Zariski dense subgroups, number theory and geometric applications research articles Gopal Prasad, Andrei Rapinchuk, Balasubramanian Sury, Aleksy Tralle, editors

Format:

Book

Contributor:

Prasad, Gopal, editor.

Rapinchuk, A. S. (Andreĭ Stepanovich), editor.

Sury, Balasubramanian, editor.

Tralle, Aleksy, 1958- editor.

Series:

Infosys Science Foundation series

Infosys Science Foundation series. Mathematical sciences

Infosys Science Foundation series 2363-6157

Infosys Science Foundation series in mathematical sciences 2364-4044

Language:

English

Subjects (All):

Algebra.

Number theory.

algebra.

Physical Description:

1 online resource

Place of Publication:

Singapore Springer [2026]

Summary:

"This book presents selected chapters from the program Zariski–Dense Subgroups, Number Theory, and Geometric Applications, held at the International Center for Theoretical Sciences (ICTS) in Bengaluru, Karnataka, India, from January 1–12, 2024. 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. Chapters 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 superstrong approximation"-- Springer Nature Link

Contents:

Convolution and square in Abelian groups III / Yves Benoist

Some recent results on the punctual Quot schemes / Indranil Biswas, Chandranandan Gangopadhyay, and Ronnie Sebastian

Properly discontinuous actions of discrete subgroups of Lie groups : Lie theory and computational methods / Maciej Bochenski and Aleksy Tralle

Word maps and random words / Emmanuel Breuillard and Itay Glazer

Things we can learn by considering random locally symmetric manifolds / Tsachik Gelander

Affine Anosov representations / Sourav Ghosh

Congruent elliptic curves over some p-adic Lie extensions / Dac-Nhan-Tam Nguyen and Sujatha Ramdorai

Rost injectivity and local global principle for classical groups over function fields of arithmetic surfaces / R. Parimala and V. Suresh

Relative Weyl character formula, relative Pieri formulas and branching rules for classical groups / C. S. Rajan and Sagar Shrivastava

Totally ramified subfields of p-algebras over discrete valued fields with imperfect residue / Srinivasan Srimathy

Residual finiteness and discrete subgroups of Lie groups / Matthew Stover

Characterization of norm and quasi-norm forms in S-adic setting / George Tomanov

Notes:

Includes bibliographical references

Online resource; title from PDF title page (Springer Nature Link, viewed August 6, 2026)

Other Format:

Print version Zariski dense subgroups, number theory and geometric applications

ISBN:

9789819534425

9819534429

OCLC:

1609858428

Access Restriction:

Restricted for use by site license