Artem Sapozhnikov: Introduction to percolation theory
- Lecturer: Artem Sapozhnikov
- Date: Thursday 13:15 - 14:45
- Room: Leipzig University, Augusteum, room A-314
- Language: English
- Target audience: undergraduate students, PhD students, Postdocs
- Keywords: Phase transition, correlation inequalities, coarse graining, number of infinite components, Russo-Seymour-Welsh theory, conformal invariance of the scaling limit
- Prerequisites: Basic knowledge of probability.
Abstract
In the classical mathematical theory of percolation, the edges (or vertices) of an infinite lattice are deleted independently with probability 1-p, and properties of the remaining components are studied. Despite its simple description, this model captures a variety of phenomena, including structural phase transition, self-similarity, universality. It has been used in studies of materials, social and computer networks, epidemic spreading. This course will provide an introduction to the subject of percolation, focusing on basic results and techniques.
Regular Lectures (Summer 2019)
- Artificial Neural Networks and Machine Learning: Theoretical Foundations II
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- Thursday, 11:15 - 12:45, MPI MiS A3 01
- Embedding theorems in complex geometry
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- Tuesday, 11:15 - 12:45, University Augusteum A-314
- Continuum Mechanics
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- Wednesday, 9:15 - 10:45 and Friday, 9:15 - 10:45, University Augusteum A-314
- Modern Algebraic Geometry
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- Monday, 11:15 - 12:45, University SG 3-13 and Friday, 13:15 - 14.45, University Augusteum A-314
- Introduction to Computer Algebra
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- Wednesday 13:15 - 14:45, University HS-19 and Thursday 9:15 - 10:45, University SG 3-20
- Enumerative geometry
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- Wednesday, 09:30 - 11:00, and Thursday, 13:30 - 15:00, MPI MiS G3 10
- Stochastic variational inequalities
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- Monday, 16:15 - 17:45, MPI MiS A3 01
- Schemes and Sheaves
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- Monday, 13:30 - 15:00, MPI MiS A3 01
- Information and Complexity
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- Thursday, 9:15 - 10:45, MPI MiS A3 01, starting May 16
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- Introduction to Microlocal Analysis
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- Introduction to percolation theory
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- May 6 - 10, MPI MiS G3 10, details see extra page
- Introduction to D-modules
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- Friday, 11:00 - 12:30, MPI MiS G3 10
- Invitation to Nonlinear Algebra
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- June 4 - 14, MPI MiS, details see extra page
- Population Dynamics
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- Lectures: Tuesday, 10:15 - 11:45, MPI MiS G3 10
- Exercises: Thursday, 15:30 - 17:00 (at 04.04.: 13:00 - 14:00), MPI MiS G3 10