Misha Verbitsky

Instituto Nacional de Matemática Pura e Aplicada

METRIC GEOMETRY

17:00-18:30, Mondays, Wednesdays, Fridays, Sala 236, January-February 2023

Slides:

• Lecture 1: Length structures (January 2).
• Lecture 2: Intrinsic metrics (January 4).
• Lecture 3: Local metrics (January 6).
• Lecture 4: Hopf-Rinow theorem (January 9).
• Lecture 5: Quotient spaces (January 11).
• Lecture 6: Polyhedral spaces (January 13).
• Lecture 7: Metric cone and the angles (January 16).
• Lecture 8: Alexandrov spaces (January 18).
• Lecture 9: Convexity in CAT(0)-spaces (January 23).
• Lecture 10: Cartan-Hadamard theorem (January 25).
• Lecture 11: Hadamard spaces are CAT(0) (January 27).
• Lecture 12: Hyperbolic space (January 30).
• Lecture 13: Hyperbolic space is CAT(0) (February 1).
• Lecture 14: Gromov hyperbolic spaces (February 3).
• Lecture 15: Gromov product (February 6).
• Lecture 16: Quasi-isometries (February 8).
• Lecture 17: Approximation tree (February 10).
• Lecture 18: Gromov hyperbolicity is equivalent to Rips hyperbolicity (February 13).
• Lecture 19: Morse lemma (February 15).
• Lecture 20: Rips polyhedron (February 17).
• Lecture 21: Hyperbolic groups are finitely presented (February 27).
• Lecture 22: Word problem in hyperbolic groups (March 3).

Assignmemts

• Assignment 1: Remedial topology (January 2).
• Assignment 2: Intrinsic metrics (January 9).
• Assignment 3: Metric quotient (January 16).
• Assignment 4: Alexandrov spaces (January 23).
• Assignment 5: Convexity in CAT(0)-spaces (January 30).
• Assignment 6: δ-slim triangles and quasi-isometry (February 6).
• Assignment 7: δ-slim triangles and quasi-isometry (February 13).
• Assignment 8: Gromov hyperbolic groups and spaces (February 22).

Miscellanea:

• Classroom assignments.
• Exam problems.
• Personal problem sets, obtained randomly with this program.
• Final results.