Calendar
- 17May 17, 2020No events
- 18May 18, 2020No events
- 19May 19, 2020
Buildings, C*-algebras and new higher dimensional analogues of the Thompson groups
We present explicit constructions of infinite families of CW- complexes of arbitrary dimension with buildings as the universal covers. These complexes give rise to new families of C*-algebras, classifiable by their K-theory. The underlying building structure allows explicit computation of the K-theory. We will also present new higher dimensional generalizations of the Thompson groups, which are usually difficult to distinguish, but the K-theory of C*-algebras gives new invariants to recognize non-isomorphic groups. We will also discuss new directions of generalizations to higher dimensions of the work of Vaughan Jones and his collaborators on connections of the Thomson’s group and Conformal Field Theory.
via Zoom: https://harvard.zoom.us/j/779283357
- 20May 20, 2020
CMSA Quantum Matter/Quantum Field Theory Seminar: Boundary States for Fermions: SPT Phases, RG Flows, and a Whole Bunch of Related Things
I’ll describe boundary conditions for fermions in d=1+1 dimensions, using the framework of boundary conformal field theory. I’ll explain how boundary states are classified by a mod 2 index, related to their SPT phase, describe how one can follow RG flows from one boundary state to another, and give a novel perspective on the Z_8 classification of d=2+1 SPT phases.
via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126
Fluctuation Results for General Ising Models -- Block Spin Ising Models and Random Interactions
Starting from the classical Curie-Weiss model in statistical mechanics, we will consider more general Ising models. On the one hand, we introduce a block structure, i.e. a model of spins in which the vertices are divided into a finite number of blocks and where pair interactions are given according to their blocks. The magnetization is then the vector of magnetizations within each block, and we are interested in its behaviour and in particular in its fluctuations. On the other hand, we consider Ising models on Erdős-Rényi random graphs. Here, I will also present results on the fluctuations of the magnetization.
- 21May 21, 2020
CMSA Condensed Matter/Math Seminar: Gauge-invariant path-integral measure for the overlap Weyl fermions in 16 of SO(10)
We consider a lattice formulation of the SO(10) chiral gauge theory with left-handed Weyl fermions in the sixteen dimensional spinor representation 16 in the framework of the overlap fermion/the Ginsparg-Wilson relation. We propose a manifestly gauge-invariant path-integral measure for the left-handed Weyl field on the lattice using all the components of the Dirac field, but the right-handed part of which is just saturated completely by inserting a suitable product of the SO(10)-invariant ‘t Hooft vertices in terms of the right-handed field. The definition of the measure applies to all possible topological sectors. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the left-handed field is anomalous due to the non-trivial transformation of the measure, while that of the right-handed field is explicitly broken by the ’t Hooft vertices. There remains the issue of smoothness/locality in the gauge-field dependence of the Weyl fermion measure.We also discuss the relations of our formulation to other approaches/proposals to decouple the species-doubling/mirror degrees of freedom. Those include Eichten-Preskill model, Ginsparg-Wilson Mirror-fermion model, Domain wall fermion model with the boundary Eichten-Preskill term, and 4D Topological Insulator/Superconductor with gapped boundary phase. We clarify the similarity and the difference in technical detail and show that our proposal is a well-defined and unified testing ground for that basic question.via Zoom: https://harvard.zoom.us/j/977347126
- 22May 22, 2020
Math Science Literature Lecture Series
Please register here to attend any of the lectures.
Title: Four-dimensional topology
Abstract: I will outline the history of four-dimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the Seiberg-Witten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the focus shifted to four-manifolds with boundary and cobordisms. Floer homology has led to numerous applications, and recently there have also been a few novel results (and proofs of old results) using Khovanov homology. The talk will be accessible to a general mathematical audience.
Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”
The schedule will be updated as talks are confirmed.
Math Science Literature Lecture Series
Please register here to attend any of the lectures.
Title: From string theory and Moonshine to vertex algebras
Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as well as some of the subsequent and recent developments. The lecture is aimed for a general audience.
Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”
The schedule will be updated as talks are confirmed.
- 23May 23, 2020No events