Random lattices and n mod 1 Gaps for random points 1 0.8 0.6 - - PDF document

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Random lattices and n mod 1 Gaps for random points 1 0.8 0.6 - - PDF document

Dec 08, 2022 477 likes •596 views

Random lattices and n mod 1 Gaps for random points 1 0.8 0.6 0.4 0.2 0.5 1 1.5 2 2.5 Gaps for n mod 1 1.0 6/ 2 0.5 0.0 0.0 0.5 1.0 1.5 2.0 The space of lattices Geodesic for 2 1 / 3 pics/CubeRoot_2 : 200

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SLIDE 1

Random lattices and √n mod 1

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SLIDE 2

Gaps for random points

0.5 1 1.5 2 2.5 0.2 0.4 0.6 0.8 1

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SLIDE 3

Gaps for √n mod 1

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 6/π2

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SLIDE 4

The space of lattices

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SLIDE 5

Geodesic for 21/3

pics/CubeRoot_2 : 200

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SLIDE 6

Geodesic for √ 12

pics/2_Sqrt_3 : 20

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SLIDE 7

Geodesic for 2e

pics/2E : 200

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SLIDE 8

Closed horocycles

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SLIDE 9

Horocycles centered at a cusp

pics/Horo1 : 6 pics/Horo4 : 24 pics/Horo8 : 48 pics/Horo16 : 100

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SLIDE 10

Long horocycles

pics/Horo32 : 200 pics/Horo64 : 400 pics/Horo128 : 800 pics/Horo256 : 1600