Triangle Seminars
Wednesday, 15 Apr 2026
Conformal field theories in dimensions two and three
📍 London
Zhenghan Wang
(UCSB)
Abstract:
Conformal field theories are both experimentally relevant and mathematically rigorous. One mathematical approach is via generalized spin chains–-anyonic chains in two spacetime dimensions, and fuzzy sphere models in three spacetime dimensions. The anoyon chain approach in two dimensions has applications to the bulk-edge correspondence of 3d TQFTs and 2d CFTs, and the quantum extended Church-Turing thesis, where Temperley-Lieb and Virasoro algebras are crucial. Fuzzy sphere models conjecturally realize 3d CFTs, and there appears an intriguing fuzzy sphere algebra generated by electron density operators on the two-sphere. I will explain a program based on fuzzy sphere algebra and representation theory to find analogues of the Temperley-Lieb and Virasoro algebras from the fuzzy sphere algebra and the diffeomorphism group of S^1 xS^2 aiming at a generalization to one dimension higher of the 3d TQFT—2d CFT correspondence. This talk is based on joint works with M. Shokrian Zini (arXiv:1706.08497), L. Eck (arXiv:2602.15025), and B. Janssens (arXiv:2603.06876).
Conformal field theories are both experimentally relevant and mathematically rigorous. One mathematical approach is via generalized spin chains–-anyonic chains in two spacetime dimensions, and fuzzy sphere models in three spacetime dimensions. The anoyon chain approach in two dimensions has applications to the bulk-edge correspondence of 3d TQFTs and 2d CFTs, and the quantum extended Church-Turing thesis, where Temperley-Lieb and Virasoro algebras are crucial. Fuzzy sphere models conjecturally realize 3d CFTs, and there appears an intriguing fuzzy sphere algebra generated by electron density operators on the two-sphere. I will explain a program based on fuzzy sphere algebra and representation theory to find analogues of the Temperley-Lieb and Virasoro algebras from the fuzzy sphere algebra and the diffeomorphism group of S^1 xS^2 aiming at a generalization to one dimension higher of the 3d TQFT—2d CFT correspondence. This talk is based on joint works with M. Shokrian Zini (arXiv:1706.08497), L. Eck (arXiv:2602.15025), and B. Janssens (arXiv:2603.06876).
Posted by: David Vegh
(A)dS Double Copy in Twistor Space
📍 East of England
Mariana Carrillo-González
(Imperial College London)
Abstract:
The double copy, which relates gravity to the square of Yang–Mills theory, is usually studied in flat spacetime and is known to hold both for scattering amplitudes and for classical field configurations. In this talk, I will present a new approach to extending these results to maximally symmetric curved spacetimes. The new relations are formulated in twistor space, a complex projective space that encodes solutions to the equations of motion as holomorphic data. First, I will discuss the case of AdS₃, where a double copy structure for bulk to boundary correlators and black hole solutions naturally arises in minitwistor space. Then, I will show how in (A)dS₄ one can construct bulk correlation functions using only twistors, dual twistors, and the infinity twistor as building blocks. The relation to coordinate space arises via nested Penrose transform. The boundary limit of these correlators yields CFT correlators that satisfy the expected Ward identities and obey a simple double copy relation.
The double copy, which relates gravity to the square of Yang–Mills theory, is usually studied in flat spacetime and is known to hold both for scattering amplitudes and for classical field configurations. In this talk, I will present a new approach to extending these results to maximally symmetric curved spacetimes. The new relations are formulated in twistor space, a complex projective space that encodes solutions to the equations of motion as holomorphic data. First, I will discuss the case of AdS₃, where a double copy structure for bulk to boundary correlators and black hole solutions naturally arises in minitwistor space. Then, I will show how in (A)dS₄ one can construct bulk correlation functions using only twistors, dual twistors, and the infinity twistor as building blocks. The relation to coordinate space arises via nested Penrose transform. The boundary limit of these correlators yields CFT correlators that satisfy the expected Ward identities and obey a simple double copy relation.
Posted by: Julian Kupka
Automorphic forms, L-functions, and the conformal bootstrap
📍 London
Dalimil Mazáč
(IPhT, Saclay)
Abstract:
I will review an analogy between conformal field theory in d dimensions, and spectral theory of automorphic forms on hyperbolic (d+1)-manifolds. Building on this analogy, I will prove a new bound on triple product L-functions, using the conformal bootstrap. I will discuss in which sense the conformal bootstrap axioms may be complete. Finally, I will review a recent remarkable theorem of Adve that establishes such completeness in the context of the above mentioned analogy. Based on works with A. Adve, J. Bonifacio, P. Kravchuk, S. Pal, A. Radcliffe, and G. Rogelberg.
I will review an analogy between conformal field theory in d dimensions, and spectral theory of automorphic forms on hyperbolic (d+1)-manifolds. Building on this analogy, I will prove a new bound on triple product L-functions, using the conformal bootstrap. I will discuss in which sense the conformal bootstrap axioms may be complete. Finally, I will review a recent remarkable theorem of Adve that establishes such completeness in the context of the above mentioned analogy. Based on works with A. Adve, J. Bonifacio, P. Kravchuk, S. Pal, A. Radcliffe, and G. Rogelberg.
Posted by: David Vegh
Thursday, 16 Apr 2026
Weak Hopf monad symmetries of anyon models
📍 London
Zhenghan Wang
(UCSB)
Abstract:
Part of QMUL-LIMS Quantum London Seminar series
Finite group symmetries of anyon models and their gauging are well-understood. It is natural to wonder what are the most general symmetries of anyon models beyond groups. I will argue that it should be weak Hopf monad generalizing weak Hopf algebras and categorical weak Hopf algebras. This is work in progress with many others, so the talk will be informal and guided by the audience.
Part of QMUL-LIMS Quantum London Seminar series
Finite group symmetries of anyon models and their gauging are well-understood. It is natural to wonder what are the most general symmetries of anyon models beyond groups. I will argue that it should be weak Hopf monad generalizing weak Hopf algebras and categorical weak Hopf algebras. This is work in progress with many others, so the talk will be informal and guided by the audience.
Posted by: Matthew Buican