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Many algebraic counting problems give rise to integer sequences that hold information which is best accessed by encoding these numbers in appropriate generating functions. Numerous classical zeta and L-functions testify to this principle: Dirichlet’s zeta function enumerates ideals of a number field; Witten’s zeta function counts representations of Lie groups; Hasse– Weil zeta functions encode the numbers of rational points of algebraic varieties over finite fields. Analytic and arithmetic properties of these zeta functions hold or are expected to hold, the key to a treasure trove of information about the underlying structures.Zeta functions of groups and rings are invaluable tools in asymptotic group theory and ring theory. Often, they admit Euler product decompositions, with rational local factors that reflect regularity of structure in the underlying data.We aim to bring together experts in the various relevant subject areas, including those in zeta functions of groups and rings and...

With the advent of modern noisy, intermediate-scale quantum (NISQ) devices, the synergy between quantum many-body physics and quantum information is stronger than ever. Quantum information concepts have led to the characterisation of novel quantum phases, both in and out of equilibrium, in many-body systems. Properties such as entanglement structure and information scrambling have provided new insights into the equilibrium and dynamical behavior of these systems. While NISQ devices are a stepping stone towards future fault-tolerant quantum computers, advancements in this direction are greatly benefiting from progress in both theoretical and experimental quantum physics. These include fundamental insights into the dynamics of quantum systems, whether isolated or influenced by environmental noise, and the classification of quantum materials essential for device platforms. Such understanding informs the potential of NISQ devices to discover exotic quantum states that could serve as resour...

Cloud clusters cover a wide range of scales: from the turbulent cloud cluster that we observe in the sky with our naked eyes to the gigantic organized cloud bands such as Monsoons, The Inter-Tropical Convergence Zone (ITCZ), Cyclones,  the Madden-Julian oscillation (MJO) etc. that satellites observe. On these different scales clouds either aggregate through their own local cloud-circulation feedbacks or sometimes they are seen to ride on top of vortices linked to waves and instabilities. Although the monsoon dynamics has been studied for a long time, how monsoon convection organizes on a variety of time-scales is an unresolved enigma. This program will be organized around this unresolved scientific direction.Topics covered will include:Geophysical fluid dynamics of moist flows: Intro to GFD, Shallow Water equations, Two-layer models, Moist dynamics on equatorial beta plane, Waves and Instabilities, Idealised modeling, parameterisation of precipitation in GFD models.Physics of convectiv...

The proposed program will discuss climate dynamics and networks, with special attention to climate networks, a network paradigm for the organization and analysis of climate data. We hope to bring together researchers on both aspects.  A good fraction of talks will be talks so that researchers on each aspect will be able to familiarize themselves with the other. We will  involve a good fraction of younger researchers, so that activity in this area, which has important applications can grow in the country.The lectures will  focus on the methods and characterizers required for the analysis of climate systems, both from the point of view of analysis and predictions. This involves the study of climate dynamical systems and bifurcation behavior, network characterizers, as well as percolation based measures. We hope to have short pedagogic modules which will introduce each of these separately, and also  discuss their implications for phenomena like the El Nino and La Nina phenomena, the India...