(09/09/2025) Meeting 1: Preliminaries on the Grassmannian

Event: From Dimers to Webs Reading Group — University of Melbourne

Links:(Handwritten Notes / Slides / Recording)

Abstract: This was the first meeting of the reading group 'From Dimers to Webs', where we covered some preliminaries on the Grassmannian. In particular, we stated and proved the Plücker embedding.

(01/08/2025) Introduction to the representation theory of quivers

Event: Statistics and Mathematics Postgraduate Society (StAMPS) Seminar — University of Melbourne

Links:(Handwritten Notes / Slides / Recording)

Abstract: Take a directed graph but replace the vertices with vector spaces and the edges with linear maps - that’s a quiver representation! In this short talk, you will learn the basics of the representation theory of quivers through the examples of the Jordan and A_2 quivers.

(20/06/2024) Statistics on Young diagrams

Event: Symmetric Functions Seminar — University of Melbourne

Abstract: How good is counting? Don't you wish that you could count more stuff? This talk will be about counting standard and semi-standard tableaux. In learning to count these things, you will find out that you are actually counting the dimensions of irreducible representations of S_n and SL_n.

(22/03/2024) What is a parking function?

Event: Pure Mathematics Student Seminar — University of Melbourne

Abstract: A big part of combinatorics is taking some big and scary-looking maths and creating a pretty picture that contains all that same maths. For my talk, parking functions are the pretty picture and the big scary maths comes from quotient-ing out a 2n-dimensional polynomial ring in two variables by the ideal generated by the S_n invariant polynomials via the diagonal action. For a little peek into this particular world of algebraic combinatorics, come to the talk! (undergraduates should be able to understand - the maths isn't too scary, I promise!).

(14/10/2021) From Boxes to Polynomials

Event: Mathematics & Statistics Society (MUMS) Seminar — University of Melbourne

Links:(Handwritten Notes / Slides / Recording)

Abstract: In this talk, we will take you on a journey from some ostensibly inauspicious boxes all the way to a sneak peek at the Macdonald polynomials, which were introduced by Ian G. Macdonald in 1987 and have since been an area of great research interest. Symmetric functions are functions that remain the same when interchanging variables. They appear in all sorts of areas in mathematics and have many well known examples, such as the elementary symmetric functions, the Schur functions and the Hall–Littlewood symmetric functions. Wouldn’t it be nice to have a general form that captures them all? Especially when it starts with something as simple as counting boxes?