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Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number theory, communication theory, Lie theory, optimization) as well as, physics, material science and chemistry. In the recent years, there have been some remarkable advances in higher-dimensional sphere packing and the associated physics question of energy minimization, coming from methods of modular forms and optimization. Sphere packing continues to be an active area of research, with a long list of interesting and accessible questions.  The goal of this meeting is to introduce the subject to a diverse group of mathematicians, and to updated them on the new developments and research problems faced in this area of research.A series of lectures will address the different facets of sphere packing and questions associated with it. It will also highlight, new techniques and open-up the challenges and problems that one can come across. A total of ten lectures will be held over...

Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number theory, communication theory, Lie theory, optimization) as well as, physics, material science and chemistry. In the recent years, there have been some remarkable advances in higher-dimensional sphere packing and the associated physics question of energy minimization, coming from methods of modular forms and optimization. Sphere packing continues to be an active area of research, with a long list of interesting and accessible questions.  The goal of this meeting is to introduce the subject to a diverse group of mathematicians, and to updated them on the new developments and research problems faced in this area of research.A series of lectures will address the different facets of sphere packing and questions associated with it. It will also highlight, new techniques and open-up the challenges and problems that one can come across. A total of ten lectures will be held over...

Determining explicit algebraic structures of semisimple group algebras is a fundamental problem, which has played a central role in the development of representation theory of finite groups. The tools of representation theory of finite groups extend in various ways to profinite groups such as compact linear groups over ring of integers of a local field (for example GL_n(Z_p)). However the continuous representations or even representation growth of profinite groups is not well understood and is one of the current exciting areas of research. The importance of computational methods in all pursuits of pure mathematics is no more obscure, and the subject has established itself as a powerful tool, aiding quick maturing of intuition about concrete mathematical structures. The focus of this program is on theoretical aspects of group algebras and representation theory of finite and profinite groups complemented by computational techniques using discrete algebra system GAP.The first part of this...

Determining explicit algebraic structures of semisimple group algebras is a fundamental problem, which has played a central role in the development of representation theory of finite groups. The tools of representation theory of finite groups extend in various ways to profinite groups such as compact linear groups over ring of integers of a local field (for example GL_n(Z_p)). However the continuous representations or even representation growth of profinite groups is not well understood and is one of the current exciting areas of research. The importance of computational methods in all pursuits of pure mathematics is no more obscure, and the subject has established itself as a powerful tool, aiding quick maturing of intuition about concrete mathematical structures. The focus of this program is on theoretical aspects of group algebras and representation theory of finite and profinite groups complemented by computational techniques using discrete algebra system GAP.The first part of this...

Ergodic theory has its origins in the the work of  L. Boltzmann on the kinetic theory of gases. The closely related field of dynamical systems has a much older origin, going back at least to Newtonian mechanics. Both subjects have since flourished into extremely active subjects with connections to many parts of mathematics and the physical sciences. Progress has been especially rapid in the last few years in differentiable dynamics and homogeneous dynamics. Differentiable dynamics studies flows on smooth manifolds and has links with geometry while homogeneous dynamics is the study of subgroup actions on homogeneous spaces of Lie groups and has connections to number theory. It is the aim of this two week workshop to gather top experts in these two subjects to deliver expositions on the state of the art in these subjects. The first week will be devoted to differentiable dynamics and the second week to homogeneous dynamics.During the program, the Infosys-ICTS Ramanujan lectures will be de...

Ergodic theory has its origins in the the work of  L. Boltzmann on the kinetic theory of gases. The closely related field of dynamical systems has a much older origin, going back at least to Newtonian mechanics. Both subjects have since flourished into extremely active subjects with connections to many parts of mathematics and the physical sciences. Progress has been especially rapid in the last few years in differentiable dynamics and homogeneous dynamics. Differentiable dynamics studies flows on smooth manifolds and has links with geometry while homogeneous dynamics is the study of subgroup actions on homogeneous spaces of Lie groups and has connections to number theory. It is the aim of this two week workshop to gather top experts in these two subjects to deliver expositions on the state of the art in these subjects. The first week will be devoted to differentiable dynamics and the second week to homogeneous dynamics.During the program, the Infosys-ICTS Ramanujan lectures will be de...

Scientific committee:Jacques Tilouine (University of Paris, France)Eknath Ghate (TIFR, India)Marie France Vigneras (Institute de Mathématiques de Jussieu, France)Sujatha Ramdorai (University of British Columbia, Canada)Adrian Iovita (Concordia University,  Canada)Workshop on "Perfectoid spaces" will be from 09 - 13th September, 2019 and the discussion meeting on "p-adic automorphic forms and perfectoid spaces" will be from 16-20th September, 2019.In this school, we intend to understand connections between the arithmetic theory of modular forms and new developments in p-adic Hodge theory that grew from the breakthrough work of Peter Scholze on perfectoid spaces (see P. Scholze "Perfectoid spaces" Publ. Math. de l’IHES 116 (2012)). p-adic methods play a key role in the study of arithmetic properties of modular forms. This theme takes its origins in Ramanujan congruences between the Fourier coeffcients of the unique eigenform of weight 12 and the Eisenstein series of the same weight modul...

Scientific committee:Jacques Tilouine (University of Paris, France)Eknath Ghate (TIFR, India)Marie France Vigneras (Institute de Mathématiques de Jussieu, France)Sujatha Ramdorai (University of British Columbia, Canada)Adrian Iovita (Concordia University,  Canada)Workshop on "Perfectoid spaces" will be from 09 - 13th September, 2019 and the discussion meeting on "p-adic automorphic forms and perfectoid spaces" will be from 16-20th September, 2019.In this school, we intend to understand connections between the arithmetic theory of modular forms and new developments in p-adic Hodge theory that grew from the breakthrough work of Peter Scholze on perfectoid spaces (see P. Scholze "Perfectoid spaces" Publ. Math. de l’IHES 116 (2012)). p-adic methods play a key role in the study of arithmetic properties of modular forms. This theme takes its origins in Ramanujan congruences between the Fourier coeffcients of the unique eigenform of weight 12 and the Eisenstein series of the same weight modul...

Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modelled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous media. Mathematically, homogenization deals with the study of asymptotic analysis of the solutions of PDEs by obtaining the equation satisfied by the limit. This limit equation will characterize the bulk or overall behaviour of the material, which does not consist of microscopic heterogeneities and can be solved or computed.Topics to be covered in the workshop include the following but not limited to:Multi-scale problems in application...

Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modelled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous media. Mathematically, homogenization deals with the study of asymptotic analysis of the solutions of PDEs by obtaining the equation satisfied by the limit. This limit equation will characterize the bulk or overall behaviour of the material, which does not consist of microscopic heterogeneities and can be solved or computed.Topics to be covered in the workshop include the following but not limited to:Multi-scale problems in application...

This discussion meeting, organized in celebration of the work of Indian gravitational-wave (GW) physicist Bala Iyer, will bring together researchers from various aspects of GW science and related areas. As GW observations are emerging as a powerful probe of the fundamental physics and astrophysics, this meeting will try to identity the future challenges and opportunities. The meeting will entirely consist of panel discussions with plenty of room for discussions and interactions. Participation is by invitation only. 

This discussion meeting, organized in celebration of the work of Indian gravitational-wave (GW) physicist Bala Iyer, will bring together researchers from various aspects of GW science and related areas. As GW observations are emerging as a powerful probe of the fundamental physics and astrophysics, this meeting will try to identity the future challenges and opportunities. The meeting will entirely consist of panel discussions with plenty of room for discussions and interactions. Participation is by invitation only.