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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...

In this program, we will discuss current challenges and recent advances in Health and Disease. The aim of the program is to explore different mathematical, statistical and computational approaches to integrate experimental and clinical data, and to discuss how mathematical modeling can help to interpret and integrate experimental data, frame and test hypotheses, and suggest novel experiments allowing for more conclusive and quantitative interpretations of biological, immunological and disease-related processes. Among others, the following problems will be addressed in this program: The analysis of disease-related processes occurring across different scales: from the genetic, to the cellular, host and population levels. At the cellular level, the mechanisms by which cells regulate proliferation, death, differentiation, in childhood, adulthood and old age, and how receptor-mediated signaling and intra-cellular receptor trafficking correlate with cellular fate. The mechanisms that can aff...

In this program, we will discuss current challenges and recent advances in Health and Disease. The aim of the program is to explore different mathematical, statistical and computational approaches to integrate experimental and clinical data, and to discuss how mathematical modeling can help to interpret and integrate experimental data, frame and test hypotheses, and suggest novel experiments allowing for more conclusive and quantitative interpretations of biological, immunological and disease-related processes. Among others, the following problems will be addressed in this program: The analysis of disease-related processes occurring across different scales: from the genetic, to the cellular, host and population levels. At the cellular level, the mechanisms by which cells regulate proliferation, death, differentiation, in childhood, adulthood and old age, and how receptor-mediated signaling and intra-cellular receptor trafficking correlate with cellular fate. The mechanisms that can aff...

This advanced level school is the tenth in the series.This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in statistical physics at the frontline of current research. It is intended for Ph.D. students, post-doctoral fellows and interested faculty members at the college and university level. The following courses will be offered.1. From classical elasticity to topological mechanics by Tom Lubensky (UPENN., USA)2. Statistical physics of hard rods by Deepak Dhar (IISER, Pune)3. Statistical physics of biological evolution by Joachim Krug (Cologne, Germany)4. Random matrix theory and related topics by Satya N. Majumdar (Orsay, France) 5. Heat transport in low-dimensional systems by Abhishek Dhar (ICTS, Bangalore)6. Extremes and records by Sanjib Sabhapandit (RRI, Bangalore)Registration opens on 15 December 2018

This advanced level school is the tenth in the series.This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in statistical physics at the frontline of current research. It is intended for Ph.D. students, post-doctoral fellows and interested faculty members at the college and university level. The following courses will be offered.1. From classical elasticity to topological mechanics by Tom Lubensky (UPENN., USA)2. Statistical physics of hard rods by Deepak Dhar (IISER, Pune)3. Statistical physics of biological evolution by Joachim Krug (Cologne, Germany)4. Random matrix theory and related topics by Satya N. Majumdar (Orsay, France) 5. Heat transport in low-dimensional systems by Abhishek Dhar (ICTS, Bangalore)6. Extremes and records by Sanjib Sabhapandit (RRI, Bangalore)Registration opens on 15 December 2018