We will develop geometric techniques for counting BPS states in five-dimensional gauge theories engineered by M theory on a toric Calabi-Yau threefold. The problem is approached by studying framed 3d-5d wall-crossing in presence of a single M5 brane wrapping a special Lagrangian submanifold L. The spectrum of 3d-5d BPS states is encoded by the geometry of the manifold of vacua of the 3d-5d system, which further coincides with the mirror curve describing moduli of the Lagrangian brane. The information about the BPS spectrum is extracted from the geometry of the mirror curve by construction of a nonabelianization map for the exponential networks. We will start by reviewing exponential networks, sketch the computation for a particular toric Calabi-Yau threefold. Finally, we will finish by remarking about several aspects of enumerative invariants for the Calabi-Yau threefolds.

Condensed He-4 is a fascinating system because it exhibits quantum properties at the macroscopic scale. The most famous of these is probably the transition of the liquid into a so called superfluid state when cooled down below 2.17 K at vapor pressure. I will present and discuss experiments investigating the metastable phases of liquid and solid He-4. Achieving a metastable phase of (for instance) liquid 4 He consists in bringing a sample of liquid 4 He at a temperature and a pressure (or density) where the thermal equilibrium phase is not the liquid phase but rather the solid one or the gaseous one. We experimentally realize these states by focusing an acoustic wave (pressure/density wave) in the bulk of the liquid (solid). We measure the local density within the metastable state thanks to an optical time-resolved interferometric method. In both metastable liquid and solid He-4, we have observed instabilities at densities which are not compatible with theoretical predictions. These results are interesting because metastable liquid He-4 is a model system to study homogeneous cavitation and because solid metastable solid He-4 is a potential candidate for a hypothetical (not yet discovered) supersolid state of matter.

$T^3$ in Grande Ourse*

*tea/coffee/biscuits break around 4pm

Vivian will entertain us pedagogically with The Hubble Tension:
Local measurements of the Hubble parameter (the current expansion rate of our
Universe) from type 1a supernovae disagree at 4.4sigma with the value inferred from a
ΛCDM fit to the cosmic microwave background (CMB), with local measurements
suggesting a higher value. This discrepancy is not easily circumvented by any obvious
systematic effect in either measurement, and so increasing attention is given to the
possibility that this “Hubble tension” indicates new physics beyond ΛCDM. In this tea-time talk, I
would like to (pedagogically) review how one can measure the Hubble constant thanks to
the classical ``distance ladder’’ and the CMB. I will argue that discrepancy in the
Hubble parameter should be interpreted as a tension between our understanding
of the early and late universe cosmology, rather than a tension between two
datasets. I will then explain why it is not trivial (and therefore interesting) to solve this
discrepancy and discuss promising solutions (Early Dark Energy, additional
relativistic degrees of freedom, phantom dark energy...).

Skyrmions are topologically stable excitations that appear in magnetic systems, as non-trivial spin textures typically composed of tens of spins. In chiral magnetic systems, skyrmions are stabilized by the antisymmetric Dzyaloshinskii–Moriya (DM) interaction. Recent experimental studies observed the magnetic skyrmions in chiral magnets with the DM interaction like MnSi and FeGe. In three-dimensional bulk systems of chiral magnets, skyrmions are thermodynamically stable in a tiny window of the phase diagram only as a triangular crystal state. In contrast to the three-dimensional case, even isolated skyrmions are also stable in two dimensions, and a melting transition from an ordered phase to a liquid phase of skyrmions occurs at finite temperature.
In this seminar, we present numerical results on the melting transition in a two-dimensional classical Heisenberg model of a chiral magnet. By mapping skyrmions to two-dimensional point particles, we compute the orientational and the positional orders of skyrmions. We discuss our results from the viewpoint of the Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting of particles.