Zariski-dense subgroups Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Discrete Subgroups with Finite Bowen-Margulis-Sullivan Measure in Higher Rank - Part 1

Explore discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank semisimple real algebraic groups, including classification and applications to L^2 spectrum.

• YouTube
• 56 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Zariski Dense Subgroups, Number Theory and Geometric Applications - 2024

Explore advanced topics in Zariski dense subgroups, arithmetic groups, and their geometric applications through expert lectures on algebraic geometry and number theory.

• YouTube
• 1 day 17 hours 53 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Pseudo-Reductive Groups by Brian Conrad

Explore pseudo-reductive groups with Brian Conrad, covering definitions, properties, and key theorems in this advanced mathematics lecture on algebraic group theory.

• YouTube
• 56 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

On the Hasse Principle for Reductive Algebraic Groups Over Finitely Generated

Explore the Hasse Principle for reductive algebraic groups over finitely generated fields, delving into advanced number theory and algebraic geometry concepts.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Uniform Stability of Higher-rank Lattices - Lecture 2

Explore uniform stability in higher-rank arithmetic groups, focusing on advanced mathematical concepts and their applications in group theory and geometry.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Introduction to Bruhat-Tits Theory - Lecture 1

Comprehensive introduction to Bruhat-Tits theory, exploring its foundations and applications in algebraic groups and number theory. Ideal for advanced mathematics students and researchers.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 1

Explore Zariski-dense subgroups, number theory, and geometric applications in this lecture on bounded generation of linear groups and Diophantine approximation.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Arithmetic Groups of Higher Real Rank Are Not Left-orderable

Explore the non-left-orderability of arithmetic groups with higher real rank in this mathematical lecture, delving into advanced concepts in group theory and algebraic structures.

• YouTube
• 53 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

CSP and Unipotent Generators for Higher Rank Nonuniform Arithmetic Groups

Exploration of CSP and unipotent generators in higher rank nonuniform arithmetic groups, discussing recent advancements and applications in algebraic and differential geometry.

• YouTube
• 53 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Hypergeometric Groups and their Arithmeticity

Explore hypergeometric groups and their arithmeticity in this advanced mathematics lecture, delving into Zariski-dense subgroups and their applications in geometry and number theory.

• YouTube
• 59 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Non-virtually Abelian Discontinuous Group Actions vs Proper SL(2,R)-Actions - Aleksy Tralle

Explore non-virtually Abelian discontinuous group actions and proper SL(2,R)-actions in this advanced mathematics lecture, part of a program on Zariski dense subgroups and geometric applications.

• YouTube
• 47 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Systolic Geometry of Arithmetic Locally Symmetric Spaces

Explore systolic geometry of arithmetic locally symmetric spaces, focusing on recent advancements and applications in algebraic and differential geometry, number theory, and related fields.

• YouTube
• 45 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Introduction to Bruhat-Tits Theory - Lecture 3

Explore Bruhat-Tits theory in algebraic groups with Brian Conrad, focusing on applications to arithmetic, geometry, and number theory in this advanced mathematics lecture.

• YouTube
• 58 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 2

Explore advanced topics in linear groups and Diophantine approximation, focusing on bounded generation and its applications in number theory and geometric analysis.

• YouTube
• 53 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Introduction to Bruhat-Tits Theory - Lecture 2

Explore Bruhat-Tits theory in this advanced mathematics lecture, focusing on Zariski dense subgroups and their applications in algebraic geometry and number theory.

• YouTube
• 56 minutes
• On-Demand
• Free Video