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#Zariski-dense subgroups

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International Centre for Theoretical Sciences

Pseudo-Reductive Groups by Brian Conrad

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Explore pseudo-reductive groups with Brian Conrad, covering definitions, properties, and key theorems in this advanced mathematics lecture on algebraic group theory.
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8 Lesons
56 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Lower Dimensional Betti Numbers of Homogeneous Spaces of Lie Groups

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Exploration of lower dimensional Betti numbers in homogeneous spaces of Lie groups, discussing mathematical techniques and applications in algebraic topology and differential geometry.
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1 Lesons
26 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Genus of Division Algebras Over Discrete Valued Fields

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Exploration of division algebras over discrete valued fields, focusing on their genus. Covers advanced algebraic concepts and their applications in number theory and field theory.
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1 Lesons
21 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Property (T) for Fiber and Semidirect Products - Lecture by Arghya Mondal

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Explore Property (T) for fiber and semidirect products in this mathematical lecture, delving into advanced concepts in group theory and their applications.
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1 Lesons
20 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Uniform Stability of Higher-rank Arithmetic Groups - Lecture 1

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Explore uniform stability in higher-rank arithmetic groups. Delve into advanced mathematical concepts and their applications in algebraic and differential geometry.
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1 Lesons
59 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rigidity and Stiffness of Arithmetic Groups

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Explore rigidity and stiffness properties of arithmetic groups, examining recent advancements in Zariski-dense subgroup theory and its applications to geometry and number theory.
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1 Lesons
22 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Sum of Squares, Positivity and Property (T) - Lecture 1

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Explore sum of squares, positivity, and Property (T) in this lecture by Marek Kaluba. Gain insights into advanced mathematical concepts and their applications in group theory and geometry.
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1 Lesons
50 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On Kissing Number of Hyperbolic Manifolds

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Explore hyperbolic manifolds' kissing numbers with Plinio G. P. Murillo. Delve into Zariski dense subgroups, number theory, and geometric applications in this theoretical sciences lecture.
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1 Lesons
30 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Arithmetic Groups of Higher Real Rank Are Not Left-orderable

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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.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

CSP and Unipotent Generators for Higher Rank Nonuniform Arithmetic Groups

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Exploration of CSP and unipotent generators in higher rank nonuniform arithmetic groups, discussing recent advancements and applications in algebraic and differential geometry.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Hypergeometric Groups and their Arithmeticity

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

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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.
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1 Lesons
47 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Systolic Geometry of Arithmetic Locally Symmetric Spaces

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Explore systolic geometry of arithmetic locally symmetric spaces, focusing on recent advancements and applications in algebraic and differential geometry, number theory, and related fields.
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1 Lesons
45 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Bruhat-Tits Theory - Lecture 3

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Explore Bruhat-Tits theory in algebraic groups with Brian Conrad, focusing on applications to arithmetic, geometry, and number theory in this advanced mathematics lecture.
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1 Lesons
58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 2

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Explore advanced topics in linear groups and Diophantine approximation, focusing on bounded generation and its applications in number theory and geometric analysis.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Bruhat-Tits Theory - Lecture 2

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Explore Bruhat-Tits theory in this advanced mathematics lecture, focusing on Zariski dense subgroups and their applications in algebraic geometry and number theory.
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1 Lesons
56 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 3

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Explore advanced concepts in linear groups and Diophantine approximation, focusing on bounded generation techniques and their applications in number theory and geometric analysis.
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1 Lesons
49 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Standard Compact Clifford-Klein Forms and Lie Algebra Decompositions

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Explore Lie algebra decompositions and standard compact Clifford-Klein forms in this advanced mathematics lecture, delving into geometric applications of Zariski dense subgroups and number theory.
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1 Lesons
44 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Uniform Stability of Higher-rank Arithmetic Groups - Lecture 1

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Explore uniform stability in higher-rank arithmetic groups with Alex Lubotzky & Bharatram. Delve into advanced mathematical concepts and their applications in this in-depth lecture.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Random Walks on Group Extensions

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Explore random walks on group extensions in this advanced mathematics lecture, covering Zariski dense subgroups and their applications in algebraic geometry and number theory.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Hasse Principle for Reductive Groups over P-Adic Function Fields

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Explore the Hasse Principle for reductive groups over p-adic function fields in this advanced mathematics lecture by Raman Parimala, part of a program on Zariski dense subgroups and number theory.
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1 Lesons
58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Sum of Squares, Positivity and Property (T) - Lecture 1

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Explore sum of squares, positivity, and Property (T) in this lecture by Marek Kaluba. Gain insights into advanced mathematical concepts and their applications in group theory and geometry.
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1 Lesons
50 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Existence Problem of Compact Quotients of Pseudo-Riemannian Homogeneous Spaces

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Explore the existence of compact quotients in pseudo-Riemannian homogeneous spaces, delving into advanced geometric concepts and their applications in mathematical physics and topology.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Thin Orbits and Applications

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Explore thin orbits in number theory and their geometric applications with Alex Kontorovich. Gain insights into Zariski-dense subgroups and their impact on various mathematical fields.
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1 Lesons
56 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Minicourse: Uniform Stability of Higher-rank Arithmetic Groups - Lecture 3

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Explore uniform stability in higher-rank arithmetic groups. Delve into advanced mathematical concepts, focusing on Zariski dense subgroups and their applications in geometry and number theory.
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1 Lesons
56 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

On the Hasse Principle for Reductive Algebraic Groups Over Finitely Generated

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Explore the Hasse Principle for reductive algebraic groups over finitely generated fields, delving into advanced number theory and algebraic geometry concepts.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Uniform Stability of Higher-rank Lattices - Lecture 2

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Explore uniform stability in higher-rank arithmetic groups, focusing on advanced mathematical concepts and their applications in group theory and geometry.
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1 Lesons
1 hour 24 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Bruhat-Tits Theory - Lecture 1

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Comprehensive introduction to Bruhat-Tits theory, exploring its foundations and applications in algebraic groups and number theory. Ideal for advanced mathematics students and researchers.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 1

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Explore Zariski-dense subgroups, number theory, and geometric applications in this lecture on bounded generation of linear groups and Diophantine approximation.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

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

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Explore discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank semisimple real algebraic groups, including classification and applications to L^2 spectrum.
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1 Lesons
56 minutes
On-Demand
Free-Video