09:15 AM  09:30 AM


Welcome to MSRI

 Location
 MSRI: Simons Auditorium
 Video


 Abstract
 
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09:30 AM  10:30 AM


Orbit growth rate for maximal representations
Maria Beatrice Pozzetti (RuprechtKarlsUniversitÃ¤t Heidelberg)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
Maximal representations form unexpected connected components of the character variety of the fundamental group of a hyperbolic surface in a semisimple Lie group, that only consist of injective homomorphsims with discrete image. They thus generalize the Teichmüller space, and can be thought of as parametrizing certain locally symmetric spaces of infinite volume. After a general introduction to character varieties and maximal representations, I will discuss joint work with Andres Sambarino and Anna Wienhard in which we prove a sharp upper bound for the exponential orbit growth rate of the associated actions on the symmetric space.
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10:30 AM  11:00 AM


Break

 Location
 MSRI: Atrium
 Video


 Abstract
 
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11:00 AM  12:00 PM


(0, 2) dualities and the 4simplex
Natalie Paquette (California Institute of Technology)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
I describe a program, in work with T. Dimofte, to associate 2d supersymmetric field theories to triangulated 4manifolds, complementary to recent advances associating field theories to smooth 4manifolds initiated by GaddeGukovPutrov. BPS observables in the field theory capture topological invariants of the 4manifold. In particular, this field theoretic prescription can be used to associate chiral algebras, and corresponding graded traces, to triangulated 4manifolds with boundary. I will propose the 2d theory that should be associated to the simplest triangulated 4manifold, the 4simplex, and discuss how elementary field theory dualities encode 4d Pachner moves.
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12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
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02:00 PM  03:00 PM


The moduli space of Riemann surfaces and the WeilPetersson metric
Xuwen Zhu (University of California, Berkeley)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
The subject of this talk is the moduli space of Riemann surfaces, which is the set of isometry classes of constant curvature metrics on a surface. The cotangent space of the moduli space is given by holomorphic quadratic differentials, and there is a natural WeilPetersson metric defined by an $L^2$type pairing. I will discuss the behavior of the moduli space when approaching the boundary of the DeligneMumford compactification, and show how to use tools from microlocal analysis to understand the degeneration of the WeilPetersson metric.
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03:00 PM  03:30 PM


Tea

 Location
 MSRI: Simons Auditorium
 Video


 Abstract
 
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03:30 PM  04:30 PM


qabelianization for line defects
Fei Yan (Rutgers University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
I will talk about some joint work with Andrew Neitzke, where we introduce a new "invariant" (with possible wallcrossing) for framed links in a threemanifold M=C \times R with C being an oriented surface. This invariant, denoted as F(L) for a framed link L, is valued in the GL(1) skein algebra of another threemanifold M'=C' \times R, where C' is an Nfold cover of C.
Under various special limits, F(L) turns into more familiar objects. When L is contained in a 3ball in M, F(L) reproduces certain onevariable limit of the HOMFLY polynomial of L. When the projection of L to C has no crossings and the homology class of L is nontrivial, F(L) becomes a generating function encoding the spectrum of framed BPS states associated with certain halfBPS line defect in a 4d N=2 supersymmetric theory. In general, F(L) is a "hybrid" of the above two quantities.
The construction of F(L) is realized via a homomorphism from the GL(N) skein algebra of M to the GL(1) skein algebra of M'. In my talk I will first review the notion of skein algebras. Then I will describe this homomorphism for the special case of N=2, followed by some examples.
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04:30 PM  05:30 PM


Panel Discussion

 Location
 MSRI: Commons Room
 Video


 Abstract
 
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05:30 PM  07:00 PM


Dinner at MSRI

 Location
 MSRI: Atrium
 Video


 Abstract
 
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