(The longest journey begins with a single step)
Welcome to the homepage of Thomas Quella at the University of Melbourne. I am a Mathematical Physicist working at the School of Mathematics and Statistics and currently a Distinguished Research Fellow of the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS). My main research interests are 2D conformal field theory and topological aspects of quantum systems. My work frequently touches representation theoretic questions, especially in the context of finite and infinite dimensional Lie (super)algebras, diagram algebras and quantum groups.
I am a member of the School's research groups "Mathematical Physics" and "Algebra".
|04/10/2016||Nobel Prize awarded to three pioneers of topology in condensed matter physics, David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz. See here for the official press release.|
|15/09/2016||I am currently offering projects for the School's Vacation Scholarship Program. Please see the School's website for details of the projects and how to apply.|
|02/05/2016||Started at the University of Melbourne as a Senior Lecturer|
My research interests are centered around various aspects of Mathematical Physics. In particular, I have been working on two dimensional exactly solvable quantum field theories, their mathematical structure and their applications. Most of my group is busy with one or more of the following subjects...
I am available (and more than happy) to supervise undergraduate and graduate theses in representation theory and in fields related to more mathematical aspects of quantum condensed matter physics, quantum field theory and statistical physics. This includes, in particular, theoretical research in the fields of quantum spin liquids, fractional quantum Hall systems, topological insulators, tensor network states and conformal field theory.
Projects with me might centre around the following questions:
If you would like to learn more about available projects please simply send me an email, including a transcript of your previous courses. Note: For some of the projects, some background knowledge in physics, especially quantum mechanics, is required.
Previous projects at the University of Cologne:
I will be offering student projects for the summer break 2019-2020. Please see the School's website for details of the projects and how to apply for the Vacation Scholarship. The Australian Mathematical Sciences Institute (AMSI) also offers Vacation Research Scholarships. Please note that I am also offering to supervise projects outside of the vacation scholarship scheme. In order to ensure enough time commitment this would need to take place outside of regular semester time though.
Previous projects at the University of Melbourne:
Here is a brief description of projects that I have offered in the past
Matter can exist in various different phases. Water for instance can exist in a frozen, a liquid or a gaseous state depending on external parameters such as temperature and pressure. Other materials may exhibit a very complicated phase diagram involving lots of parameters and many distinct phases, potentially even phases of topological origin. When looking at a specific Hamiltonian describing the dynamics of a classical or quantum system with a large number of particles it is usually highly non-trivial to determine the phase the system resides in for a given set of parameters.
In this project the vacation scholar will explore how to describe phases of matter mathematically and use machine learning techniques to map out the phase diagrams of some model systems. Affinity to physics and basic programming experience will be assumed but besides numerical work (with Python) there will also be ample opportunity to gain new analytical insights.
The physical properties of a quantum system generally depend on parameters which determine the strength of various interactions, e.g. the coupling to a magnetic field. Upon variation of these parameters the system exhibits different physical phases with qualitatively different features. Some of these phases can be distinguished by a discrete invariant that takes one value in one phase and another one in a second. This observation provides a link to the mathematical field of topology which studies the properties of geometric objects, such as knots, up to continuous deformations. In view of this connection, one frequently speaks about topological phases of matter. There are various prominent examples which have only been discovered in the last couple of years - first theoretically, then also experimentally.
Building on the example of Kitaev's so-called Majorana chain, a simple free fermion model of a 1D superconductor, the Vacation Scholar will develop some intuition about the associated topological invariant which, essentially, counts the number of Majorana edge modes. She or he will then apply these insights to a closely related system of so-called parafermions and try to derive a topological invariant for these. While the project has a strong analytical/mathematical component, there will also be the possibility to analyse different parafermion systems using computer algebra in case of interest
According to a famous theorem by E. Wigner (1931), symmetries in quantum mechanics need to be implemented by unitary or anti-unitary operators acting on Hilbert space. While known for a long time and responsible for some of the astonishing properties of certain physical models, the implications for some more modern areas of mathematics and mathematical physics seemingly have not been analysed so far.
In this project, the summer vacation scholar will first of all reproduce the statement and the proof of Wigner's Theorem before trying to understand its consequences in various physical situations and making an attempt to incorporate the newly gained freedom in order to generalise established higher algebraic structures such as Hopf algebras and quantum groups.
|2019||Lecture||Mathematical Statistical Mechanics (University of Melbourne)|
|2018||Lecture||Introduction to String Theorygrou (University of Melbourne)|
|2018||Lecture||Complex Analysis (University of Melbourne)|
|2018||Lecture||Advanced Methods: Transforms (University of Melbourne)|
|2017||Lecture||Complex Analysis (University of Melbourne)|
|2017||Lecture||Calculus 2 (University of Melbourne)|
|2016||Lecture||Calculus 2 (University of Melbourne)|
|2016||Block Course||Conformal Field Theory (EPFL, Lausanne)|
|2015||Seminar||Advanced Aspects of Gauge theory (University of Cologne)|
|2015||Lecture||Conformal Field Theory (University of Cologne)|
|2014||Mini Course||Tools from Quantum Information Theory (Bonn-Cologne Graduate School of Physics and Astronomy)|
|2013||Lecture||Quantum Field Theory II (University of Cologne)|
|2013||Seminar||Spin Models (University of Cologne)|
|2012||Lecture||Conformal Field Theory (University of Cologne)|
|2011||Lecture||Quantum Field Theory I (University of Cologne)|
|2010||Lecture||Supersymmetry (University of Cologne)|
|2010||Seminar||Diagram Algebras and their Applications (University of Amsterdam)|
|2009||Mini Course||Conformal Field Theory (National Dutch Seminar)|
|2009||Lecture||Complex Analysis and Laplace Transforms (University of Amsterdam)|
|2007||Seminar||Index Theorems and Anomalies (University of Amsterdam)|
I am more than glad to supervise projects for master students and PhD students. Please simply contact me with details of your academic record and your general research interests. Please note that I currently do not have funding for PhD students or postdocs. If you are interested in applying for one of the competitive internal or external grant schemes please drop me line.
This page provides a brief summary of my academic development.
I am interested in a variety of things. One of them is (moderate) sports. You can find me swimming regularly or inline skating. When I have time during weekends I also enjoy vegetarian cooking (one of my specialties is 红烧茄子) or visiting modern art exhibitions. My attempts to master the secrets of 中文 are probably also worth mentioning.
|Thomas Quella||Visiting address|
The University of Melbourne
School of Mathematics and Statistics
Parkville VIC 3010
Peter Hall Building
813 Swanston Street
Parkville VIC 3052
|02/05/2018||Thomas||Kick-off meeting and outline (Notes)||--||--|
|09/05/2018||Nick||Conformal transformations (Additional Notes)||Ginsparg 1.1-1.2||Special relativity|
|23/05/2018||Thomas||Constraints from conformal invariance||Ginsparg 1.3|
|30/05/2018||Tianshu||CFT in two dimensions||Ginsparg 2.1|
|06/06/2018||Thomas||Radial quantization and the energy momentum tensor||Ginsparg 2.2 (parts of)||Some idea of quantum field theory|
|13/06/2018||Luke||Operator product expansions||Ginsparg 2.2 (parts of)|
|20/06/2018||Zac||Free boson||Ginsparg 2.3|
|27/06/2018||Anas||The central charge and the Virasoro algebra||Ginsparg 3.1 and 3.3|
|04/07/2018||Allan||Free fermion||Ginsparg 3.2 and parts of 6.1|
|11/07/2018||Zac||Hermitean conjugation and in/out states||Ginsparg 3.4|
|18/07/2018||Tyson||Highest weight states||Ginsparg 3.5|
|25/07/2018||Will||Descendant fields||Ginsparg 3.6|
|01/08/2018||Luke||Idea of the conformal bootstrap||Ginsparg 3.7|
|08/08/2018||Anas||Representations of the Virasoro algebra||Ginsparg 4.1|
|15/08/2018||Tyson||The Kac determinant||Ginsparg 4.2|
|Skipped||?||(Non-)Unitarity||Ginsparg 4.3 + Others|
|22/08/2018||Jiyuan||Kac tables and relation to statistical mechanics||Ginsparg 4.4, 4.5 and 5.1 + Others|
|29/08/2018||Zac||Null vectors and correlation functions||Ginsparg 5.2|
|05/09/2018||Tianshu||Fusion rules for minimal models||Ginsparg 5.3|
|Skipped||tba||N=1 superconformal algebra (also N=2?)||Ginsparg 5.4 + Others|
|12/09/2018||Nick||Twist fields and their correlators||Ginsparg 6.2|
|tba||tba||Torus partition functions and modular invariance||Ginsparg|
|tba||tba||Affine Kac-Moody algebras and Wess-Zumino-Witten models||Ginsparg|
Together with Daniel Murfet and Charles Hill I am organising a reading seminar on Quantum Computation. Please follow this link for more details. All seminars will be held Fridays at 10am in the Evan Williams Theatre in the Peter Hall Building (at least until 27/7/2019).
|15/3/2019||James Clift||Universal Turing Machines (notes)|
|22/3/2019||Will Troiani||Reversible Turing Machines (notes)|
|29/3/2019||Thomas Quella||Crash course in quantum mechanics (notes)|
|5/4/2019||Isaac Smith||Feynman’s quantum circuits (notes)|
|12/4/2019||Isaac Smith||Deutsch’s universal quantum computer (Part 1)|
|19/4/2019||No Seminar||Easter Holidays|
|26/4/2019||No Seminar||(Non-teaching week)|
|3/5/2019||Sam Tonetto and Gary Mooney||On the complexity of Ising Spin Glass Models|
|10/5/2019||Stephane Dartois||Deutsch’s universal quantum computer (Part 2)|
|17/5/2019||Charles Hill||Applications of quantum computers 1: Algorithms|
|24/5/2019||Charles Hill||Applications of quantum computers 2: Quantum Annealers|
|Thomas Quella||Physical realisations of quantum computers|
|5/8/2019||James Clift||Classical error correcting codes (notes)|
|13/8/2019||Will Troiani||A Crash Course in Simplicial Homology with Coefficients in Z mod 2 (notes)|
|20/8/2019||Isaac Smith||Quantum error correcting codes (notes)|
|27/8/2019||Isaac Smith||Stabilizer formalism and the toric code (notes)|
|2/8/2019||Thomas Quella||Matrix Product States (notes)|
|Charles Hill||Open problems for mathematicians|