32:22

Lesson 44: A metric characterization of Carnot groups

54:37

Lesson 43: Isometrically homogeneous geodesic manifolds

32:29

Lesson 42: Rank-one symmetric spaces as Heintze groups

46:22

Lesson 41: Negatively curved homogeneous manifolds

34:53

Lesson 40: Equicontinuity of Carnot-Carathéodory distances

46:21

Lesson 39: Proof of convergence of Carnot-Carathéodory structures.

40:25

Lesson 38: Limits of CC bundle structures

44:36

Lesson 37: A discussion on Mitchell's theorem

42:04

Lesson 36: An example: the asymptotic cone of the Riemannian Heisenberg group

44:38

Lesson 35: Limits of Carnot-Carathéodory distances

41:00

Lesson 34: Tangent spaces and asymptotic spaces

36:01

Lesson 33: Limits of metric spaces

15:35

Lesson 32: a biLipschitz non-embeddability consequence

43:01

Lesson 31: Proof of Pansu's Rademacher Theorem

35:22

Lesson 30: Pansu's Rademacher Theorem for curves

32:03

Lesson 29: Differentiability of Lipschitz maps between Carnot groups

23:38

Lesson 28: Measures on Carnot groups

53:06

Lesson 27: Examples of Carnot groups and Carnot algebras

37:00

Lesson 26: Dilations on Carnot groups

35:33

Lesson 25: Introduction to Carnot groups

32:44

Lesson 24: Exponential coordinates on simply connected nilpotent Lie groups

41:50

Lesson 23: Nilpotent Lie groups

35:18

Lesson 22: Extremal equations of energy minimizers

32:30

Lesson 21: First-order necessary conditions for energy minimizers

42:49

Lesson 20: Space of controls, energy minimizers, and End-point map

32:28

Lesson 19: SubFinsler Lie groups

31:41

Lesson 18: Some important formulas on Lie group

34:41

Lesson 17: Exponential map and general linear group

38:43

Lesson 16: Review of Lie groups and Lie algebras

49:13

Lesson 15: Equiregular distributions and the Ball-Box Theorem

43:36

Lesson 14: Length structures for Carnot-Carathéodory metrics

45:13

Lesson 13: The topology of Carnot-Carathéodory metrics: Chow-Rashevsky Theorem

30:32

Lesson 12: The definition of Carnot-Carathéodory space

39:45

Lesson 11: A review of Differential Geometry (continuation)

33:14

Lesson 10: A review of Differential Geometry

36:11

Lesson 9: A review of Metric Geometry (continuation)

47:20

Lesson 8: A review of Metric Geometry

35:17

Lesson 7: Metric balls in the subRiemannian Heisenberg group

28:16

Lesson 6: Dilations in the Heisenberg group

30:11

Lesson 5: Geodesics in the subRiemannian Heisenberg group

35:19

Lesson 4: The subRiemannian Heisenberg group

32:12

Lesson 3: The Heisenberg group (continuation)

26:55

Lesson 2: The Heisenberg group structure in contact geometry

45:10

Lesson 1: An isoperimetric problem by Queen Dido, and its contact-geometry formulation

16:17

Introduction to the course "SubRiemannian geometry"

35:48

Francesca Tripaldi: Rumin complex on nilpotent Lie groups and applications

01:38:22

Elefterios Soultanis: Solving the Plateau-Douglas problem in homotopy classes

01:07:46

Gabriel Pallier: Cone-equivalent nilpotent groups with different Dehn function

01:33:30

Alberto Saracco: Of ducks and paths, of math and mice -- the mathematics of Disney comics