The Simons Center for Geometry and Physics is pleased to announce the following talks during the week of Monday, July 20th - Saturday, July 25th
Workshop: Lightning Talks
Monday, July 20th at 11:15am in SCGP 102
Title: Lightning Talks
Workshop Mini Course: Justin Salez
Tuesday, July 21st at 9:15am in SCGP 102
Speaker: Justin Salez
Title: Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Part 1
Abstract: The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their distance to equilibrium remains close to its maximal value for a while and suddenly drops to zero as the time parameter reaches a critical threshold. Discovered four decades ago in the context of card shuffling, this surprising phenomenon has since then been observed in a variety of models, from random walks on groups or complex networks to interacting particle systems. It is now believed to be universal among fast-mixing high-dimensional processes. Yet, current proofs are heavily model-dependent, and identifying the general conditions that trigger a cutoff remains one of the biggest challenges in the quantitative analysis of finite Markov chains. The purpose of this mini-course is to provide a self-contained introduction to this fascinating question, and to describe its recently uncovered relations with entropy, curvature and concentration.
Workshop: Lightning Talks
Tuesday, July 21st at 11:15am in SCGP 102
Title: Lightning Talks
Summer Concert Series: Performance by Colin Carr (cello) and Wan-Chi Su (piano)
Tuesday, July 21st at 5:00pm in 103
Workshop Mini Course: Justin Salez
Wednesday, July 22nd at 9:15am in SCGP 102
Speaker: Justin Salez
Title: Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Part 2
Abstract: The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their distance to equilibrium remains close to its maximal value for a while and suddenly drops to zero as the time parameter reaches a critical threshold. Discovered four decades ago in the context of card shuffling, this surprising phenomenon has since then been observed in a variety of models, from random walks on groups or complex networks to interacting particle systems. It is now believed to be universal among fast-mixing high-dimensional processes. Yet, current proofs are heavily model-dependent, and identifying the general conditions that trigger a cutoff remains one of the biggest challenges in the quantitative analysis of finite Markov chains. The purpose of this mini-course is to provide a self-contained introduction to this fascinating question, and to describe its recently uncovered relations with entropy, curvature and concentration.
Workshop Mini Course: Justin Salez
Wednesday, July 22nd at 11:15am in SCGP 102
Speaker: Justin Salez
Title: Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Part 3
Abstract: The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their distance to equilibrium remains close to its maximal value for a while and suddenly drops to zero as the time parameter reaches a critical threshold. Discovered four decades ago in the context of card shuffling, this surprising phenomenon has since then been observed in a variety of models, from random walks on groups or complex networks to interacting particle systems. It is now believed to be universal among fast-mixing high-dimensional processes. Yet, current proofs are heavily model-dependent, and identifying the general conditions that trigger a cutoff remains one of the biggest challenges in the quantitative analysis of finite Markov chains. The purpose of this mini-course is to provide a self-contained introduction to this fascinating question, and to describe its recently uncovered relations with entropy, curvature and concentration.
Opening Reception: Altgeld Math Models Exhibition featuring lecture by Sheldon Katz
Wednesday, July 22nd at 4:00pm in 102
Workshop Collaboration Time
Thursday, July 23rd at 9:15am
Workshop Collaboration Time
Friday, July 24th at 9:15am