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Applied probability has seen a revolutionary growth in research activity, driven by the information age and exploding technological frontiers. Applications include the Internet and the world wide web, social networks, integrated supply chains in manufacturing networks, the highly intertwined international economies, and so on. The common thread running through these is that they are large interconnected systems that are emergent with very little top down design to optimize them. Probabilistic methods with limit theorems as their mainstay are best suited to find structure and regularity to help model, analyze and optimize such systems. Interface of probability with optimization and control, statistics, and machine learning has been the driving force behind the emerging paradigms, techniques and mathematics to address the huge scale of problems seen in such technological and commercial applications, not to mention several in biological or physical systems.In this two-week program on adva...

Applied probability has seen a revolutionary growth in research activity, driven by the information age and exploding technological frontiers. Applications include the Internet and the world wide web, social networks, integrated supply chains in manufacturing networks, the highly intertwined international economies, and so on. The common thread running through these is that they are large interconnected systems that are emergent with very little top down design to optimize them. Probabilistic methods with limit theorems as their mainstay are best suited to find structure and regularity to help model, analyze and optimize such systems. Interface of probability with optimization and control, statistics, and machine learning has been the driving force behind the emerging paradigms, techniques and mathematics to address the huge scale of problems seen in such technological and commercial applications, not to mention several in biological or physical systems.In this two-week program on adva...

The geo-political unit of South Asia is formed by ten modern nation-states that include Afghanistan, Bangladesh, Bhutan, India, Maldives, Mauritius, Myanmar, Nepal, Pakistan and Sri Lanka. These South Asian countries have a long shared history of over 3 millennia. Their common religious and cultural heritage can be traced back in the more recent past to the hold of the Mughal rulers over large parts of the region as also to British colonisation of different territories of South Asia. Today, South Asia accounts for 24% of the world’s population including 27% of the world’s youth, 29% of the world’s ‘illiterates’ and 40% of the world’s poor. The region is also home to a high concentration of linguistic, cultural and religious diversities as well as economic and social inequalities that give its politics, institutions and development a unique character while also posing unique challenges.At present, scholarship on the education systems in South Asia is very limited. Each country with its ...

The geo-political unit of South Asia is formed by ten modern nation-states that include Afghanistan, Bangladesh, Bhutan, India, Maldives, Mauritius, Myanmar, Nepal, Pakistan and Sri Lanka. These South Asian countries have a long shared history of over 3 millennia. Their common religious and cultural heritage can be traced back in the more recent past to the hold of the Mughal rulers over large parts of the region as also to British colonisation of different territories of South Asia. Today, South Asia accounts for 24% of the world’s population including 27% of the world’s youth, 29% of the world’s ‘illiterates’ and 40% of the world’s poor. The region is also home to a high concentration of linguistic, cultural and religious diversities as well as economic and social inequalities that give its politics, institutions and development a unique character while also posing unique challenges.At present, scholarship on the education systems in South Asia is very limited. Each country with its ...

Complex analysis is one of the central areas of modern mathematics, and deals with holomorphic functions, which are solutions of the Cauchy-Riemann partial differential equations. The classical theory of functions of one complex variable was developed in the nineteenth century by such giants as Cauchy, Riemann and Weierstrass, and has had a profound impact not only within mathematics, but in applications to physics and engineering. The twentieth century saw the development of the theory of functions of several complex variables in various directions. One of these approaches is to use precise estimates on the Cauchy-Riemann equations in spaces of square integrable functions and differential forms to obtain quantitative understanding of holomorphic function theory on complex manifolds of higher dimensions. Referred to as the “$L^2$-theory of the $\overline{\partial}$-problem”, this method originated in the 1960s in the work of Hörmander, Kohn, Andreotti-Vesentini and since that time has ...

This school is part of the annual ICTS summer schools on gravitational-wave (GW) astronomy. As GW observations are becoming a precision tool for fundamental physics, astrophysics and cosmology, improving the theoretical understanding of the physics and astrophysics involved become crucial. This year’s school will focus on theoretical modeling of some of the promising astrophysical and cosmological sources of gravitational radiation. Courses Advanced course in general relativity (Sudipta Sarkar, IIT Gandhinagar) Primordial black holes and gravitational wave astronomy (Teruaki Suyama, Tokyo Institute of Technology)Gravitational radiation from post-Newtonian sources and inspiralling compact binaries (Luc Blanchet, Institute of Astrophysics of Paris) Self-force and radiation reaction in general relativity (Adam Pound, University of Southampton) The school is primarily meant for graduate students and postdocs in gravitational physics and related fields. A small number of highly motivated se...

Complex analysis is one of the central areas of modern mathematics, and deals with holomorphic functions, which are solutions of the Cauchy-Riemann partial differential equations. The classical theory of functions of one complex variable was developed in the nineteenth century by such giants as Cauchy, Riemann and Weierstrass, and has had a profound impact not only within mathematics, but in applications to physics and engineering. The twentieth century saw the development of the theory of functions of several complex variables in various directions. One of these approaches is to use precise estimates on the Cauchy-Riemann equations in spaces of square integrable functions and differential forms to obtain quantitative understanding of holomorphic function theory on complex manifolds of higher dimensions. Referred to as the “$L^2$-theory of the $\overline{\partial}$-problem”, this method originated in the 1960s in the work of Hörmander, Kohn, Andreotti-Vesentini and since that time has ...

This school is part of the annual ICTS summer schools on gravitational-wave (GW) astronomy. As GW observations are becoming a precision tool for fundamental physics, astrophysics and cosmology, improving the theoretical understanding of the physics and astrophysics involved become crucial. This year’s school will focus on theoretical modeling of some of the promising astrophysical and cosmological sources of gravitational radiation. Courses Advanced course in general relativity (Sudipta Sarkar, IIT Gandhinagar) Primordial black holes and gravitational wave astronomy (Teruaki Suyama, Tokyo Institute of Technology)Gravitational radiation from post-Newtonian sources and inspiralling compact binaries (Luc Blanchet, Institute of Astrophysics of Paris) Self-force and radiation reaction in general relativity (Adam Pound, University of Southampton) The school is primarily meant for graduate students and postdocs in gravitational physics and related fields. A small number of highly motivated se...