Registration: 8:15 to 9:00 in Jefferson Physics Research Library (Room 450)
Monday, December 10
Welcome at 9:00 by Christopher Stubbs
Time  Speaker  Title/Abstract 
9:05 – 10:05am 
James Glimm Stony Brook 
Title: From Constructive Quantum Field Theory to Type Ia Supernova Abstract: We sketch some of the major developments for constructive quantum field theory. We note the fundamental obstacle at 4 space time dimensions, and continue with discussion of renormalization group ideas. Here we find analogies to fluid turbulence useful. Turbulence, as with Quantum Chromodynamics, has the simplifying property of asymptotic freedom. We assume a Kolmogorov 1941 style bound and prove as a result existence of solutions to the Euler equation. This can be thought of as a handle on the inessential variables in the RNG terminology. The Euler equation solutions are not unique and in need of an admissibility condition. Here a major scientific controversy occurs. We comment on the solution of the deflagration to detonation transition in SN Ia, and its relation to this controversy. 
10:05 – 10:30am  Break  Jefferson Physics Research Library (Room 450) 
10:30 – 11:30am 
Vaughan Jones Vanderbilt University 
Title: Factors and subfactors in one dimensional quantum physics Abstract: Factors and subfactors arise as algebras of observables in quantum spin chains and conformal field theory. The subfactors in the two cases appear to be the same up to a type III factor. Whether the CFT subfactors can be obtained as limits of the quantum spin chain ones is a brutal open question. As is the question of which subfactors arise in CFT. The techniques of constructive quantum field theory offer the only hope of progress in this area. 
11:30 – 12:30am 
Giovanni Felder ETH Zurich 
Title: Representation homology and supersymmetric gauge theory Abstract:

2:00 – 3:00pm 
Edward Witten IAS 
Title: Nonsupersymmetric DBranes Abstract: Nonsupersymmetric Dbranes were discovered by Sen 20 years ago. I will explain a perspective on them that is based on a discrete anomaly.

3:00 – 3:20pm  Break  Jefferson Physics Research Library (Room 450) 
3:20 – 4:20pm 
Zhengwei Liu Harvard 
Title: Geometric Quantum ErrorCorrecting Codes Abstract: I give a new geometric construction of quantum errorcorrecting codes using the quon language. This provides new pictorial insights for Kitaev’s toric code. It also gives a geometric realization of all stabilizer codes, which represents both the stabilizer group and stabilizer states in a geometric way simultaneously. In particular, I construct the 5,1,3 code using the complete graph K5 which encodes a S5 Symmetry. 
4:20 – 5:20pm 
Cumrun Vafa Harvard 
Title: String Theory and the Unity of Quantum Toplogical Invariants Abstract: I review the connections between quantum systems and topological invariants in low dimensions and explain how a stringy perspective not only gives a unified description of them, but also leads to new invariants for 4manifolds as topological modular forms.

7:30 – 8:30pm Robert D. Levin, Public Lecture (with music) in Science Center B
Title: Who Cares if Classical Music Dies?
Tuesday, December 11
Time  Speaker  Title/Abstract 
9:00 – 10:00am 
David Evans Cardiff University 
Title: Conformal Field Theory: the search for the exotic and reconstruction. Abstract: Modular tensor categories arise in Conformal Field Theory through conformal nets of von Neumann algebras, vertex operator algebras and twisted equivariant Ktheory. I will discuss the issue of constructing models with specific modular data, including the double of the Haagerup subfactor. This is joint work with Terry Gannon.

10:00 – 10:20am  Break  Jefferson Physics Research Library (Room 450) 
10:20 – 11:20am 
Anke Pohl University of Bremen 
Title: Automorphic functions twisted with nonexpanding cusp monodromies, and dynamics
Abstract: Automorphic functions play an important role in several subareas of mathematical physics, e.g., in rational conformal field theories. The correspondence principle between quantum und classical mechanics suggests that automorphic functions are closely related to 
1:00 – 2:00pm 
Jennifer Chayes Microsoft 
Title: Graphons: A Nonparametric Method to Model, Estimate, and Design Algorithms for LargeScale Networks Abstract: Many systems are naturally represented as networks, from offline and online social networks, to bipartite networks, like Netflix and Amazon, between consumers and products, to proteomic networks in biological contexts. Graphons, developed as limits of graphs, are a natural, nonparametric method to describe and estimate (machine learn) large networks like Facebook and LinkedIn. Here I describe the development of the theory of graphons, for both dense and sparse networks, over the last decade. I also give theorems showing that we can consistently estimate graphons from massive networks in a wide variety of models. Finally, I show how to use graphons to estimate missing links in a sparse network, which has applications from estimating social and information networks in development economics, to rigorously and efficiently doing collaborative filtering with applications to movie recommendations in Netflix and product suggestions in Amazon, to inferring missing links in biological networks.

2:00 – 2:20pm  Break  Jefferson Physics Research Library (Room 450) 
2:20 – 3:20pm 
Shamil Shakirov Harvard & Uppsala University 
Title: Higher genus analogues of Jack polynomials Abstract: We construct systems of commuting differential operators associated with quivers with g loops, whose common eigenfunctions may be called genus g Jack polynomials. 
3:20 – 4:20pm 
Christoph Schweigert University of Hamburg 
Title: Bulk Fields in Conformal Field Theory
Abstract: Twodimensional conformal field theories are examples of quantum field theories that allow for mathematically precise statements about the field content and the existence of consistent sets of correlators.

5:00pm The conference dinner (for those signed up) will be at Loeb House, 17 Quincy Street, Cambridge.
Wednesday, December 12
Time  Speaker  Title/Abstract 
9:00 – 10:00am 
Klaus Hepp ETH 
Title: Phase Transitions in the Brain
Abstract: First we analyse microsleep, which happens during drowsy driving and to students in our lectures. Then we relate the neuronal data on microsleep in the oculomotor system to nonequilibrium phase transitions, guided by our work with E Lieb on the reservoirdriven finitemode laser. Finally 
10:00 – 10:20am  Break  Jefferson Physics Research Library (Room 450) 
10:20 – 11:20am 
XiaoGang Wen MIT 
Title: Emergce of higher symmetry in lattice (condensed matter) systems Abstract: TBD 
11:20 – 12:20pm 
Mikhail Lukin Harvard 
Title: Exploring new frontiers in quantum science Abstract: TBD 
2:00 – 2:30pm 
Christian Jaekel University of Sao Paulo 
Title: On reflection positivity, modular localisation and Connes cocycles
Abstract: The unitary irreducible representations of the Lorentz group carry an intrinsic notion of localisation on de Sitter space, known as modular localisation. An extension of Araki’s perturbation theory of modular automorphisms can be used to define interacting representations of the Lorentz group, as well as the corresponding HaagKastler nets. The analyticity properties of the correlation functions allow us to extend these theories to “nets" of (nonabelian) von Neumann algebras on the sphere. Reflection positivity can be used to recover the interacting quantum (field) theories 
2:30 – 3:00pm 
Bas Janssens Delft University of Technology 
Title: Reflection Positivite Doubles Abstract: Reflection Positive Doubles constitute a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. In this context, we give sufficient (and, under extra assumptions, necessary) conditions for reflection positivity. The main novelty here is that the systems under consideration can be not only bosonic or fermionic, but also parafermionic. (Joint work with Arthur Jaffe) 
3:00 – 3:20pm 
Davis Lazowski Harvard 
Title: Lie Algebras and Quiver Representations Abstract: This talk will survey methods of recovering information about a Lie algebra from the quiver representation theory of its finite or affine ADE Dynkin diagram. 
3:40 – 4:10pm 
William Norledge Penn State University 
Title: The Combinatorial Lie Coalgebra of Permutohedral Cones Abstract: We study permutohedral cones as realvalued functions on the chambers of the adjoint braid arrangement. The discrete differentiation of functions across hyperplanes equips the linear span of permutohedral cones with the structure of a combinatorial Lie coalgebra. Using this Lie structure, we show that permutohedral cones satisfy the Steinmann relations of axiomatic quantum field theory, and we give an algorithm for expressing any function which satisfies the Steinmann relations in terms of permutohedral cones. We show that the universal enveloping coalgebra is the dual Hopf algebra of the braid arrangement, which is a combinatorial analog of the shuffle algebra.

4:10 – 4:40pm 
Yunxiang Ren Harvard 
Title: Locally compact planar algebras Abstract: For a finite group G, it is wellknown that the monodical category of Ggraded vector spaces and that of the representations of G are Morita equivalent. In this talk, we introduce locally compact planar algebras with reflection positivity. Within this framework, we can generalize the two monodical categories for locally compact groups. Moreover, we formalize and prove their Morita equivalence for compact groups. Our definition and proof also work for locally compact groups R^n. It requires a deep understanding of the analytic properties, particularly the uncertainty principle, to prove this Morita equivalence for locally compact groups and locally compact quantum groups in general. Discrete or compact planar algebras are closely related to infiniteindex subfactors. 
4:40 – 5:00pm 
Michele Tienni Harvard 
Title: Algebraic and Topological Structures of Subfactors Abstract: It is wellknown that a (finite depth) subfactor is associated to a fusion category and a planar algebra. In this talk we will explore how these two algebraic structure give rise to TQFTs in dimension 2+1 and 1+1 respectively. 
6:00pm There will be a concert and dinner for persons who have signed up with the American Academy of Arts and Sciences.