The purpose of this course is to give an in-depth overview to the theory and computational methods for the rare event studies. Some open issues will also be discussed. The students are required to have basic knowledge on stochastic ordinary differential equations. |

**Lect01 Introduction: Formulation, examples and issues**

**
Transition State Theory: RMP review 1990**

**
Transition State Theory: Review 2005**

**
Transition Path Theory: Review 2010**

**Part 1: Zero temperature regime**

**Lect02 Gradient system: LDT and transition path computation**

**
Accelerated MD by OM functional**

**Lect03 Transition rate asymptotics: 1D and Multi-D**

**
1D Rate formula by exit problem**

**
Multi-D Rate formula by exit problem**

**Lect04 Saddle points finding: Dimer, GAD etc.**

**Lect05 Non-gradient sytems: CKS, Large volume limit and LDT**

**
Application in phenotype switching**

**
Two-scale LDT by path integral**

**Lect06 Energy landscape and gMAM**

**Lect07 Non-gradient systems: Difficulties and unsolved issues**

**
Maier-Stein PRL: non-Arrhenius law**

**Lect08 Onsager-Machlup and Freidlin-Wentzell dilemma **

**Lect09 Spectral theory approach and applications**

**Part 2: Finite temperate case**

**Lect10 Potential theory for Markov processes: I**

**Lect11 Potential theory for Markov processes: II**

**Syski's book: Passage times for Markov chains**

**Lect12 Transtion path theory: Diffusion and jump models**

**Lect13 Finite temperature string method**

**Lect14 Markov state modeling: Formulation and computation**

**Lect15 Markov state modeling: Analysis and applications**

**Part 3: Sampling approach**

**Lect16 Accelerated MD, TAMD, AFED etc.**

**Lect17 Umbrella sampling, meta-dynamics, replica exchange etc**