
November 16, 2023: UNSW pure mathematics seminar (Honours talk). Cubic surfaces and their 27 lines
Abstract: Anyone who deals with algebraic geometry has at some point in their lives heard the phrase "every cubic surface has 27 lines." The result itself was first proved in 1849 by Cayley and Salmon, and yet continues to charm modern geometers. Why, for instance, should we expect an arbitrary cubic surface to have finitely many lines? Moreover, why is the symmetry group acting on the configuration of lines the Weyl group W(E_6) of the exceptional root system E_6? I plan to discuss the answer to both of these questions. I will conclude by briefly placing the story of cubic surfaces (and more generally, del Pezzo surfaces) in a modern context, with a view towards two active areas of research: the Minimal Model Program on one side, and the intersection between del Pezzo surfaces and representations of Lie algebras on the other.
In this section, you can find a selection of my writings. There are bound to be errors and such, so my apologies in advance. In addition, I have typed notes and typed problem set solutions for some UNSW pure math courses, so contact me if you would like access to those.
My Honours project was under the supervision of Daniel Chan. For those interested, a version of my thesis can be found here.
T3, 2025: MATH2069 Mathematics 2A tutor, MATH2701 Algebra and Analysis assignment marking
T1, 2025: MATH1141 Higher Mathematics 1A tutor, MATH2019 Engineering Mathematics 2E tutor, Drop-in centre tutor
T3, 2024: Drop-in centre tutor, Nura Gili ITP tutor, private tutoring
T2, 2024: MATH1231 Mathematics 1B tutor, Drop-in centre tutor, Nura Gili ITP tutor, private tutoring
T1, 2024: Drop-in centre tutor, private tutoring
6 September, 2025: Outreach work for UNSW Mathematics and Statistics, UNSW Open Day 2025
T2, 2025: Member of the organising committee, speaker, and plenary chair for the UNSW Mathematics and Statistics postgraduate conference 2025
T2, 2025: Supporting demonstrater for the Do The Maths workshop outreach event
T2, 2025 - Present: UNSW Mathematics and Statistics HDR representative
T2, 2025 - Present: Weekly organiser (and sometimes presenter) for the local fields reading group at UNSW
T1, 2025: Weekly presenter for the algebraic geometry reading group at UNSW
T1, 2025 - Present: Member of the UNSW Mathematics and Statistics social committee
T1, 2025 - Present: Founder and organiser for the UNSW Mathematics and Statistics PhD/Masters seminar
16-18 December, 2024: Attended the SMRI Algebraic Geometry workshop
9-13 December, 2024: Attended the MATRIX Algebraic Geometry conference
T2, 2024: Informal assistance with the course MATH5535 Algebraic Geometry, typed (incomplete) notes which I plan to get back to at some point