In this talk, I will discuss various possibilities of producing dark matter in the early universe. By describing the transition between an inflationary epoch to a late time cosmology, I will emphasize how the dynamics of the universe can affect dark matter production and leave a cosmological imprint, allowing some of these scenarios to be constrained.

In this talk, I will describe the connection of two geometric objects: Apollonian (sphere) packings and knots. Both objects have several applications in mathematics, physics, chemistry and computer science. Indeed, recent models in soft and condensed matter use Apollonian packings as a simple discrete method to describe foam structures, polydisperse emulsions or granular crushing. On the other hand, knotted and linked molecules appear naturally in biopolymers like proteins, DNA or RNA. In biochemical synthesis, there is a great interest on developing methods for the construction of knotted and linked synthetic molecules, since they reveal greater elasticity than simple molecules. I will give a brief survey on the geometry behind Apollonian packings, and I will present new methods for the construction of optimal knotted and linked structures based on a 3D generalization of Apollonian packings.

Joint work with Jorge L. Ramírez Alfonsín.

We study N=1 superconformal theory in the context of AdS/CFT correspondence in the large central charge limit using Chern-Simons formulation of 3d gravity. In this limit conformal dimensions of a subclass of so-called light primary superfields remain finite and are governed by osp(1|2) subalgebra of N=1 super-Virasoro algebra. We describe the construction of osp(1|2) conformal blocks in terms of Wilson lines of the Chern-Simons 3d gravity. We consider examples of two and three-point blocks on the sphere and one-point torus blocks of light superprimary fields, which belong to finite-dimensional representations of osp(1|2). We study the correlation function for lower and upper components of the primary osp(1|2) doublets and show that the associated conformal blocks are obtained via Wilson line construction in Chern-Simons theory.

Liquids are usually described within classical physics, whereas solids require the tools of quantum mechanics. I will show how in nanoscale systems this distinction no longer holds. At these scales, liquid flows may in fact exhibit quantum effects as they interact with electrons in the solid walls. I will first discuss the quantum friction phenomenon, where charge fluctuations in the liquid interact with electronic excitations in the solid to produce a hydrodynamic friction force [1]. Using many-body quantum theory, we predict that this effect is particularly important for water flowing on carbon-based materials, and we obtain experimental evidence of the underlying mechanism from pump-probe terahertz spectroscopy [2]. I will then show how the theory can be pushed one step further to describe hydrodynamic Coulomb drag – the generation of electric current by a liquid in the solid along which it flows. This phenomenon involves a subtle interplay of electrostatic and electron-phonon interactions, and suggests strategies for designing materials with low hydrodynamic friction [3].

[1] N. Kavokine, M.-L. Bocquet and L. Bocquet. Fluctuation-induced quantum friction in nanoscale water flows. Nature 602, 84-90 (2022).
[2] X. Yu, …, M. Bonn and N. Kavokine. Water-mediated electron cooling in graphene. In preparation.
[3] B. Coquinot, L. Bocquet and N. Kavokine. Quantum feedback at the solid-liquid interface: flow-induced electronic current and negative friction. ArXiV 2205.03250.

Zoom link: contact J. Palmeri, L2C

Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling black holes, if each constituent carries a non-vanishing magnetic charge corresponding to a D4-brane in string theory, or equivalently M5-brane in M-theory. For three constituents, we demonstrate that the partition function is a mock modular form of depth two, and we determine the appropriate non-holomorphic completion using generalized error functions. From the four-dimensional perspective, the modular parameter is the axion-dilaton, and our results show that S-duality leaves this subset of the spectrum invariant. From the five-dimensional perspective, the modular parameter is the complex structure of a torus $T^2$, and the scaling black holes are dual to states in the dimensional reduction of the M5-brane worldvolume theory to $T^2$. As a case study, we specialize the compactification manifold to a K3 fibration, and explicitly evaluate holomorphic parts of partition functions.

Memory effects in disordered matter – granular suspensions, ferromagnets, crumpled paper…– can be described as pathways between the different states visited by the system upon driving. However, due to their complexity, we lack strategy to experimentally probe, understand and control such pathways in most memory forming systems.

We introduce mechanical driving of corrugated elastic sheets to precisely observe and manipulate complex, multi-step pathways. These systems respond to simple 1D forcing via sequences of elastic snap-through instabilities, leading to complex– yet controlled–deformation pathways, reminiscent of memory effects. In particular we use manipulations of the boundaries to elicit a multitude of pathways from a single sample, and show how interactions between the instabilities lead to new pathways, akin to information processing.

Supersymmetric extensions of conformal gravity have been known for a long time. In four spacetime dimensions, N=4 conformal supergravity is the maximally supersymmetric theory of this type. While the underlying multiplet of fields and their full non-linear transformations rules were already derived 40 years ago, no complete invariant action had been constructed so far. I will present the most general class of actions which turns out to be characterized by a holomorphic function of the scalar fields. This deviates from the non-maximally supersymmetric cases for which there is a unique action. I will then discuss how these results can be used to study certain higher-derivative couplings of N=4 (gauged) Poincaré supergravities.

Higgs precision measurements and resonance searches at the LHC have made sharper than ever the electroweak naturalness problem. In response, the particle physics community has begun to question symmetry-based solutions. We provide a new perspective by proposing a symmetry-based framework which does not require any fine-tuning to comply with current experimental observations. This is achieved by abandoning the additional constraint of minimality typically imposed on the structure of symmetry breaking. Single-Higgs coupling deviations of a few percent and trilinear self-coupling deviations of order one are irreducible in the natural parameter space.