Anita Kristine Ponsaing Home
School of Mathematics and Statistics, University of Melbourne

About Me

I am a lecturer of Complex Analysis (MAST30021) at the University of Melbourne.

Last semester I was a lecturer of Calculus 2 (MAST10006). I have also worked on some science outreach projects for the Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS).

Until November 2014, I was a post-doc with Paul Zinn-Justin at the Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie – Paris VI. Before this I was at the University of Geneva, doing a post-doc under Stanislav Smirnov. I did my PhD at the University of Melbourne under the supervision of Jan de Gier, and my undergraduate (BSc) and honours degrees at the University of Queensland. My honours project was supervised by Tony Bracken.

Research Interests

My mathematical research interests lie in the integrability of lattice models in statistical mechanics. My interest is divided into three main camps:

Physics: The main part of my work is focused on the exact solvability of loop models, and calculating finite-size correlation functions that are related to interesting physical quantities in the continuum limit. Lattice models have many connections to areas such as conformal field theory and phenomena such as Schramm—Loewner Evolution and the Hall effect.

Combinatorics: The finite-size solutions of lattice models often have strong combinatorial properties, a fact which allows both techniques from combinatorics to assist in the discovery of solutions of lattice models, and the properties of lattice models to provide inspiration for the discovery of combinatorial identities. A special example of this is the relationship between alternating sign matrices and the 6-vertex model with domain wall boundary conditions.

Polynomial and representation theory: The solutions of problems posed by lattice models often come in the form of symmetric polynomials. There is wide interest in the role that the representation theory of such polynomials plays in the structure of the lattice models. In addition, polynomial theory has the potential to provide great insight into the possible solutions of a model, as properties of the polynomials (such as recursive properties, symmetries and vanishing conditions) are often mirrored by similar properties in the lattice models.

Other Interests

In the past few years I have developed a strong interest in various aspects of biology, including neuroscience (particularly research on the mind-brain interface), infectious diseases and evolution. I also enjoy tutoring, playing piano, programming, organising events, and birdwatching, in decreasing order of experience.