Monday, May 14th, 2018

Mini Course by Paul Wiegmann

Time: 10:30 AM - 12:30 PM

Location: SCGP 313

Description:

__Title__: Selberg integrals and their applications to conformal field theory, quantum Hall effect and hydrodynamics.

__Abstract__: Seemingly different phenomena such as quantum Hall effect, superfluids, instabilities in hydrodynamics, models of unstable growth (such as Hele-Shaw problem) have common geometric properties. They could be studied on a unified platform based on Selberg integrals with large number of variables. In the series of talks I will review recent advances in some of these fields emphasizing their common geometric aspects.

Poisson Geometry Program Seminar: Richard Hain

Time: 3:00 PM - 4:00 PM

Location: SCGP 102

Description:

__Title__: Hodge theory and the Goldman-Turaev Lie bialgebra Part II

__Abstract__: In this talk I will explain why the completion of the Goldman-Turaev Lie bialgebra of a framed, oriented surface has a natural mixed Hodge structure (MHS) for each choice of complex structure on the surface and the framing. This MHS is compatible with the Hodge theory on the relative unipotent completion of the corresponding mapping class group. One ingredient in the proof is a homological formula for it which may be of independent interest. We describe several applications and potential applications.

Tuesday, May 15th, 2018

Poisson Geometry Program Seminar: Kenji Fukaya

Time: 10:00 AM - 12:00 PM

Location: 102

Description:

__Title__: Renormalization, String topology, Perturbative Chern Simons and Pseudo holomorphic curve

__Abstract__: I will first explain the way to construct system of smooth differential forms on the product of given manifolds which becomes the Schwartz kernel of the A infinity operations. Then I will explain how its generalization to the case of `higher loop' are related to the above 4 topics in the title.

SCGP Weekly Talk: Alexander Goncharov (Yale)

Time: 1:00 PM - 2:00 PM

Location: SCGP 102

Description:

__Title__: Hodge Correlators

__Abstract__: The real mixed Hodge structure on the pronilpotent completion of the fundamental group of a Riemann surface can be described by a perturbative expansion of Feynman integral. The Hodge correlators are the finite dimensional integrals describing the expansion. They are convergent integrals. The simplest examples of Hodge correlators provide new integral representations of the single-valued cousins of the classical polylogarithms and their generalisations.

Wednesday, May 16th, 2018

Poisson Geometry Program Seminar: Anastasia Volovich

Time: 11:00 AM - 12:00 PM

Location: SCGP 313

Description:

__Title__: Cluster Algebras, Landau Singularities and Scattering Amplitudes

Poisson Geometry Program Seminar: Simon Donaldson

Time: 2:00 PM - 4:00 PM

Location: 102

Description:

__Title__: Survey of Geometry in G_2 manifolds.

__Abstract__: We will discuss geometric objects in and over manifolds with special structures in dimensions 6,7,8. The main focus will be on 7-dimensional manifolds, with exceptional holonomy G_2. The geometric objects in question are calibrated sub manifolds and "instanton" solutions of the Yang-Mills equations. In the first part of the talk we will recall the basic definitions and special properties of these objects. We will explain some motivations for developing "enumerative" theories, or other algebraic structures, built out of these objects. The main point of the talk will be to describe some of the obstacles which arise in trying to develop such theories, and a programme of Haydys and Walpsuski which may address some of these. This programme utilises the ADHM construction of instantons in 4 dimensions and the hyperkahler geometry of moduli spaces.

Thursday, May 17th, 2018

Poisson Geometry Program Seminar: Alexander Goncharov

Time: 10:00 AM - 12:00 PM

Location: SCGP 102

Description:

__Title__: Quantum Hodge Field Theory

Public Lecture by Kim Froyshov

Time: 1:00 PM - 2:00 PM

Location: 102

Description:

__Title__: Mod 2 instanton Floer homology.

__Abstract__: I will describe work in progress on some constructions in mod 2 instanton homology of oriented homology 3-spheres which exhibit formal analogies with monopole Floer theory of rational homology 3-spheres. This picture includes an integer valued homology cobordism invariant which constrains the intersection forms of cobounding smooth 4-manifolds, as well as two flavors of instanton Floer groups which have good functoriality properties with respect to cobordisms.