Heegaard Floer homology and concordance bounds on the Thurston norm

We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class of a 2-component link $L$ in $S^3$. We then specialise this procedure to knots in $S^2\times S^1$, and obtain a lower bound on their geometric winding number. Furthermore we produce an obstruction for a knot in $S^3$ to have untwisting number 1. We then provide an infinite family of null-homologous knots with increasing geometric winding number, on which the bound is sharp.Comment: With an appendix with Adam Simon Levine; 24 pages, 8 figures; comments welcome! V2: Fixed a few typos, wrong citations and figures, removed a proposition. This version to appear in Transactions of the AM

Cuspidal curves and Heegaard Floer homology

We give bounds on the gap functions of the singularities of a cuspidal plane curve of arbitrary genus, generalising recent work of Borodzik and Livingston. We apply these inequalities to unicuspidal curves whose singularity has one Puiseux pair: we prove two identities tying the parameters of the singularity, the genus, and the degree of the curve; we improve on some degree-multiplicity asymptotic inequalities; finally, we prove some finiteness results, we construct infinite families of examples, and in some cases we give an almost complete classification.Comment: 39 pages, 4 figures. Exposition improved. This preprint version differs from the final version which is to appear in the Proceedings of the London Mathematical Societ

Porting of DSMC to multi-GPUs using OpenACC

The Direct Simulation Monte Carlo has become the method of choice for studying gas flows characterized by variable rarefaction and non-equilibrium effects, rising interest in industry for simulating flows in micro-, and nano-electromechanical systems. However, rarefied gas dynamics represents an open research challenge from the computer science perspective, due to its computational expense compared to continuum computational fluid dynamics methods. Fortunately, over the last decade, high-performance computing has seen an exponential growth of performance. Actually, with the breakthrough of General-Purpose GPU computing, heterogeneous systems have become widely used for scientific computing, especially in large-scale clusters and supercomputers. Nonetheless, developing efficient, maintainable and portable applications for hybrid systems is, in general, a non-trivial task. Among the possible approaches, directive-based programming models, such as OpenACC, are considered the most promising for porting scientific codes to hybrid CPU/GPU systems, both for their simplicity and portability. This work is an attempt to port a simplified version of the fm dsmc code developed at FLOW Matters Consultancy B.V., a start-up company supporting this project, on a multi-GPU distributed hybrid system, such as Marconi100 hosted at CINECA, using OpenACC. Finally, we perform a detailed performance analysis of our DSMC application on Volta (NVIDIA V100 GPU) architecture based computing platform as well as a comparison with previous results obtained with x64 86 (Intel Xeon CPU) and ppc64le (IBM Power9 CPU) architectures

Primordial Non-Gaussianity in Supersolid Inflation

We study primordial non-gaussianity in supersolid inflation. The dynamics of supersolid is formulated in terms of an effective field theory based on four scalar fields with a shift symmetric action minimally coupled with gravity. In the scalar sector, there are two phonon-like excitations with a kinetic mixing stemming from the completely spontaneous breaking of diffeomorphism. In a squeezed configuration, $f_{\text{NL}}$ of scalar perturbations is angle dependent and not proportional to slow-roll parameters showing a blunt violation of the Maldacena consistency relation. Contrary to solid inflation, the violation persists even after an angular average and generically the amount of non-gaussianity is significant. During inflation, non-gaussianity in the TSS and TTS sector is enhanced in the same region of the parameters space where the secondary production of gravitational waves is sizeable enough to enter in the sensitivity region of LISA, while the scalar $f_{\text{NL}}$ is still within the current experimental limits.Comment: 54 pages, 13 figures. Latex file. A number of typos corrected with the JHEP versio

Beyond Perturbation Theory in Inflation

Inflationary perturbations are approximately Gaussian and deviations from Gaussianity are usually calculated using in-in perturbation theory. This method, however, fails for unlikely events on the tail of the probability distribution: in this regime non-Gaussianities are important and perturbation theory breaks down for $|\zeta| \gtrsim |f_{\rm \scriptscriptstyle NL}|^{-1}$. In this paper we show that this regime is amenable to a semiclassical treatment, $\hbar \to 0$. In this limit the wavefunction of the Universe can be calculated in saddle-point, corresponding to a resummation of all the tree-level Witten diagrams. The saddle can be found by solving numerically the classical (Euclidean) non-linear equations of motion, with prescribed boundary conditions. We apply these ideas to a model with an inflaton self-interaction $\propto \lambda \dot\zeta^4$. Numerical and analytical methods show that the tail of the probability distribution of $\zeta$ goes as $\exp(-\lambda^{-1/4}\zeta^{3/2})$, with a clear non-perturbative dependence on the coupling. Our results are relevant for the calculation of the abundance of primordial black holes.Comment: 37 pages, 14 figures. Matches JCAP versio