אביב 2018

מרצה/ים: 
ד"ר דורון פודר
תיאור: 

syllabus:

  1.  Classification of surfaces 
  2.  The arc complex
  3.  Surfaces and commutator length
  4. Random Gaussian matrices and enumeration of graphs on surfaces
  5.  Mapping Class Groups
  6. Random Unitary Matrices and Surfaces
סיכומים: 
PDF icon lecture_1_1.pdf
Sunday, March 4, 2018
נושאי השיעור: 
  • Introduction
  • Definition of a surface
  • Connected sum
  • Euler Characteristics of surfaces
  • Orientability
PDF icon lecture_2_1.pdf
Monday, March 5, 2018
נושאי השיעור: 

Classification of surfaces:

  • Dehn - Heegard theorem:
    • steps of proof:
      1. Reduction to a single equvalence class of vertices
      2. crosscap normalization (lecture 3)
      3. Handle normalization (lecture 3)
      4. from crosscaps and handles to only crosscaps (lecture 3)
  • Canonical representation of surfaces
  • Seifert - Van Kampen theorem
  • Triangulation, Rado theorem
PDF icon lecture_3_1.pdf
Sunday, March 11, 2018
נושאי השיעור: 

Classification of surfaces:

  • steps 2,3,4 of Dehn - Heegard's theorem
  • classification of connected compact surfaces with punctures
PDF icon lecture_4_1.pdf
Monday, March 12, 2018
נושאי השיעור: 

The arc complex:

  • definitions: arcs, essential arcs, arc systems, ambient isotopy, arc complex
  • examples of arc complices
  • Horer's theorem + corollary
PDF icon lecture_5_1.pdf
Sunday, March 18, 2018
נושאי השיעור: 

The arc complex:

  • definitons: simplicial complex, star, link
  • steps in proof of Harer's theorem
PDF icon lecture_6_1.pdf
Monday, March 19, 2018
נושאי השיעור: 

The arc complex:

  • proof of Harer's theorem

Surffaces and commutator length:

  • definition of commutator length