Lectures and speakers
Scientific program
The five courses that make up the school will each have 5 lectures and around 3 hours of tutorial time. The school will take place at Maynooth University from 21 to 27 April 2024.
Pre-courses (online)
Mathematical foundations, by Pieralberto Marchetti
CFT basics, by Christian Northe
Courses (in person at Maynooth U.)
Chern-Simons and Anyons, by Pieralberto Marchetti
Topological insulators, by Flore Kunst
Defects and boundaries, by Christian Northe
Generalised and non-invertible symmetries, by Ho Tat Lam
Topology in quantum computation, by Yizhi You
The arrival day of the school is the 21st and the departure day is the 27th.
The lectures will start on the morning of the 22nd and end in the late afternoon of the 26th.
Chern-Simons and anyons, Pieralberto Marchetti
In quantum systems the complex-valued wave-function of identical - particle excitations acquires a phase factor under an exchange between two of them. If exchanges with opposite orientation produce inverse but different phase factors such particles are called (abelian) anyons. The same phase factors arise in the quantum field theory framework if we perform an equal-time oriented exchange of the fields creating the corresponding particle excitations.
Anyons can only exist in d<3 space dimensions, where the exchanges can be oriented, namely one can distinguish an exchange from its inverse.
Since oriented exchanges generate the braid groups, the corresponding statistics is called braid statistics.
In this course we will firstly show the emergence of braid statistics from general considerations, then introduce a quantum-mechanical toy model of anyons and afterward the quantum field theory treatment of anyons using Chern-Simons theory.
Then we will present the system where such particle excitations have been experimentally proved to appear in the physical world: the fractional quantum Hall effect.
Next we will discuss general properties of anyons: the relation with parity- breaking, spin-statistics connection and scattering theory.
Finally we will briefly consider a non-abelian generalization of anyons, for which the representation of the braid groups is higher dimensional, its relation with Yang-Baxter equations and possible applications to quantum computation.
Pieralberto Marchetti
Pieralberto Marchetti got his PhD from the International School for Advanced Studies of Trieste with supervisor J. Froehlich (ETH Zuerich) and currently is Associate Professor at Padova University.
Topological insulators, Flore Kunst
Since the discovery of the quantum Hall effect in 1980 and the subsequent realization that electronic bands can have topologically non-trivial properties, the field of topological phases of matter has been thriving. In this course, the concept of topological insulators will be introduced as well as experimental realizations of these phases. In particular, we will cover topics ranging from topological band theory and the integer and fractional quantum Hall effect to Chern insulators and their connection to Weyl semimetals. We will encounter concepts such as the bulk-boundary correspondence, topological invariants, topological boundary states, and the tenfold way. Realizations of these phases both in solid-state materials as well as artificial platforms will be reviewed. If time permits, we will also briefly discuss topology in the context of non-Hermitian systems, which opens up a whole new avenue of fascinating phenomena to explore.
Flore Kunst
Flore Kunst (Max Planck Institute for the Science of Light) works on non-Hermitian topological phenomena. She studies a wide range of topics in this field varying from simple toy models to open and correlated quantum systems, while also closely collaborating with experimental colleagues. She obtained her PhD in 2019 at Stockholm University, after which she joined the Max Planck Institute of Quantum Optics for a Postdoc. In November 2021, she started her independent research group at the Max Planck Institute for the Science of Light in Erlangen, Germany.
Defects and boundaries, Christian Northe
An introduction to boundaries, defects and interfaces is provided. Time is spent explaining Ishibashi states and the Cardy constraint. Using the folding trick, the more general notion of a defect and interface is introduced. Application to boundary RG flows or the study of entanglement will be discussed.
Christian Northe
Christian Northe, currently a postdoctoral fellow at Ben-Gurion University, works with various aspects in low-dimensional quantum field theories, including RG flows, topological phases of matter and holography. Lately, his focus has shifted to entanglement studies in conformal field theories in presence of boundaries and defects.
Generalised and non-invertible symmetries, Ho Tat Lam
This course will provide an introduction to generalized global symmetry, with a specific emphasis on non-invertible symmetry. Non-invertible symmetries are symmetries characterized by the absence of inverse operations. Despite this distinction, many properties associated with ordinary symmetries remain applicable to non-invertible symmetries. These non-invertible symmetries lead to conservation laws, selection rules and constraints on renormalization group flow. Throughout the course, we will explore generalized symmetries through a diverse range of examples.
Ho Tat Lam
Ho Tat Lam is currently interested in various aspects of quantum field theories with connections to particle and condensed matter physics. He obtained his PhD from Princeton University in 2021 and is now a postdoctoral researcher at Massachusetts Institute of Technology.
Topology in quantum computations, Yizhi You
In this lecture, we will commence by exploring the concept of permutation groups within the context of quantum computation. Subsequently, we'll delve into stabilizer codes and their significance in quantum computation. Special emphasis will be given to measurement-based quantum computation and the impact of decoherence under quantum channels on stabilizer codes.
Yizhi You
Yizhi You's research focuses on a variety of problems in the field of quantum many-body theory. Her primary focus is the study of collective phenomena arising due to quantum mechanical effects in systems of correlated electrons. Areas of research include the study of fracton phases of matter, quantum field theory, and entanglement dynamics. She is currently at Northeastern University.