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Due to the ongoing COVID-19 pandemic,  the discussion meeting will be conducted through online lectures.The Standard Model (SM) of particle physics has now reached a major milestone in its development after the discovery of Higgs boson by the ATLAS and CMS experiments at the LHC, CERN, in 2012. Since the first observation of this new scalar state, detailed investigations of its properties have increasingly confirmed it to be consistent with the SM Higgs boson. While SM is a highly successful theory of the fundamental particles and their interactions at the lowest length scale probed so far in experiments, it has serious shortcomings. New fundamental interactions are required to address them. The main focus of particle physics community at present involves searching for these new theories/interactions and associated new particles.  One of the most popular theories that go beyond SM is “Super-Symmetry (SUSY)” theory.  However, this theory requires the presence of new set of particles (su...

This week-long program will consist of several lectures by experts on different types of inverse problems and the underlying basic techniques to understand them. The targeted audience for these lectures are Master's and PhD students, and researchers with a strong background in PDEs. Prior experience of research in inverse problems will not be assumed.The topics that we cover during this week-long program are:1. Calderon problem.2. Fractional Calderon problem.3. Geometric inverse problems.4. Integral geometry problems.5. Inverse problems for Maxwell's equations.6. Inverse problems involving non-linear equations.7. Inverse problems for hyperbolic and transport equations.8. Probabilistic inverse problems.9. Machine Learning approaches in inverse problems.The Zoom link for the program will be sent to those who complete the Application

This week-long program will consist of several lectures by experts on different types of inverse problems and the underlying basic techniques to understand them. The targeted audience for these lectures are Master's and PhD students, and researchers with a strong background in PDEs. Prior experience of research in inverse problems will not be assumed.The topics that we cover during this week-long program are:1. Calderon problem.2. Fractional Calderon problem.3. Geometric inverse problems.4. Integral geometry problems.5. Inverse problems for Maxwell's equations.6. Inverse problems involving non-linear equations.7. Inverse problems for hyperbolic and transport equations.8. Probabilistic inverse problems.9. Machine Learning approaches in inverse problems.The Zoom link for the program will be sent to those who complete the Application

The topological properties of quantum field theories are responsible for several exotic phenomena occurring over many length scales, from nano-materials to the early universe. A fundamental phenomena in gauge theories,  confinement, is believed to be intimately related to topology. The techniques used by the condensed matter and the high energy communities to address such problems are, at least superficially, quite different. Within the condensed matter community, the interplay of topology and interactions is still in a developing phase. Researchers working in gauge theories, on the other hand, have made some progress in the understanding of non-perturbative phenomena related to topology. It thus makes it timely and appropriate to bring the two groups together to understand the techniques currently in use and to develop a common ground. Given the conceptual and technical challenges, specially for understanding phenomena beyond perturbation theory, insights and results from different in...

In recent years we have seen a lot of new successful theoretical frameworks and applications of hydrodynamic approaches in various fields of physics. The aim of this workshop is to bring together people working on the subject and discuss recent developments. Aspects of hydrodynamics at the macroscopic scale as well as at the level of fluctuations will be discussed. The themes of the workshop include recent applications and fundamental aspects in the areas of generalized hydrodynamics, active matter and condensed matter physics.Eligibility criteria: Registration is open to Ph.D students, postdocs and other researchers/faculties working in related areas.

The topological properties of quantum field theories are responsible for several exotic phenomena occurring over many length scales, from nano-materials to the early universe. A fundamental phenomena in gauge theories,  confinement, is believed to be intimately related to topology. The techniques used by the condensed matter and the high energy communities to address such problems are, at least superficially, quite different. Within the condensed matter community, the interplay of topology and interactions is still in a developing phase. Researchers working in gauge theories, on the other hand, have made some progress in the understanding of non-perturbative phenomena related to topology. It thus makes it timely and appropriate to bring the two groups together to understand the techniques currently in use and to develop a common ground. Given the conceptual and technical challenges, specially for understanding phenomena beyond perturbation theory, insights and results from different in...

In recent years we have seen a lot of new successful theoretical frameworks and applications of hydrodynamic approaches in various fields of physics. The aim of this workshop is to bring together people working on the subject and discuss recent developments. Aspects of hydrodynamics at the macroscopic scale as well as at the level of fluctuations will be discussed. The themes of the workshop include recent applications and fundamental aspects in the areas of generalized hydrodynamics, active matter and condensed matter physics.Eligibility criteria: Registration is open to Ph.D students, postdocs and other researchers/faculties working in related areas.

Understanding the structure of the set of rational points on an elliptic curve - essentially a cubic equation - has been an aim in number theory for over a century. It has connections to open problems buried in antiquity, such as the congruent number problem. The  Birch and Swinnerton-Dyer (BSD) conjecture, a Clay millennium problem, predicts a mystifying interrelation among the rational points and the associated L-function. The  Bloch-Kato conjecture is a vast generalisation of the BSD conjecture. Over the last decade, the BSD has witnessed notable progress.In this precursor to the upcoming program on the recent progress, a series of mini-courses is intended mainly as an introduction to some of the breakthroughs towards the BSD conjecture from the mid 1970's - the early 1990's; namely after: Coates-Wiles, Gross-Zagier and Kolyvagin, Kato. An introduction to recent progress towards the Gross-Stark conjecture will also appear.List of speakers and mini courses for the online precursor:He...

Understanding the structure of the set of rational points on an elliptic curve - essentially a cubic equation - has been an aim in number theory for over a century. It has connections to open problems buried in antiquity, such as the congruent number problem. The  Birch and Swinnerton-Dyer (BSD) conjecture, a Clay millennium problem, predicts a mystifying interrelation among the rational points and the associated L-function. The  Bloch-Kato conjecture is a vast generalisation of the BSD conjecture. Over the last decade, the BSD has witnessed notable progress.In this precursor to the upcoming program on the recent progress, a series of mini-courses is intended mainly as an introduction to some of the breakthroughs towards the BSD conjecture from the mid 1970's - the early 1990's; namely after: Coates-Wiles, Gross-Zagier and Kolyvagin, Kato. An introduction to recent progress towards the Gross-Stark conjecture will also appear.List of speakers and mini courses for the online precursor:He...

M. S. Narasimhan (1932-2021) and C. S. Seshadri (1932-2020) were doyens of Indian Science who placed Tata Institute of Fundamental Research (TIFR) on the mathematical map of the world in the early days of independent India. Together with their students, they played an important role in the establishing and maintaining of various institutions to support mathematical research in India.Their work in studying moduli of vector and principal bundles was pioneering and has played a foundational role in the modern development of algebraic geometry. Their subsequent works touched upon a wide variety of subjects at the intersection of geometry and representation theory. In many cases, their work also had deep connections to theoretical physics through, for example, the mathematics of gauge theories, conformal field theories and string theory.This special event, which is a part of the Quantum Fields, Geometry and Representation Theory 2021 program, is held to honor and celebrate their work. A dis...

M. S. Narasimhan (1932-2021) and C. S. Seshadri (1932-2020) were doyens of Indian Science who placed Tata Institute of Fundamental Research (TIFR) on the mathematical map of the world in the early days of independent India. Together with their students, they played an important role in the establishing and maintaining of various institutions to support mathematical research in India.Their work in studying moduli of vector and principal bundles was pioneering and has played a foundational role in the modern development of algebraic geometry. Their subsequent works touched upon a wide variety of subjects at the intersection of geometry and representation theory. In many cases, their work also had deep connections to theoretical physics through, for example, the mathematics of gauge theories, conformal field theories and string theory.This special event, which is a part of the Quantum Fields, Geometry and Representation Theory 2021 program, is held to honor and celebrate their work. A dis...