The Mathematics of Conformal Field Theory

The rich and varied cross-fertilisation between physics and mathematics has led to fantastic advances in each field. An standout example is two-dimensional conformal field theory (CFT), these being two-dimensional quantum field theories that are covariant with respect to local conformal transformations. Thanks to their intricate symmetry algebras, CFTs belong to the exceedingly rare class of exactly solvable interacting quantum field theories. Moreover, CFTs provide a natural source of new mathematical structures and so build bridges between seemingly disparate mathematical fields. This conference will bring together international leaders from the mathematics and mathematical physics communities to foster communication and collaboration.

Invited Speakers

Professor Matthias Gaberdiel (ETH Zurich)
Professor Gaberdiel is, by no stretch of the imagination, one of the luminaries of mathematical conformal field theory and string theory research. His work is always of the highest standard and has garnered a reputation for being able to bring clarity to even the most difficult conceptual problems and then solve them “properly”, even while addressing all the mathematical technicalities that this entails. He is also one of the few people in the world who can tell Witten when he’s made a mistake (and be correct). Gaberdiel is one of the key figures in the higher spin community and has recently co-edited a special issue of the Journal of Physics A on this topic. His earlier work on logarithmic theories, which amounts to studying non-semisimple modules for vertex operator algebras, coupled with his unsurpassed reputation, makes him a perfect drawcard for domestic and international attendees. We are very lucky to have secured his attendance.

Professor Terry Gannon (University of Alberta)
Professor Gannon works at the interface between vertex operator algebras, number theory and subfactors. He is well known for his work on the classification of modular invariant partition functions in rational conformal field theory, for introducing Galois symmetries to physicists, for proving some of the main conjectures of Mathieu moonshine and for being the only person in the world able to talk shop with both the CFT and subfactor communities. He is also a talented expositor, as his monograph on monstrous moonshine indicates, and will make a perfect plenary speaker for mathematicians attending this conference.

Professor Geoff Mason (University of California, Santa Cruz)
Professor Mason is a highly acclaimed algebraist who has made many important contributions to the representation theory of vertex operator algebras with a strong recent focus on modular forms and their generalisations as well as earlier contributions to the classification of finite simple groups. His recent work on logarithmic vector-valued modular forms is a crucial part of current efforts to advance our understanding of logarithmic conformal field theory. Mason is renowned as a speaker able to convey complicated ideas in an easygoing and natural manner as evidenced by his frequent invitations to present lecture courses to graduate students. We therefore expect that students will welcome the opportunity to interact with him during this conference.

Professor Paul Pearce (University of Melbourne)
Professor Pearce is one of the local experts on the relationship between statistical lattice models and conformal field theories. He is highly regarded for his ongoing work analysing certain lattice models that are believed to realise logarithmic conformal field theories in the continuum limit. Many recent advances in this area have been spurred by the many conjectures that his numerical investigations have indicated. He is a perfect representative for the domestic math physics community and is very well respected as a speaker.

Professor Ingo Runkel (University of Hamburg)
Professor Runkel is an expert on category-theoretic aspects of conformal field theories and integrable models. He is probably best known for a series of groundbreaking, and enormously influential, papers that use the mathematical structures underlying topological field theories to rigorously define, and then prove deep results about, (rational) conformal field theory. His more recent work has focused on the braided monoidal categories that arise in seemingly disparate areas of mathematics and physics. Aside from the interest of math physicists in these structures, we expect that his work will be of significant interest to a large cross-section of the domestic mathematics community.

Professor Hubert Saleur (CEA Saclay / University of Southern California)
Professor Saleur has been at the forefront of statistical lattice model research for almost thirty years. A hugely influential figure in mathematical physics, he is widely credited with demonstrating the effectiveness of associative algebra representation theory, particularly that of the diagram or cellular algebras, to the physics community. His recent work on combining the representation theories of these algebras with those of quantum groups to analyse spin chain models with logarithmic scaling limits indicates that many paradigms long-cherished by physicists are about to be overturned.

Professor Alexei Semikhatov (Lebedev Physical Institute)
Professor Semikhatov is an extremely highly regarded researcher at the leading edge of mathematical conformal field theory research with nearly 100 publications in the best mathematical physics journals. In particular, his work on logarithmic theories with Feigin and Tipunin was instrumental in reinvigorating the field and his recent work on characterising these types of theories using the (currently hot) formalism of Nichols algebras represents a huge advance in our understanding. In addition, he is an extremely entertaining speaker with an infectious manner of encouraging discussion.