New tools for optimal mixing of Markov chains: Spectral independence
and entropy decay
Monday, August 8 - Friday, August 12, 2022.
Program
Sunday evening (August 7): 5:30pm: Reception at The Club hotel (on-campus)
Talks will be held in Bren Hall room 1414.
Breakfast is 8 - 9am at Carrillo Dining Commons.
Lunch is 12:30 -1:30pm at De La Guerra Dining Commons.
Dinner is 6 - 7:15pm at De La Guerra Dining Commons.
Monday morning:
Pietro Caputo: 9:30 - 10:45am
MC basics (discrete+continuous time), mixing time
Functional analysis approach (Dirichlet form, spectral gap, MLSI)
Entropy tensorization
Connections b/w above concepts
10:45am: Coffee break in Bren courtyard
Tali Kaufman:
11:15am - 12:30pm
Intro to simplicial complexes, down-up and up-down random walks
Oppenheim's Trickle-down theorem and Garland's method
Monday afternoon:
Nima Anari:
2:30 - 3:45pm
Matroids and Bases exchange walk
Log-concave polynomials
Rapid mixing of bases exchange walk ([ALOV] proof approach)
Tuesday morning:
Tali Kaufman: 9:30 - 10:45am
Local to Global: [Kaufman-Oppenheim, Alev-Lau]
10:45am: Coffee break in Bren courtyard
Pietro Caputo: 11:15am - 12:30pm
Conditional entropy observations/tools
Block factorization, SSM, and optimal mixing
Tuesday afternoon:
Heng Guo: 2:30 - 3:45pm
Entropy decay for bases exchange walk ([CGM] proof approach)
Tuesday evening: 5:30pm: Reception/Dinner at Goleta Beach (~1 mile walk)
Wednesday morning:
Kuikui Liu:
9:30 - 10:45am
Spectral independence (SI) and rapid mixing
10:45am: Coffee break in Bren courtyard
Kuikui Liu:
11:15am - 12:30pm
Optimal mixing of Glauber dynamics (Gibbs sampler)
Wednesday afternoon:
Heng Guo: 2:30 - 3:45pm
Tutte polynomial
Connections with and related open problems for matroids, reliability, random cluster
Open problem session: 4:15pm →
Thursday morning:
Zongchen Chen: 9:30 - 10:45am
Correlation decay ➔ SI
10:45am: Coffee break on side of Bren courtyard
(go to the Red Fish statue between Bren and Marine Science Institute)
Zongchen Chen: 11:15am - 12:30pm
Coupling, zero-free ➔ SI
Thursday afternoon:
Nima Anari: 2:30 - 3:45pm
Domain sparsification and an application of average-case local-to-global theorems
Friday morning:
(20 minute student/postdoc talks plus 5 minute gap)
9:30am: Thuy-Duong Vuong (Stanford): Entropic independence
9:55am: Frederic Koehler (Stanford): Sampling Low-Rank Ising models
10:20am: Weiming Feng (Edinburgh): Optimal mixing for all degrees
10:45am: Coffee break in Bren courtyard
11:15am: Dorna Abdolazimi (Washington): Edge colorings via matrix trickle-down
11:40am: Max Hopkins (UCSD): HDX
12:05pm: Charlie Carlson (Colorado): Fixed-Magnetization Ising Model
Friday afternoon: (40 minute talk)
2:30 - 2:50pm: Daniel Frishberg (UC Irvine): Triangulations
2:55 - 3:35pm: Huy Pham (Stanford): Proof of Kahn-Kalai conjecture
3:45pm: Program concludes