Wednesday, 5 June @ @EMPG seminar, 2:30-3:30pm
Guglielmo Lockhart (Bonn)
Wednesday, 13 March @ @EMPG seminar, 4:00pm
Murad Alim (HW)
Wednesday, 28 Feb @ @EMPG seminar, 4:00pm
Andrea Ferrari (UoE)
Wednesday, 31 January @EMPG seminar, 2:30-3:30pm
Ibou Bah (John Hopkins)
Wednesday, 17 Jan @Algeba seminar
9:30 - 10:30 Jenny Brown (Edinburgh)
Wednesday, 10 Jan @Algeba seminar
9:30 - 10:30 David Ben Zvi (Austin)
Wednesday, 13 December @EMPG seminar, 4-5pm
Alba Grassi (Geneva)
Wednesday, 29 November
Algebra seminar 9:30am Dylan Butson (Oxford)
Category theory seminar 12pm Martin Zika (Charles University)
EMPG seminar 2:30pm Mikhail Bershtein (Edinburgh)
Wednesday, 4 October @EMPG seminar, 4-5pm
Ian Strachan (Glasgow)
Wednesday, 13 September @Algebra Seminar, Bayes 5.46 9:30-10:30am
Joerg Teschner (Hamburg): Quantum Analytic Langlands correspondence
Wednesday, 6 September @Algebra Seminar, Bayes 5.46 9:30-10:30am
Thomas Creutzig (Alberta): Tensor categories for vertex algebras and quantum groups
Abstract: Representation categories of quantum groups and vertex algebras are often braided tensor categories. I want to introduce a few different ways on how to think about categories of modules of quantum groups and in particular use this to explain how they relate to categories of modules of certain vertex algebras.
Wednesday, 24 May @EMPG seminar, Room S.1 of 7 George Square,14:30-15:30pm
Michele del Zotto (Uppsala): Higher symmetries and geometry
Abstract: I will review some recent progress in the context of geometric engineering limits of M-theory and their interplay with higher symmetries of (supersymmetric) field theories.
Wednesday, 19 October @EMPG seminar, Appleton LT2 4-5pm
Alessandro Tomasiello (Milan): Supersymmetry enhancement and the geometry of three-manifolds
Models with large supersymmetry are unrealistic, but over the years they have proven to be a very fruitful playground for improving our understanding of quantum field theory. In this talk we will consider a new class with eight supercharges in three spacetime dimensions. The simplest example gives a way to enhance the supersymmetry of a model with three Chern--Simons gauge fields (which generically only allows for six supercharges), when the inverses of the levels sums up to zero. We will also see evidence that our class arises by compactifying the mysterious six-dimensional 'M5' model on a three-manifold. Our method reproduces for example the condition for a Seifert manifold to have enhanced holonomy. More generally our class should be related to so-called graph-manifolds. The condition for enhancement is related to a jump in homology groups, and seems to suggest a non-abelian analogue of the theory of 'transversely holomorphic foliations'.
Friday, 11 February
Mathew Bullimore (Durham): Generalized symmetries in 3d N=4 theories
I will discuss aspects of higher-form and higher-group symmetries and their 't Hooft anomalies in supersymmetric theories in three dimensions and comment on the action of 2-group symmetries on categories of line operators in topological twists of 3d N = 4 theories.
Andrea Ferrari (Durham): Generalized symmetries and moduli stacks of vacua
3d N=4 supersymmetric gauge theories enjoy geometrically rich moduli spaces of vacua that capture important aspects of their infrared behaviour. For instance, the moduli spaces sometimes take the form of conical symplectic singularities or resolutions thereof, with global IR symmetries of the theories acting as Hamiltonian isometries. I will suggest that it is useful to promote these spaces to stacks, which encode the presence of topological sectors and carry the action of higher-form and higher-group symmetries.
Friday, 11 March
Ingmar Saberi (LMU Munich): Twisted eleven-dimensional supergravity and exceptional Lie superalgebras
In recent years, there has been a great deal of progress on ideas related to twisted supergravity, building on the definition given by Costello and Li. Much of what is explicitly known about these theories comes from the topological B-model, whose string field theory conjecturally produces the holomorphic twist of type IIB supergravity. By contrast, no topological string theory approach to eleven-dimensional supergravity is available, so that one must work directly in the target space. I will discuss a rigorous computation of the twist of the eleven-dimensional supergravity multiplet, as well as an interacting BV theory with this field content that conjecturally describes the twist of interacting perturbative supergravity. Surprisingly, the resulting holomorphic theory on flat space is closely related to the infinite-dimensional exceptional simple Lie superalgebra E(5,10), while the theory on the M5 brane is related to another exceptional simple algebra called E(3,6), which provides an infinite-dimensional enhancement of six-dimensional superconformal symmetry in the twist.
Murad Alim (Hamburg): Non-perturbative quantum geometry, resurgence and BPS structures
BPS invariants of certain physical theories correspond to Donaldson-Thomas (DT) invariants of an associated Calabi-Yau geometry. BPS structures refer to the data of the DT invariants together with their wall-crossing structure. On the same Calabi-Yau geometry another set of invariants are the Gromov-Witten (GW) invariants. These are organized in the GW potential, which is an asymptotic series in a formal parameter and can be obtained from topological string theory. A further asymptotic series in two parameters is obtained from refined topological string theory which contains the Nekrasov-Shatashvili (NS) limit when one of the two parameters is sent to zero. I will discuss in the case of the resolved conifold how all these asymptotic series lead to difference equations which admit analytic solutions in the expansion parameters. A detailed study of Borel resummation allows one to identify these solutions as Borel sums in a distinguished region in parameter space. The Stokes jumps between different Borel sums encode the BPS invariants of the underlying geometry and are captured in turn by another set of difference equations. I will further show how the Borel analysis of the NS limit connects to the exact WKB study of quantum curves. This is based on joint works with Lotte Hollands, Arpan Saha, Iván Tulli and Jörg Teschner.
Friday, 8 April
Dylan Butson (Oxford): Vertex algebras of divisors in toric Calabi-Yau threefolds from perverse coherent extensions
I'll explain work in progress, joint with Miroslav Rapcak, on geometric constructions of vertex algebras associated to divisors in toric Calabi-Yau threefolds, in terms of moduli stacks of objects in certain exotic abelian subcategories of complexes of coherent sheaves on the underlying threefold. These vertex algebras were originally proposed by Gaiotto-Rapcak, in analogy with those proposed by Feigin-Gukov for smooth four manifolds, and constructed mathematically in the example of affine space by Rapcak-Soibelman-Yang-Zhao, building on Schiffmann-Vasserot's proof of the AGT conjecture. We give a geometric explanation and generalization of the quivers with potential that feature in the latter results, and outline the analogous construction of vertex algebras in this setting.
Friday, 6 May
Ingo Runkel (Hamburg): Topological defects and generalised orbifolds
Topological defects in quantum field theory can be understood as a generalised notion of symmetry, where the operation is not required to be invertible. Duality transformations are an important example of this. By considering defects of various dimensions, one is naturally led to more complicated algebraic structures than just groups. So-called 2-groups are a first instance, which arise from invertible defects of codimension 1 and 2. Without invertibility one arrives at so-called fusion categories. I would like to explain how one can "gauge" such non-invertible symmetries in the case of topological field theories, and I will focus on results in two and three dimensions. This talk is based on joint work with Nils Carqueville, Vincentas Mulevicius, Gregor Schaumann, and Daniel Scherl.