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The program will bring together machine learning experts, statisticians, clinicians, and public health experts to discuss how to harness modern mathematical and computational techniques to better understand health-related data across multiple domains. Basics of various machine learning techniques, including logistic regression, tree-based methods, support vector machines, Bayesian methods, and deep networks will be covered with examples of their applicability in biomedicine and health. Applications will include predicting outcomes for individual patients from clinical and lifestyle parameters, analysing patient data such as X-rays, ultrasound images and ECG measurements, genomic variant analysis, and inferring patterns in heterogeneous large-scale data.  Speakers from both computational/statistical and clinical backgrounds will be invited.While the overarching goal is to bridge the gap between mathematical modelling and clinical problems in general, the program has these specific aims:...

Numerical Relativity strives to solve the field equations of General Relativity in conjunction with equations of magnetohydrodynamics using supercomputers. These numerical simulations are essential tools for accurately modeling mergers of black holes or neutron stars, collapse of massive stars (possibly resulting in supernovae), and accreting black holes (in X-ray binaries or in galactic cores). Recent observations of nearly a hundred gravitational-wave (GW) signals from coalescing binaries of black holes, and multi-messenger observations  of coalescing neutron stars have firmly established the role of Numerical Relativity in astrophysics. Such high-energy astrophysical phenomena are prime targets for the upcoming GW-, electromagnetic- and neutrino observatories. This two-week summer school, jointly organized by ICTS and Raman Research Institute, is part of our annual summer school series on GW astronomy. The lectures will be organized into four graduate-level mini courses:Courses: Num...

Quantum physics has come a long way since its inception 120 years ago to the application of quantum effects in day-to-day life in the form of quantum technologies that are emerging rapidly across multiple fields. What began as a powerful theory on nature that describes the properties of particles, atoms led to a deep understanding of matter, energy, and their behavior at various scales. Over the past decade, there has been a paradigm shift with the development of the ability to control individual quantum systems. Applicable quantum technologies ranging from quantum computers, sensors, and encryption tools incorporating individual quantum systems have come to the force. Quantum resources like entanglement, superposition, and coherence can be used to attain unprecedented accuracies that are not achievable using classical methods and comparable resources. Pushing the boundaries of measurement precision is not only interesting in its own right but also fundamental to discovering new scienc...

Quantum physics has come a long way since its inception 120 years ago to the application of quantum effects in day-to-day life in the form of quantum technologies that are emerging rapidly across multiple fields. What began as a powerful theory on nature that describes the properties of particles, atoms led to a deep understanding of matter, energy, and their behavior at various scales. Over the past decade, there has been a paradigm shift with the development of the ability to control individual quantum systems. Applicable quantum technologies ranging from quantum computers, sensors, and encryption tools incorporating individual quantum systems have come to the force. Quantum resources like entanglement, superposition, and coherence can be used to attain unprecedented accuracies that are not achievable using classical methods and comparable resources. Pushing the boundaries of measurement precision is not only interesting in its own right but also fundamental to discovering new scienc...

The current boom in data science, in reality an umbrella term for diverse but loosely connected activity, has been brought about by rapid advances in techniques for collection, storage and dissemination of data, along with increased computational abilities to process it. It is on the scale of the industrial revolution except that it is now the abstract symbols rather than energy and material that is being generated, stored and distributed. This is affecting the older sciences as well where pure model based approaches are being combined with purely data driven ones, to get the best of both the worlds. The major action, however, is on a different front -- that of fast processing tools for the enormous data that is being generated, sometimes at a high speed. This is the analytic and algorithmic side of data science on which this workshop is focused. This in itself is a multi-verse, ranging from high end pure mathematics feeding it and being fed back in by it, to pure heuristics, often bas...

The current boom in data science, in reality an umbrella term for diverse but loosely connected activity, has been brought about by rapid advances in techniques for collection, storage and dissemination of data, along with increased computational abilities to process it. It is on the scale of the industrial revolution except that it is now the abstract symbols rather than energy and material that is being generated, stored and distributed. This is affecting the older sciences as well where pure model based approaches are being combined with purely data driven ones, to get the best of both the worlds. The major action, however, is on a different front -- that of fast processing tools for the enormous data that is being generated, sometimes at a high speed. This is the analytic and algorithmic side of data science on which this workshop is focused. This in itself is a multi-verse, ranging from high end pure mathematics feeding it and being fed back in by it, to pure heuristics, often bas...

The goal of this program is to introduce some of the path breaking developments in harmonic analysis in recent years. In particular, the program is focused on polynomial methods in harmonic analysis and discrete harmonic analysis. Polynomial methods in harmonic analysis: In the recent years there have been remarkable developments in the direction of Fourier restriction and Bochner-Riesz conjectures using the polynomial method. This method involves using tools from algebraic geometry to solve problems in various areas of mathematics. In particular, the method has been fruitful in addressing outstanding open problems in harmonic analysis. Discrete harmonic analysis: The discrete analogues in harmonic analysis with connections to number theoretic problems have been an active area of research in harmonic analysis. It is quite remarkable that in the recent years the powerful technique of sparse domination in the continuous setting has been developed to address problems related to discrete a...

This pedagogical program is aimed at students across the country, with special emphasis on Masters students and final year undergraduate degree students. Lecturers at this program will discuss fluid dynamics of the atmosphere and the ocean and its impact on climate scale processes. No prior background in climate-atmosphere-ocean dynamics is expected of participants. Topics that will be discussed include turbulent dynamics and convection in the ocean, monsoon dynamics, dynamical systems approach to climate models, and machine learning techniques for atmosphere-ocean processes. Eligibility criteria: Students from final year undergraduate and masters in physics, mathematics, and all streams of engineering.ICTS acknowledges the strong support received from Dr. Vivek V. (Friend of ICTS) towards this program, and other ICTS efforts on the science of climate and human interactions with our environment.ICTS is committed to building an environment that is inclusive, non discriminatory and welco...

The goal of this program is to introduce some of the path breaking developments in harmonic analysis in recent years. In particular, the program is focused on polynomial methods in harmonic analysis and discrete harmonic analysis. Polynomial methods in harmonic analysis: In the recent years there have been remarkable developments in the direction of Fourier restriction and Bochner-Riesz conjectures using the polynomial method. This method involves using tools from algebraic geometry to solve problems in various areas of mathematics. In particular, the method has been fruitful in addressing outstanding open problems in harmonic analysis. Discrete harmonic analysis: The discrete analogues in harmonic analysis with connections to number theoretic problems have been an active area of research in harmonic analysis. It is quite remarkable that in the recent years the powerful technique of sparse domination in the continuous setting has been developed to address problems related to discrete a...

This pedagogical program is aimed at students across the country, with special emphasis on Masters students and final year undergraduate degree students. Lecturers at this program will discuss fluid dynamics of the atmosphere and the ocean and its impact on climate scale processes. No prior background in climate-atmosphere-ocean dynamics is expected of participants. Topics that will be discussed include turbulent dynamics and convection in the ocean, monsoon dynamics, dynamical systems approach to climate models, and machine learning techniques for atmosphere-ocean processes. Eligibility criteria: Students from final year undergraduate and masters in physics, mathematics, and all streams of engineering.ICTS acknowledges the strong support received from Dr. Vivek V. (Friend of ICTS) towards this program, and other ICTS efforts on the science of climate and human interactions with our environment.ICTS is committed to building an environment that is inclusive, non discriminatory and welco...