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The program encompassed a rich array of topics centered around Zariski-dense subgroups, with connections to algebraic and Lie groups, geometry, and number theory. It highlights the application of Diophantine approximation techniques to questions on linear groups with bounded generation, as well as innovative developments in the Bruhat–Tits theory for algebraic groups over local fields. These ideas were explored through four mini-courses alongside numerous research and expository lectures.\u003c\/p\u003e\n\u003cp\u003eChapters are published in two volumes: Volume 1 features expanded notes from four mini-courses and two expository talks, while Volume 2 comprises twelve original research articles. Collectively, the volumes make recent advances in the theory of Zariski-dense subgroups accessible to a broad mathematical audience. The topic has continued to draw significant interest, building on discussions from earlier meetings such as the MSRI workshop in Berkeley (2012) and the IPAM workshop at UCLA (2015). Over the past two decades, Zariski-dense subgroups of algebraic groups have become a focal point of intense research, yielding a wealth of results with far-reaching applications. Notably, this line of inquiry has contributed to the construction of expander graphs and the study of spectral gaps, developments that culminated in the theory of \u003cem\u003esuperstrong approximation\u003c\/em\u003e.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":53483887919377,"sku":"NGR9789819534364","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819534364.jpg?v=1787944417"},{"product_id":"complex-geometry-and-mathematical-physics-book-elisabetta-barletta-9789819219384","title":"Complex Geometry and Mathematical Physics","description":"\u003cp\u003eThis book, \u003cem\u003eComplex Geometry and Mathematical Physics: Complex Analysis versus General Relativity Theory (Book III-C)\u003c\/em\u003e, examines the impact of results from complex analysis and complex geometry on certain aspects of mathematical physics, such as quantization theory, with an emphasis on the novel aspects in A. Odzijewicz’s scientific creation, as related to the use of complex analysis tools (for example, weighted Bergman kernels) in the calculation of transition probability amplitudes from a classical state (identified to a coherent state) of a mechanical system. The third in a captivating series of three books, it is devoted to applying ideas and methods from GRG (that is, from the theory of singularities—classical and quantum—of spacetimes) to complex analysis. The other two books of the series are:\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eComplex Geometry and Mathematical Physics: Lorentzian Geometry and Field Equations (Book III-A)\u003c\/em\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eComplex Geometry and Mathematical Physics: Classical and Quantum Singularities of Space-Times (Book III-B)\u003c\/em\u003e\u003c\/p\u003e\n\u003cp\u003e\"Complex Geometry and Mathematical Physics\" is part of the ampler book project \"Differential Geometry, Partial Differential Equations and Mathematical Physics\", by the same Authors, and aims to demonstrate the interaction between complex analysis and complex geometry on one hand, and general relativity and (quantum) gravity theory on the other, with an emphasis on the modern and contemporary trends of applying ideas from GRG theory to certain\u003cbr\u003eproblems arising in complex analysis, such as the many pathologies of the Diederich–Fornæss worm domains.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53605884068113,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":53605884494097,"sku":"NGR9789819219384","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819219384.jpg?v=1782891953"},{"product_id":"complex-geometry-and-mathematical-physics-book-elisabetta-barletta-9789819214426","title":"Complex Geometry and Mathematical Physics","description":"\u003cp\u003eThis book, \u003cem\u003eComplex Geometry and Mathematical Physics: Classical and Quantum Singularities of Space-Times (Book III-B)\u003c\/em\u003e, presents results from the theory of singularities of space–times, embracing both classical (curvature singularities, bundle boundary constructions) and quantum aspects (G.T. Horowitz and D. Marolf’s theory of quantum probes of spacetime singularities, resolution of negative mass naked singularities, resolution of singularities from the loop perspective). The second in a captivating series of three books, it addresses the mathematical analysis and the geometry of black holes, for example R. Penrose’s treatment of gravitational collapse, stability of black holes exteriors, wave functions of black holes and B-Y. Chen’s approach to marginally trapped surfaces relying on the geometry of the second fundamental form of an immersion into a Lorentzian manifold. The other two books of the series are:\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eComplex Geometry and Mathematical Physics: Lorentzian Geometry and Field Equations (Book III-A)\u003c\/em\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eComplex Geometry and Mathematical Physics: Complex Analysis versus General Relativity Theory (Book III-C)\u003c\/em\u003e\u003c\/p\u003e\n\u003cp\u003e\"Complex Geometry and Mathematical Physics\" is part of the ampler book project \"Differential Geometry, Partial Differential Equations and Mathematical Physics\", by the same authors, and aims to demonstrate the interaction between complex analysis and complex geometry on one hand, and general relativity and (quantum) gravity theory on the other, with an emphasis on the modern and contemporary trends of applying ideas from GRG theory to certain\u003cbr\u003eproblems arising in complex analysis, such as the many pathologies of the Diederich–Fornæss worm domains.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":53680207233297,"sku":"NGR9789819214426","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819214426.jpg?v=1781681649"},{"product_id":"complex-geometry-and-mathematical-physics-book-elisabetta-barletta-9789819214266","title":"Complex Geometry and Mathematical Physics","description":"\u003cp\u003eThis book, \u003cem\u003eComplex Geometry and Mathematical Physics: Lorentzian Geometry and Field Equations (Book III-A)\u003c\/em\u003e, presents results from Lorentzian geometry (causality theory of spacetimes, submanifolds of Lorentzian manifolds, compact Lorentzian holonomy) and general relativity and gravitation theory. The first in a captivating series of three books, it demonstrates the bond between physics and geometry such as the mathematical structure of Maxwell’s equations predicting Minkowskian geometry, geodesic motion in the Newtonian limit, Kepler’s problem and Mercury’s perihelic shift, Morse theory for light rays). The book also includes discussion on certain quantum mechanical aspects (bending of light in quantum gravity) and the structure of Einstein’s (linearized) field equations in empty space or in the presence of matter. The other two books of the series are:\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eComplex Geometry and Mathematical Physics: Classical and Quantum Singularities of Space-Times (Book III-B)\u003c\/em\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eComplex Geometry and Mathematical Physics: Complex Analysis versus General Relativity Theory (Book III-C)\u003c\/em\u003e\u003c\/p\u003e\n\u003cp\u003e\"Complex Geometry and Mathematical Physics\" is part of the ampler book project \"Differential Geometry, Partial Differential Equations and Mathematical Physics\" by the same Authors, and aims to demonstrate the interaction between complex analysis and complex geometry on one hand, and general relativity and (quantum) gravity theory on the other, with an emphasis on the modern and contemporary trends of applying ideas from GRG theory to certain problems arising in complex analysis, such as the many pathologies of the Diederich–Fornæss worm domains.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":53680216506641,"sku":"NGR9789819214266","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819214266.jpg?v=1782891936"},{"product_id":"lectures-on-advanced-functional-analysis-and-its-applications-book-s-kesavan-9789819234059","title":"Lectures on Advanced Functional Analysis and its Applications","description":"\u003cp\u003eThis book is a collated form of the lectures given in a series of events titled “Advanced Functional Analysis and its Applications” conducted at Indian Institute of Technology Hyderabad between years 2019 to 2024. These winter schools focused on various developments on the aforesaid topic. This book is intended to serve the purpose of adding to the knowledge of researchers who are working in Functional Analysis or its allied fields. Additionally, these highlight material that is not included in a typical Functional Analysis or Operator Theory course, but which, if understood, would bring a better level of maturity to those areas. This book serves as a refresher course for college lecturers interested in learning the current developments of Mathematical Analysis. We express our gratitude to our sponsors for their endorsement of the funding for these workshops. We have secured funding from TEQIP MHRD, NBHM, ANRF, as well as from IIT Hyderabad. Finally, each of the lecturers of these workshops have consciously stepped forward to contribute to the success of each and every event. 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