This is a follow up of the conference organized last year around similar theme. As in the previous conference, we are interested in the $p$-adic properties of modular forms.The general framework for the study of congruences between modular forms is provided by the theory of $p$-adic modular forms developed in fundamental papers of Serre, Katz, Hida, Ribet, Mazur and Coleman (1970's-1990's).Given a modular form, we associate a Galois representation to that by a classical theorem due to Deligne. We can restrict this Galois representation to different decomposition groups. There is a recent interest to understand the representation for the case $l=p$. Starting with the work of Breuil to formulate mod $p$ and $p$ adic Langlands programme similar to the usual Langlands programme. This representations appear in the cohomology groups of modular curves. Recent development on the subject will be studied for different groups.In the other direction, we will be interested in understanding the Eise...
The Winter School on Quantitative System Biology has been held every year since 2012 at ICTP in Trieste, Italy and ICTS in Bangalore, India in alternating years.The topic of the 2020 School is Ecosystems Ecology, with a special focus on quantitative methods and modelling techniques.Ecology views biological systems as composed of many interdependent parts, whose interactions between themselves and the environment span a wide range of spatial and temporal scales (from cells to the biosphere). This incredible complexity of interactions parallels often with the simplicity of emergent statistical patterns of abundance and biodiversity, as well as nutrient cycling. Describing quantitatively the dynamics of populations, communities and ecosystems requires therefore a broad range of mathematical and modelling techniques. Thanks to new experimental and sequencing techniques, community and ecosystem ecology are experiencing a revolution, as they are transitioning from a traditionally data-poor d...
The existence of dark matter (DM) has been inferred from its gravitational interactions, yet the identity of the dark matter particles remains completely unknown. The dominant candidate for DM over the last 30 years has been Weakly Interacting Massive Particles (WIMPs). However, despite extensive underground (direct), telescope (indirect), and collider searches, dedicated experiments have not found any evidence of WIMPs. Meanwhile, several astrophysical small-scale structure and cosmological hints might be an indication that DM has non-gravitational interactions that cannot easily be explained with vanilla WIMPs.This online workshop on the Less Travelled Path of Dark Matter (LTPDM) will bring together particle physicists and cosmologists from all over the world to address current trends in DM searches, focused on axions and primordial black holes, and map the way forward. The program will also include a school, with lectures addressed to students and postdocs, familiarizing them with n...
The existence of dark matter (DM) has been inferred from its gravitational interactions, yet the identity of the dark matter particles remains completely unknown. The dominant candidate for DM over the last 30 years has been Weakly Interacting Massive Particles (WIMPs). However, despite extensive underground (direct), telescope (indirect), and collider searches, dedicated experiments have not found any evidence of WIMPs. Meanwhile, several astrophysical small-scale structure and cosmological hints might be an indication that DM has non-gravitational interactions that cannot easily be explained with vanilla WIMPs.This online workshop on the Less Travelled Path of Dark Matter (LTPDM) will bring together particle physicists and cosmologists from all over the world to address current trends in DM searches, focused on axions and primordial black holes, and map the way forward. The program will also include a school, with lectures addressed to students and postdocs, familiarizing them with n...
Understanding quantum gauge theories is one of the remarkable challenges of the millennium. In particular, the phenomenon of confinement in Quantum Chromodynamics (QCD) is regarded as one of the most fundamental unsolved problems in physics. A fantastic opportunity to combine our theoretical understanding with experiments has emerged from the recent heavy-ion collision experiments at RHIC and CERN, which have reported a plasma of deconfined coloured degrees of freedom called the quark-gluon plasma (QGP). However it is not yet understood how such a near-thermal plasma is formed within a remarkably short time scale under such non-equilibrium conditions. The microscopic processes which lead to thermalisation or rather hydrodynamisation of the QGP and eventually to hadronisation, could hold the key to our understanding of the inner workings of gauge theories. The study of non-equilibrium phenomena in QCD at extreme temperatures and densities along with their perplexing complexities has t...
Understanding quantum gauge theories is one of the remarkable challenges of the millennium. In particular, the phenomenon of confinement in Quantum Chromodynamics (QCD) is regarded as one of the most fundamental unsolved problems in physics. A fantastic opportunity to combine our theoretical understanding with experiments has emerged from the recent heavy-ion collision experiments at RHIC and CERN, which have reported a plasma of deconfined coloured degrees of freedom called the quark-gluon plasma (QGP). However it is not yet understood how such a near-thermal plasma is formed within a remarkably short time scale under such non-equilibrium conditions. The microscopic processes which lead to thermalisation or rather hydrodynamisation of the QGP and eventually to hadronisation, could hold the key to our understanding of the inner workings of gauge theories. The study of non-equilibrium phenomena in QCD at extreme temperatures and densities along with their perplexing complexities has t...
CANCELLED DUE TO COVID-19 RISK. Thermodynamics plays a fundamental role in all branches of physics and in many other fields of science and technology. The theory is particularly well established for macroscopic systems at or close to equilibrium. In the last 25 years, however, very significant progress has been made in our understanding of a vast variety of nonequilibrium phenomena, and it is now clear that, under certain conditions and for certain dynamics, a consistent (statistical, in particular) description can be established for systems driven arbitrarily far away from equilibrium.Nonetheless, neither a complete description of nonequilibrium states nor a full characterization of transport processes is available, as the system state appears to strongly depend on the nature of the constraints acting on it, and on many other details of the dynamics. In particular, at present there is no universally accepted generalization of the equilibrium thermodynamic potentials, suitable to desc...
CANCELLED DUE TO COVID-19 RISK. Thermodynamics plays a fundamental role in all branches of physics and in many other fields of science and technology. The theory is particularly well established for macroscopic systems at or close to equilibrium. In the last 25 years, however, very significant progress has been made in our understanding of a vast variety of nonequilibrium phenomena, and it is now clear that, under certain conditions and for certain dynamics, a consistent (statistical, in particular) description can be established for systems driven arbitrarily far away from equilibrium.Nonetheless, neither a complete description of nonequilibrium states nor a full characterization of transport processes is available, as the system state appears to strongly depend on the nature of the constraints acting on it, and on many other details of the dynamics. In particular, at present there is no universally accepted generalization of the equilibrium thermodynamic potentials, suitable to desc...
CANCELLED DUE TO COVID-19 RISK.Suspensions of solid particles and liquid drops are ubiquitous in natural turbulent flows: riverine discharges into the open ocean, marine snow (plankton and other carbonaceous matter) in the ocean, cloud droplets, spreading of volcanic ash and dust storms. In each of them there are physical questions of importance. This meeting will bring oceanographers, cloud scientists and fluid mechanicians studying particle and droplet transport together and those making observations in contact with modellers and theorists.Plankton and other small living beings are found in relatively high concentration in the upper few metres of the ocean. The debris generated sinks to the deeper ocean, and has a major role in carbon sequestration. As they sink, hydrodynamic interactions and cohesive attractions between particles create larger particles of arbitrary shape. Droplets and ice crystals in a cloud need to come in contact and coalesce to grow into raindrops, and turbulence...
CANCELLED DUE TO COVID-19 RISK.Suspensions of solid particles and liquid drops are ubiquitous in natural turbulent flows: riverine discharges into the open ocean, marine snow (plankton and other carbonaceous matter) in the ocean, cloud droplets, spreading of volcanic ash and dust storms. In each of them there are physical questions of importance. This meeting will bring oceanographers, cloud scientists and fluid mechanicians studying particle and droplet transport together and those making observations in contact with modellers and theorists.Plankton and other small living beings are found in relatively high concentration in the upper few metres of the ocean. The debris generated sinks to the deeper ocean, and has a major role in carbon sequestration. As they sink, hydrodynamic interactions and cohesive attractions between particles create larger particles of arbitrary shape. Droplets and ice crystals in a cloud need to come in contact and coalesce to grow into raindrops, and turbulence...
The study of hydrodynamic turbulence and turbulent transport has received considerable impulse from the development of experimental, theoretical, and numerical Lagrangian techniques. Allied to this development is the increasing recognition that many aspects and implications of such studies have consequences well beyond classical turbulence. In this context, we propose a short, focused discussion meeting on recent trends at the interface of statistical physics, fluid dynamics and soft matter which deal with Lagrangian problems of particles with internal degrees of freedom as well as active and smart particles in a non-trivial fluid environment. The advances made in the last few years suggest that the interplay between particle and flow dynamics can lead to several intriguing phenomena, some of which have a direct bearing on biophysics.In particular, the main focus of the meeting is on the following themes: 1. Particles with Internal Degrees of Freedom; 2. Non-Spheric...
The study of hydrodynamic turbulence and turbulent transport has received considerable impulse from the development of experimental, theoretical, and numerical Lagrangian techniques. Allied to this development is the increasing recognition that many aspects and implications of such studies have consequences well beyond classical turbulence. In this context, we propose a short, focused discussion meeting on recent trends at the interface of statistical physics, fluid dynamics and soft matter which deal with Lagrangian problems of particles with internal degrees of freedom as well as active and smart particles in a non-trivial fluid environment. The advances made in the last few years suggest that the interplay between particle and flow dynamics can lead to several intriguing phenomena, some of which have a direct bearing on biophysics.In particular, the main focus of the meeting is on the following themes: 1. Particles with Internal Degrees of Freedom; 2. Non-Spheric...
