sss2
Moscow, June 15-26, 2020
| OVERVIEW | PROGRAM | TITLES & ABSTRACTS | REGISTRATION | PARTICIPANTS | LOCAL |


[ last update: December 10, 2019 ]


TITLES and ABSTRACTS of the LECTURES:

Week 1, June 15-19 / Factorization structures in mathematics and physics


Dennis Gaitsgory /
Harvard Univ

Vertex algebras, chiral algebras and applications

Topics include:
chiral algebras after Beilinson and Drinfeld, relation to vertex algebras and OPE, conformal blocks, BRST reduction.
Examples:
Kac-Moody and W-algebras, lattice algebras, chiral differential operators. Modules over vertex algebras, fusion product.
Applications:
Kazhdan-Lusztig equivalence (between representation of affine algebras and quantum groups).


Nick Rozenblyum /
Univ of Chicago

Topological field theories and factorization algebras

Topics include:
the notion of extended topological field theory, cobordism conjecture (with some background from higher category theory), En and factorization algebras, factorization homology)

Week 2, June 22-26 / Gibbs measures for planar dimer models


Amol Aggarwal /
Harvard Univ

Universality for lozenge tiling local statistics

Topics include:
height functions and Gibbs measure for lozenge tilings, non-intersecting random walks and coupling techniques, effective global laws of large numbers, local law and multi-scale analysis


Senya Shlosman /
Aix Marseille Univ, Skoltech

Gibbs measures (GM) in statistical mechanics

Topics include:
existence, uniqueness, and non-uniqueness of GM; the role of symmetry group (discrete – continuous – compact — non-commutative) and interaction smoothness; Gaussian random fields as GM; Ising crystal and its relation to the lozenge tilings


Andrei Okounkov /
Columbia Univ, Skoltech

Exact results about planar dimers: a tutorial

Topics include:
Kasteleyn theorem, transfer matrices, surface tension, special domains


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