We test various conjectures on quantum gravity for general 6d string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we first analyze the limit in Kähler moduli space where the gauge coupling tends to zero while gravity is kept dynamical. A key observation is made about the appearance of a tensionless string in such a limit. For a more quantitative analysis, we focus on a U(1) gauge symmetry and determine the elliptic genus of this string in terms of certain meromorphic weak Jacobi forms, of which modular properties allow us to determine the charge-to-mass ratios of certain string excitations. A tower of these asymptotically massless charged states are then confirmed to satisfy the (sub-)Lattice Weak Gravity Conjecture, the Completeness Conjecture, and the Swampland Distance Conjecture. If time permits, we interpret their charge-to-mass ratios in two a priori independent perspectives. All of this is then generalized to theories with multiple U(1)s.

Supersymmetric localization is a powerful technique to evaluate a class of functional integrals in supersymmetric field theories. It reduces the functional integral over field space to ordinary integrals over the space of solutions of the off-shell BPS equations. The application of this technique to supergravity suffers from some problems, both conceptual and practical. I will discuss one of the main conceptual problems, namely how to construct the fermionic symmetry with which to localize. I will show how a deformation of the BRST technique allows us to do this. As an application I will then sketch a computation of the one-loop determinant of the super-graviton that enters the localization formula for BPS black hole entropy.
 

 In this seminar I will discuss a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. We show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in detail the mechanism underlying this phenomenon and formulate a simple criterion for supersymmetry enhancement. 

In the first part of this talk, I will present an extension of Chebfun, called Ballfun, for computing with functions and vectors in the unit ball. I will then describe an algorithm for solving the incompressible Navier-Stokes equations in the ball. Contrary to projection methods, we use the poloidal-toroidal decomposition to decouple the PDEs and solve scalars equations. The solver has an optimal complexity (up to polylogarithmic terms) in terms of the degrees of freedom required to represent the solution.

Progress in developing a consistent theory that describes physical phenomena
at scales where quantum and general relativistic effects are large is
hindered by the lack of experiments. In this talk, we present a proposal
that would overcome this experimental obstacle by using a Bose-Einstein
condensate (BEC) to test for possible conflicts between quantum theory and
general relativity. Recent developments in large BEC systems allows us to
verify if gravitationally-induced wave function collapse occurs at the
timescales predicted by Roger Penrose. BECs with high particle numbers
(N>10^9) can also be used to demonstrate quantum field theory in curved
spacetime by observing how changes in the spacetime affect the phononic
quantum field of a BEC. These effects will enable the development of a new
generation of instruments that will be able to probe scales where new
physics might emerge, with applications including gravitational wave
detectors, gravimeters, gradiometers and dark energy probes.

Higgs bundles are pairs of holomorphic vector bundles and holomorphic 1-forms taking values in the endomorphisms of the bundle. Their moduli spaces carry a natural Hyperkahler structure, through which one can study Lagrangian subspaces (A-branes) or holomorphic subspaces (B-branes). Notably, these A and B-branes have gained significant attention in string theory. After introducing Higgs bundles and the associated Hitchin fibration, we shall look at  natural constructions of families of different types of branes, and relate these spaces to the study of 3-manifolds, surface group representations and mirror symmetry.

Polycyclic groups either have polynomial growth, in which case they are virtually nilpotent, or exponential growth. I will give two interesting examples of "small" polycyclic groups which are extensions of $\mathbb{R}^2$ and the Heisenberg group by the integers, and attempt to justify the claim that they are small by sketching an argument that every exponential growth polycyclic group contains one of these.