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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...

Even after one hundred years, the circle method remains one of the most important tools in the analytic theory of numbers. Over the years the method has gone through several modifications, resulting in novel applications. Originally introduced to study the partition function and the Waring problem, the circle method quickly became the most powerful analytic tool to count rational points on varieties. It was also adopted to study problems in the prime number theory. Recently the circle method has been extended to function fields and general number fields, and has been put on a broader adelic and geometric setting. We have also seen some striking recent applications in areas such as analytic theory of L-functions, ergodic theory, and the Langlands program. This workshop will present accessible short lecture series on the circle method and related topics, from experts in the field, aimed at senior graduate students and post-docs. The main aim will be to introduce the audience to various f...

Integrable systems share the properties of being exactly solvable in some sense and of having many conserved quantities. Investigating their behavior is key to understanding the wealth of non-integrable models falling in the same universality class. While the first examples of integrable systems were continuous, a large array of discrete integrable systems have been discovered over the last 60 years. These discrete systems hail from various branches of theoretical physics (statistical physics, string theory) and mathematics (combinatorics, representation theory, geometry, probability). They all possess remarkable algebraic structures.This program proposes to explore several interrelated aspects of discrete integrable systems. We will focus on three aspects that are currently active topics of research:1. Integrable difference equations, their soliton solutions and the rich structure of their singularities. Ultradiscretization of these equations, yielding cellular automata (e.g. box-ball...

Gravitation and cosmology allow us to probe the nature of the universe at its largest scales and gain insights into the underlying structure and dynamics of the universe. New observational techniques in the field of cosmology have allowed us to estimate various cosmological parameters with remarkable precision. Recent advancements in observational techniques have revolutionized our understanding of the universe. Some of these techniques include Cosmic Microwave Background (CMB) Observations, Large-Scale Structure Surveys, Supernova Cosmology, Baryon Acoustic Oscillations (BAO), Gravitational Lensing, Redshift Surveys etc. These techniques have collectively allowed cosmologists to estimate parameters such as the Hubble constant, the density of dark matter and dark energy, the curvature of space and the composition of the universe with remarkable accuracy.The third Indian Association for General Relativity and Gravitation (IAGRG) school on Gravitation and Cosmology aims to train young re...

All physical phenomena in areas such as physics, engineering, finance, and biology are inherently nonlinear and therefore described via models of nonlinear partial differential equations (PDEs). The Navier-Stokes and the Euler equations are thought to be the fundamental set of equations governing the motion of fluid flow. Recently, the research area related to fluid flow equations  has witnessed multiple seminal new results and groundbreaking techniques. The main aim of the program is to bring in leading researchers from the field of fluid mechanics for an active discussion on these new techniques and exchange of ideas. In his celebrated 1949 paper on statistical hydrodynamics Lars Onsager conjectured that the threshold regularity for the validity of energy conservation of weak solutions to Euler equations is the exponent 1/3. In particular he announced that for larger Hölder exponents any weak solution would conserve the energy, whereas for any smaller exponent there are solutions whi...

Chromatin is a long polymer in which the genetic code is intricately arranged in 4D (space and time). Beyond the DNA sequence, the epigenetic state and 3D organization of chromatin dictate the gene regulation in a spatio-temporal manner.The study of chromatin is at a juncture where recent advances in genomics, high-resolution microscopy, and single-cell level measurements have made it possible to understand the underlying principles behind this complex organization and gene regulation.Integrating this diverse information into a coherent understanding requires multi-disciplinary expertise, and this meeting aims to facilitate such cross-talks between specialists from different fields. Discussions during the meeting on novel experimental observations and phenomenology, along with physical principles and data-driven methods, are expected to benefit the diverse community interested in chromatin.The first week will be a pedagogical workshop that will cover diverse experimental and theoretica...