The second edition of the program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory, and Holography" aims to bring together theorists working in the areas of lattice field theory, string theory, and quantum gravity to discuss the state of the art nonperturbative methods and numerical approaches to tackle current and relevant problems in string theory and holography.The program via its strong pedagogical component aims also to build and grow a community of theorists in India who would contribute to work connecting nonperturbative field theories, string theory, supersymmetric/superconformal field theories, quantum black holes, gravity, and holography.The content of this program can be broadly divided into four topics:Lattice Supersymmetric Field Theories: Recent developments in realizing N=4 supersymmetry on the lattice (including ideas on regulating flat directions, static quark potential, anomalous dimension of Konishi operator), N=1 supersymmetry on the latti...
The second edition of the program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory, and Holography" aims to bring together theorists working in the areas of lattice field theory, string theory, and quantum gravity to discuss the state of the art nonperturbative methods and numerical approaches to tackle current and relevant problems in string theory and holography.The program via its strong pedagogical component aims also to build and grow a community of theorists in India who would contribute to work connecting nonperturbative field theories, string theory, supersymmetric/superconformal field theories, quantum black holes, gravity, and holography.The content of this program can be broadly divided into four topics:Lattice Supersymmetric Field Theories: Recent developments in realizing N=4 supersymmetry on the lattice (including ideas on regulating flat directions, static quark potential, anomalous dimension of Konishi operator), N=1 supersymmetry on the latti...
The program plans to focus on recent developments in the arithmetic of Elliptic curves and special values of L-functions.Eligibility: Any BS/BSc/MSc/MS/Mtech/PhD students in Mathematics may apply. Students in Natural science/engineering, for whom the program is relevant, may also apply. Interested faculty members can register. Deadline for on-campus applications - 15 June 2022Deadline for online applications - 01 August 2022ICTS is committed to building an environment that is inclusive, non-discriminatory and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.
The program plans to focus on recent developments in the arithmetic of Elliptic curves and special values of L-functions.Eligibility: Any BS/BSc/MSc/MS/Mtech/PhD students in Mathematics may apply. Students in Natural science/engineering, for whom the program is relevant, may also apply. Interested faculty members can register. Deadline for on-campus applications - 15 June 2022Deadline for online applications - 01 August 2022ICTS is committed to building an environment that is inclusive, non-discriminatory and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.
This program will focus on the model of first-passage percolation (FPP) --- a stochastic growth model --- and its close relatives. Stochastic growth models arise from physics and biology, and have been studied since the 1960s. Such systems address the behavior of growing interfaces, the spread of bacterial colonies, and the fluctuations of long chemical chains in a random potential.Physicists have made numerous predictions about the common behavior of models in the FPP class. One among them say that these models should have fluctuations of smaller order than is accessible with classical mathematical methods (exhibiting "super-concentration") and limiting laws that deviate from the standard Gaussian. In fact, the limiting fluctuations of models in the FPP class are thought to be universal, and appear in seemingly different contexts like random matrix theory, the zeros of the Riemann zeta function, and the representation theory of the symmetric group.Much progress has been made in a few ...
This school is the thirteenth in the series. The school this year will be conducted in the hybrid mode. Local participants in Bangalore can attend the school in-person. We expect that a few lectures will be delivered in-person.This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in statistical physics at the forefront of current research. It is intended for Ph.D. students, post-doctoral fellows and interested faculty members. The following courses will be offered.Statistical physics of Turbulence — Jérémie Bec (Université Côte d’Azur, Nice)Spin glasses — Chandan Dasgupta (ICTS and IISc, Bangalore) Stochastic chemical reaction networks — Supriya Krishnamurthy (Stockholm University, Stockholm)Pattern formation in Biology — Vijaykumar Krishnamurthy (ICTS, Bangalore)Stochastic Gradient Descent and Machine Learning — Praneeth Netrapalli (Google Research India, Bangalore)Statistical physics of long-range systems — Stefano Ruffo (SISSA, Trieste) an...
This program will focus on the model of first-passage percolation (FPP) --- a stochastic growth model --- and its close relatives. Stochastic growth models arise from physics and biology, and have been studied since the 1960s. Such systems address the behavior of growing interfaces, the spread of bacterial colonies, and the fluctuations of long chemical chains in a random potential.Physicists have made numerous predictions about the common behavior of models in the FPP class. One among them say that these models should have fluctuations of smaller order than is accessible with classical mathematical methods (exhibiting "super-concentration") and limiting laws that deviate from the standard Gaussian. In fact, the limiting fluctuations of models in the FPP class are thought to be universal, and appear in seemingly different contexts like random matrix theory, the zeros of the Riemann zeta function, and the representation theory of the symmetric group.Much progress has been made in a few ...
This school is the thirteenth in the series. The school this year will be conducted in the hybrid mode. Local participants in Bangalore can attend the school in-person. We expect that a few lectures will be delivered in-person.This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in statistical physics at the forefront of current research. It is intended for Ph.D. students, post-doctoral fellows and interested faculty members. The following courses will be offered.Statistical physics of Turbulence — Jérémie Bec (Université Côte d’Azur, Nice)Spin glasses — Chandan Dasgupta (ICTS and IISc, Bangalore) Stochastic chemical reaction networks — Supriya Krishnamurthy (Stockholm University, Stockholm)Pattern formation in Biology — Vijaykumar Krishnamurthy (ICTS, Bangalore)Stochastic Gradient Descent and Machine Learning — Praneeth Netrapalli (Google Research India, Bangalore)Statistical physics of long-range systems — Stefano Ruffo (SISSA, Trieste) an...
The circle method originated in a paper of S. Ramanujan and G. H. Hardy on the partition function. This method has evolved with time and has seen many interesting applications. The classical applications of the circle method are to the Waring’s problem, to the ternary Gold-bach problem, and to count rational points on varieties. The modern applications of this method are to the subconvexity problem on various L-functions and to the shifted convolution problem. Also, the circle method is a powerful analytical tool to study correlations between two arithmetical functions and it is very flexible to use. The analytic study of L-functions is a central theme in analytic number theory, and it has many arithmetical consequences. The growth of L-functions (few classes of L-functions) can be understood by studying a correlation problem using the circle method. We hope that this method will continue to have many more interesting applications. The aim of this programme is to explore this method an...
lgebraic geometry is the study of solutions to systems of polynomial equations. Such sets of solutions (often with additional structure) are usually referred to as algebraic varieties. Combinatorial algebraic geometry is an aspect of algebraic geometry where either combinatorial techniques are used to study algebraic varieties or methods (and analogies) from algebraic geometry are used to study combinatorial objects. Tropical geometry is a branch of algebraic geometry that is based on transforming an algebraic variety into a “polyhedral subset” called its tropicalisation. Tropicalisation has proven to be an efficient technique for dealing with limits of algebraic varieties called degenerations. This is a thriving area with connections to several other areas such as number theory and topics in physics. Real algebraic geometry is a related active area of mathematics that is inspired by Hilbert’s sixteenth and seventeenth problems, and is a fertile ground for rich interactions between alg...
The circle method originated in a paper of S. Ramanujan and G. H. Hardy on the partition function. This method has evolved with time and has seen many interesting applications. The classical applications of the circle method are to the Waring’s problem, to the ternary Gold-bach problem, and to count rational points on varieties. The modern applications of this method are to the subconvexity problem on various L-functions and to the shifted convolution problem. Also, the circle method is a powerful analytical tool to study correlations between two arithmetical functions and it is very flexible to use. The analytic study of L-functions is a central theme in analytic number theory, and it has many arithmetical consequences. The growth of L-functions (few classes of L-functions) can be understood by studying a correlation problem using the circle method. We hope that this method will continue to have many more interesting applications. The aim of this programme is to explore this method an...
lgebraic geometry is the study of solutions to systems of polynomial equations. Such sets of solutions (often with additional structure) are usually referred to as algebraic varieties. Combinatorial algebraic geometry is an aspect of algebraic geometry where either combinatorial techniques are used to study algebraic varieties or methods (and analogies) from algebraic geometry are used to study combinatorial objects. Tropical geometry is a branch of algebraic geometry that is based on transforming an algebraic variety into a “polyhedral subset” called its tropicalisation. Tropicalisation has proven to be an efficient technique for dealing with limits of algebraic varieties called degenerations. This is a thriving area with connections to several other areas such as number theory and topics in physics. Real algebraic geometry is a related active area of mathematics that is inspired by Hilbert’s sixteenth and seventeenth problems, and is a fertile ground for rich interactions between alg...
