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Convergence of functional sequences, in many cases, cannot be directly obtained from compactness properties, but requires a structural analysis of the defect of compactness. While concentration compactness techniques have been widely adopted since the 1980’s, more powerful methods have been developed in the last 15 years and applied by mathematicians working in different disciplines of analysis. The concentration argument plays a central technical role in elliptic PDE theory, geometric analysis, as well as in the analysis of NLS, wave, and Navier-Stokes equations. The original description of concentration in terms of singular weak limits for sequences of measures has been supplemented by more detailed profile decompositions. Formalization of the latter on the functional analytic level in terms of wavelet bases and cocompact imbeddings relative to a given group has been used to investigate increasingly diverse non-compact invariances involved in the loss and recovery of compactness. Con...

Convergence of functional sequences, in many cases, cannot be directly obtained from compactness properties, but requires a structural analysis of the defect of compactness. While concentration compactness techniques have been widely adopted since the 1980’s, more powerful methods have been developed in the last 15 years and applied by mathematicians working in different disciplines of analysis. The concentration argument plays a central technical role in elliptic PDE theory, geometric analysis, as well as in the analysis of NLS, wave, and Navier-Stokes equations. The original description of concentration in terms of singular weak limits for sequences of measures has been supplemented by more detailed profile decompositions. Formalization of the latter on the functional analytic level in terms of wavelet bases and cocompact imbeddings relative to a given group has been used to investigate increasingly diverse non-compact invariances involved in the loss and recovery of compactness. Con...

The WHEPPs are a series of International Workshops on Particle Physics, with the main focus being on particle phenomenology and its relation to both formal theory and experiment. They are held every alternate year and constitute the most important international event in particle physics phenomenology which is held regularly in India. Every WHEPP has led to several international collaborations and publications. Many particle phenomenologists of note around the world have been participants in previous WHEPPs, and they have served as a nursery for Indian particle physicists right since their inception.WHEPP-XII, which is also being organised as an ICTS programme, will be held at the densely wooded and pleasantly cool hill station at Mahabaleswar, about four hours drive from the international airport at Mumbai. The academic activity will take place over two weeks. The first week will be devoted to Cosmology,  Astroparticle Physics and Nonperturbative Methods in Strong Interaction Physics, ...

The new and emerging field of Network Science is based on the simple observation that large human engineered systems (e.g., communication networks, information networks, social networks, etc.) and natural systems can be modeled as networks of entities. Hence, it is possible that common principles can be brought to bear on the analysis, design and control of such systems. In addition, insights gained from networks in one domain could be brought to bear on understanding networks in other domains.For the past few years, Network Science has been an exploding research area transcending disciplinary boundaries, receiving the attention and inputs from leading figures in mathematics, physics, biology, engineering, and many other disciplines. With this in view, the IISc Mathematics Initiative (IMI) is planning a special year on network science during 2011-2012. In conjunction with this, we have planned an ICTS School and Workshop on Network Science at IISc during January 2012. The purpose of th...

The WHEPPs are a series of International Workshops on Particle Physics, with the main focus being on particle phenomenology and its relation to both formal theory and experiment. They are held every alternate year and constitute the most important international event in particle physics phenomenology which is held regularly in India. Every WHEPP has led to several international collaborations and publications. Many particle phenomenologists of note around the world have been participants in previous WHEPPs, and they have served as a nursery for Indian particle physicists right since their inception.WHEPP-XII, which is also being organised as an ICTS programme, will be held at the densely wooded and pleasantly cool hill station at Mahabaleswar, about four hours drive from the international airport at Mumbai. The academic activity will take place over two weeks. The first week will be devoted to Cosmology,  Astroparticle Physics and Nonperturbative Methods in Strong Interaction Physics, ...

The new and emerging field of Network Science is based on the simple observation that large human engineered systems (e.g., communication networks, information networks, social networks, etc.) and natural systems can be modeled as networks of entities. Hence, it is possible that common principles can be brought to bear on the analysis, design and control of such systems. In addition, insights gained from networks in one domain could be brought to bear on understanding networks in other domains.For the past few years, Network Science has been an exploding research area transcending disciplinary boundaries, receiving the attention and inputs from leading figures in mathematics, physics, biology, engineering, and many other disciplines. With this in view, the IISc Mathematics Initiative (IMI) is planning a special year on network science during 2011-2012. In conjunction with this, we have planned an ICTS School and Workshop on Network Science at IISc during January 2012. The purpose of th...

A convergence of theoretical and experimental advances in recent years has led to the insight that dynamics out of equilibrium, both classical and quantum, especially quantum phase transitions, gives rise to physics quite distinct from that of equilibrium systems. The goal of this Winter School is to take students and others who wish to learn about this subfield from the basics to the frontiers. Several sets of pedagogical lectures by pioneers in the field will be interspersed with short talks about current advances. Lecture topics will start with the foundations of classical and quantum transport, will treat quantum quenches near phase transitions, the Keldysh technique, driven systems, glasses, active systems, and gauge/gravity methods. All participants  will be encouraged to present posters about their work.

A convergence of theoretical and experimental advances in recent years has led to the insight that dynamics out of equilibrium, both classical and quantum, especially quantum phase transitions, gives rise to physics quite distinct from that of equilibrium systems. The goal of this Winter School is to take students and others who wish to learn about this subfield from the basics to the frontiers. Several sets of pedagogical lectures by pioneers in the field will be interspersed with short talks about current advances. Lecture topics will start with the foundations of classical and quantum transport, will treat quantum quenches near phase transitions, the Keldysh technique, driven systems, glasses, active systems, and gauge/gravity methods. All participants  will be encouraged to present posters about their work.