Systoles in translation surfaces - TIB AV-Portal

Systoles in translation surfaces

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Institut Fourier

Judge, Christopher

Formal Metadata

Title

Systoles in translation surfaces

Title of Series

Summer School 2018 - Teichmüller dynamics, mapping class groups and applications

Number of Parts

50

Author

Judge, Christopher

Contributors

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/63405 (DOI)

Publisher

Institut Fourier

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Abstract

I will discuss joint work with Hugo Parlier concerning the shortest noncontractible loops—’systoles’—in a translation surface. In particular, we provide estimates (some sharp) on the number of systoles (up to homotopy) in the strata H(2g-2) and the stratum H(1,1). We also determine the maximum systolic ratio (length squared/area) in H(2g-2), and we give a conjectural value for maximum systolic ratio in H(1,1).

Series

Summer School 2018 - Teichmüller dynamics, mapping class groups and applications15 / 50

1

1:01:32

Counting closed geodesics on translation surfaces

2

1:00:38

Limit sets of Teichmuller geodesic rays in the Thurston boundary of Teichmuller space

3

1:03:17

Mirzakhani's work on Earthquakes (Part 1)

4

1:01:22

Mirzakhani's work on Earthquakes (Part 3)

5

1:11:31

Mirzakhani's work on Earthquakes (Part 2)

6

1:03:54

Nearly Fuchsian surface subgroups of finite covolume Kleinian groups

7

1:09:24

Counting simple closed geodesics and volumes of moduli spaces (Part 1)

8

1:12:00

Counting simple closed geodesics and volumes of moduli spaces (Part 2)

9

1:11:55

Counting simple closed geodesics and volumes of moduli spaces (Part 3)

10

1:01:04

Monodromy of algebraic families of curves (Part 1)

11

1:31:15

Monodromy of algebraic families of curves (Part 2)

12

1:11:15

Monodromy of algebraic families of curves (Part 3)

13

1:30:18

Horocycle dynamics (Part 1)

14

1:00:38

Horocycle dynamics (Part 2)

15

57:35

Systoles in translation surfaces

16

1:02:45

Teichmüller spaces and pseudo-Anosov homeomorphism (Part 3)

17

1:08:38

Teichmüller spaces and pseudo-Anosov homeomorphism (Part 2)

18

1:22:33

Teichmüller spaces and pseudo-Anosov homeomorphism (Part 1)

19

1:05:50

Square tiled surfaces (Part 1)

20

1:03:49

Square tiled surfaces (Part 2)

21

1:18:11

Square tiled surfaces (Part 3)

22

1:05:26

Billiards, quadrilaterals and moduli spaces

23

53:00

Diffusion rate for windtree models

24

1:02:36

Are affine invariant submanifolds affine

25

53:09

Periodic paths on the pentagon

26

1:01:29

Cohomological equation and Ruelle resonnences (Part 3)

27

1:04:55

Cohomological equation and Ruelle resonnences (Part 1)

28

1:08:16

Cohomological equation and Ruelle resonnences (Part 2)

29

54:22

Deligne-Mostow lattices and cone metrics on the sphere

30

59:19

MCG and infinite MCG (Part 1)

31

1:04:44

MCG and infinite MCG (Part 2)

32

1:28:28

MCG and infinite MCG (Part 3)

33

1:29:11

Horocycle dynamics (Part 1)

34

1:02:15

Horocycle dynamics (Part 2)

35

1:00:16

Minimal dilatations on nonorientable surfaces

36

59:45

Triangle tiling billiards : a hopscotch guided by an interval exchange transformation with flips

37

45:26

Algorithms for multicurves with Dynnikov coordinates

38

58:05

Marked points in genus two and beyond

39

1:41:56

Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 2)

40

1:09:14

Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 1)

41

59:44

Quaternionic monodromies of the Kontsevich–Zorich cocycle

42

57:17

Quantum representations of surface groups

43

1:00:39

K3 surfaces and Dynamics (Part 1)

44

1:01:41

K3 surfaces and Dynamics (Part 2)

45

1:01:17

K3 surfaces and Dynamics (Part 3)

46

59:35

Diophantine interval exchange maps

47

1:07:05

Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 1)

48

1:18:07

Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 2)

49

1:03:20

An introduction to veering triangulations

50

56:07

Effective convergence of ergodic averages and cusp excursions of geodesics

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