Misha Verbitsky
Instituto Nacional de Matemática Pura e Aplicada
METRIC GEOMETRY
17:00-18:30, Mondays, Wednesdays, Fridays, Sala 236, January-February 2023
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Announcement
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:
Milnor-Schwartz theorem (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.
Misha Verbitsky
IMPA