Course Identification

Title:

Manifolds of Nonpositive curvature

Code:

20204171

Lecturers and Teaching Assistants

Lecturers:

Prof. Tsachik Gelander

TA's:

N/A

Course Schedule and Location

Year:

2020

Semester:

First Semester

When / Where:

Thursday, 10:15 - 13:00, Ziskind, Rm 155

First Lecture:

07/11/2019

Field of Study, Course Type and Credit Points

Mathematics and Computer Science: Lecture; Elective; Regular; 3.00 points

Comments

* On November 28th the lecture will be held at Goldsmith, Room 208

Prerequisites

No

Restrictions

Participants:

30

Language of Instruction

English

Attendance and participation

Required in at least 80% of the lectures

Grade Type

Pass / Fail

Grade Breakdown (in %)

Attendance

80%

Assignments:

20%

Evaluation Type

Take-home exam

Scheduled date 1

Date / due date

N/A

Location

N/A

Time

-

Remarks

N/A

Estimated Weekly Independent Workload (in hours)

1

Syllabus

Simply connected manifolds of Non-positive curvature

Local Geometry and Convexity

Cartan--Hadamard theorem

Ideal Boundary

The Tits metric at infinity

Symmetric spaces

Rigidity and Extension of Isometries

Classification of Isometries

Special Groups of Isometries

The Margulis Lemma

Crystallographic groups

General CAT(0) spaces

Learning Outcomes

Upon successful completion of the course, the students will be able to:

Understand the theory of Hadamard manifolds and Symmetric spaces. Will gain familiarity with CAT(0) spaces, discrete groups, lattices, arithmetic groups.

Reading List

1. Manifolds of NonPositive Curvature, by Ballmann, Gromov and Schroeder

2. Metric Spaces of Non-positive curvature, by Bridson and Haefliger

Website

N/A