Triangle Seminars

Abstract:
With a view towards constructing Calabi Yau manifolds, we present some rudiments of the intersection between algebraic, differential and arithmetic geometry. Throughout we will take the opposite of the Bourbaki approach and work through explicit examples, rather than to emphasise on the theory.

Address: 21 Albemarle St, London W1S 4BS
Floor 2: London Institute of Mathematical Sciences (LIMS)

Abstract:
I will present a way to promote the anomalous axial U(1) in 4d QED to an exact symmetry, with the price of losing its invertibility. I will then discuss some applications of this non-invertible U(1) symmetry. In particular, I will show how to couple this non-invertible symmetry to a gauge field. By taking this gauge field to be dynamical, we get a new type of gauge theory with unconventional interactions and constraints. By taking this gauge field to be background, we can study 't-Hooft anomalies of the non-invertible symmetry.

Abstract:
(Email m.godazgar@qmul.ac.uk for zoom link)
Abstract: The exterior dynamics of black holes has played a major role
in holographic duality, describing the approach to thermal equilibrium
of strongly coupled media. The interior dynamics of black holes in a
holographic setting has, in contrast, been largely unexplored. I will
describe recent work investigating the classical interior dynamics of
various holographic black holes. I will discuss the nature of the
singularity, the absence of Cauchy horizons and a new kind of chaotic
behavior that emerges in the presence of charged scalar fields.

Abstract:
4d gauge theories with massless fermions typically have axial U(1) transformations
that suffer from the ABJ anomaly. One can modify the theory of interest by adding
more fields in a way that restores the axial symmetry, and use it to derive rigorous
't-Hooft anomaly matching conditions. These conditions are not valid for the original
theory of interest, but for the modified theory. I will show that the modification can be
done in a specific way that allows us to relate the dynamics of the modified theory to
the dynamics of the original theory. In this way, the anomaly matching conditions of
the modified theory can be used to learn new things on the original theory even though
they involve axial transformations which are not a symmetry of the original theory.
In the talk I will describe this method and discuss some applications to various examples.

Abstract:
The Liouville equation has many applications: it describes surfaces of constant negative curvature and plays an important role in non-critical string theory. In this talk we discuss how to put the Liouville equation on the lattice in a completely integrable way; it will be possible to follow this talk online (please register at https://london-tqft.vercel.app)

Abstract:
M-theory on spaces with codimension 11-d singularities gives
rise to a rich class of d-dimensional field theories. I will discuss
how (d+1)-dimensional topological field theories (TFTs) encode the
higher symmetries and anomalies of these d-dimensional theories, and
how these TFTs can be extracted from the geometry of the singular
space. I will illustrate the discussion by analysing some simple
examples explicitly. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]