An Introduction to Arithmetic Groups by Sascha Biberhofer · An Introduction to Arithmetic Groups...

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PhD Colloquium March 15 th 2017, 15:00–15:45 Sky Lounge An Introduction to Arithmetic Groups by Sascha Biberhofer The theory of arithmetic groups and their relations to various geomet- ric and number theoretic questions can often feel a little overwhelming and complex. In contrast, this talk is meant as a gentle introduction to this subject. We will start by tak- ing a closer look at Dirichlet’s unit theorem and slowly expand its scope to a noncommutative setting, dis- covering arithmetic groups, symmet- ric spaces and some interesting facts about them along the way. Master Students, PhD Students, Postdocs and other members of the Faculty of Mathematics are cordially invited! Organised by the Vienna Doctoral School of Mathematics.

Transcript of An Introduction to Arithmetic Groups by Sascha Biberhofer · An Introduction to Arithmetic Groups...

Page 1: An Introduction to Arithmetic Groups by Sascha Biberhofer · An Introduction to Arithmetic Groups by Sascha Biberhofer The theory of arithmetic groups and their relations to various

PhD ColloquiumMarch 15th 2017, 15:00–15:45Sky Lounge

An Introduction to Arithmetic Groupsby Sascha Biberhofer

The theory of arithmetic groups andtheir relations to various geomet-ric and number theoretic questionscan often feel a little overwhelmingand complex. In contrast, this talkis meant as a gentle introduction tothis subject. We will start by tak-ing a closer look at Dirichlet’s unittheorem and slowly expand its scopeto a noncommutative setting, dis-covering arithmetic groups, symmet-ric spaces and some interesting factsabout them along the way.

Master Students, PhD Students, Postdocsand other members of the Faculty of

Mathematics are cordially invited!Organised by the Vienna Doctoral School of Mathematics.

COHOMOLOGY OF ARITHMETIC GROUPS AND PERIODS OF AUTOMORPHIC ...math.stanford.edu/~akshay/research/takagi.pdf · COHOMOLOGY OF ARITHMETIC GROUPS AND PERIODS OF AUTOMORPHIC FORMS AKSHAY

COHOMOLOGY OF ARITHMETIC GROUPS AND PERIODS OF AUTOMORPHIC ...math.stanford.edu/~akshay/research/takagi.pdf · COHOMOLOGY OF ARITHMETIC GROUPS AND PERIODS OF AUTOMORPHIC FORMS AKSHAY

An introduction to Arithmetic Chow Groups and Arakelov Theory …homepages.math.uic.edu/~henri/notes/Morelia_slides.pdf · An introduction to Arithmetic Chow Groups and Arakelov Theory

An introduction to Arithmetic Chow Groups and Arakelov Theory …homepages.math.uic.edu/~henri/notes/Morelia_slides.pdf · An introduction to Arithmetic Chow Groups and Arakelov Theory

Arithmetic Cohomology Groupsweng/AriCohRes.pdf · Arithmetic Cohomology Groups K. Sugahara and L. Weng Abstract We rst introduce global arithmetic cohomology groups for quasi-coherent

Arithmetic Cohomology Groupsweng/AriCohRes.pdf · Arithmetic Cohomology Groups K. Sugahara and L. Weng Abstract We rst introduce global arithmetic cohomology groups for quasi-coherent

Lectures on locally symmetric spaces and arithmetic groups · Lectures on locally symmetric spaces and arithmetic groups Lizhen Ji Department of Mathematics University of Michigan

Lectures on locally symmetric spaces and arithmetic groups · Lectures on locally symmetric spaces and arithmetic groups Lizhen Ji Department of Mathematics University of Michigan

Bounded Generation of Two Families of S-Arithmetic Groups Andrea ...

Bounded Generation of Two Families of S-Arithmetic Groups Andrea ...

Arithmetic Fundamental Groups and Noncommutative Algebra · Arithmetic fundamental groups and noncommutative algebra : 1999 Von Neumann Conference on Arithmetic Fundamental Groups

Arithmetic Fundamental Groups and Noncommutative Algebra · Arithmetic fundamental groups and noncommutative algebra : 1999 Von Neumann Conference on Arithmetic Fundamental Groups

FILLING FUNCTIONS OF ARITHMETIC GROUPS · 2017-10-03 · FILLING FUNCTIONS OF ARITHMETIC GROUPS ENRICO LEUZINGER AND ROBERT YOUNG Abstract. The Dehn function and its higher-dimensional

FILLING FUNCTIONS OF ARITHMETIC GROUPS · 2017-10-03 · FILLING FUNCTIONS OF ARITHMETIC GROUPS ENRICO LEUZINGER AND ROBERT YOUNG Abstract. The Dehn function and its higher-dimensional

A tale of two groups: arithmetic groups and mapping class groups

A tale of two groups: arithmetic groups and mapping class groups

Introduction to ARITHMETIC GROUPS - Deductive …deductivepress.ca/IntroArithGrps-FINAL.pdfAppendix C. A Quick Look at S-Arithmetic Groups 457 C1. Introduction to S-arithmetic groups

Introduction to ARITHMETIC GROUPS - Deductive …deductivepress.ca/IntroArithGrps-FINAL.pdfAppendix C. A Quick Look at S-Arithmetic Groups 457 C1. Introduction to S-arithmetic groups

Calculations With Matrix Groups Over Rings And ... · Arithmetic Groups Roughly: Discrete subgroup of Lie Group, defined by arithmetic properties on matrix entries(e.g. det=1, preserve

Calculations With Matrix Groups Over Rings And ... · Arithmetic Groups Roughly: Discrete subgroup of Lie Group, defined by arithmetic properties on matrix entries(e.g. det=1, preserve

Billiards, heights, and the arithmetic of non{arithmetic groupspeople.math.harvard.edu/.../home/text/papers/gold/gold.pdf · 2020-07-20 · The non{arithmetic triangle groups are

Billiards, heights, and the arithmetic of non{arithmetic groupspeople.math.harvard.edu/.../home/text/papers/gold/gold.pdf · 2020-07-20 · The non{arithmetic triangle groups are

Cohomology of Arithmetic Groups - uni-bonn.de...Cohomology of Arithmetic Groups by G. Harder. The following is a first version of Chapter VI (probably the last one) of a book on the

Cohomology of Arithmetic Groups - uni-bonn.de...Cohomology of Arithmetic Groups by G. Harder. The following is a first version of Chapter VI (probably the last one) of a book on the

Mathematics PeopleNoVeMber 2015 Notices of the AMs 1219 Mathematics People of) arithmetic groups, outer automorphism groups of the free groups, mapping class groups of surfaces, and

Mathematics PeopleNoVeMber 2015 Notices of the AMs 1219 Mathematics People of) arithmetic groups, outer automorphism groups of the free groups, mapping class groups of surfaces, and

Finiteness properties of arithmetic groups over function fieldswortman/Frozen_Artihmetic_Finiteness.pdf · Finiteness properties of arithmetic groups over function fields Kai-Uwe

Finiteness properties of arithmetic groups over function fieldswortman/Frozen_Artihmetic_Finiteness.pdf · Finiteness properties of arithmetic groups over function fields Kai-Uwe

Introduction to ARITHMETIC GROUPS - arXiv · PDF fileIntroduction to ARITHMETIC GROUPS Dave Witte Morris ... Part I. Introduction Chapter 1. ... Q-rank 23 Notes 26 References 26 Chapter

Introduction to ARITHMETIC GROUPS - arXiv · PDF fileIntroduction to ARITHMETIC GROUPS Dave Witte Morris ... Part I. Introduction Chapter 1. ... Q-rank 23 Notes 26 References 26 Chapter

Algebraic Groups : Arithmetic and Geometry Friday, March ... · Special session \Algebraic Groups : Arithmetic and Geometry" Friday, March 13th, 2020. Let X be a smooth projective

Algebraic Groups : Arithmetic and Geometry Friday, March ... · Special session \Algebraic Groups : Arithmetic and Geometry" Friday, March 13th, 2020. Let X be a smooth projective

Algorithms for the topology of arithmetic groups and Hecke ... · Algorithms for the topology of arithmetic groups and Hecke actions II: Higher skeleta Michael Lipnowski and Aurel

Algorithms for the topology of arithmetic groups and Hecke ... · Algorithms for the topology of arithmetic groups and Hecke actions II: Higher skeleta Michael Lipnowski and Aurel

Torsion homology of arithmetic Kleinian groups · 17/11/2015  · Torsion homology of arithmetic Kleinian groups Aurel Page joint works with Alex Bartel and Haluk S¸engun¨ University

Torsion homology of arithmetic Kleinian groups · 17/11/2015  · Torsion homology of arithmetic Kleinian groups Aurel Page joint works with Alex Bartel and Haluk S¸engun¨ University

Block seminar Arithmetic groups & Rigidity · Give some examples of arithmetic groups and, if possible, discuss results which describe the structure of arithmetic subgroups in a xed

Block seminar Arithmetic groups & Rigidity · Give some examples of arithmetic groups and, if possible, discuss results which describe the structure of arithmetic subgroups in a xed

Introduction to Arithmetic Groups - Heidelberg Universitywienhard/... · 3 Introduction to Semisimple Lie Groups 27 4 Basic Properties of Lattices 41 5 What is an Arithmetic Lattice?

Introduction to Arithmetic Groups - Heidelberg Universitywienhard/... · 3 Introduction to Semisimple Lie Groups 27 4 Basic Properties of Lattices 41 5 What is an Arithmetic Lattice?