Search Talks

Continuous and discrete symmetries, infinitesimal symmetries

https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020

(Super)conformal algebras on two-dimensional spacetimes play a ubiquitous role in representation theory and conformal field theory. In most cases, however, superconformal algebras are finite dimensional. In this talk, we introduce refinements of certain deformations of superconformal algebras which share many facets with the ordinary (super) Virasoro algebras. Representations of these refinements include the higher dimensional Kac—Moody algebras, and many more motivated by physics. Finally, we will show how these algebras enhance to higher dimensional chiral/factorization algebras which upon ``localization" deform to well-studied chiral algebras on Riemann surfaces.

Resource Theories and Quantum Information

https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020

The talk illuminates the role of codes and lattice vertex algebras in algebraic topology. These objects come up naturally in connection with string structures or topological modular forms. The talk tries to unify these different concepts in an introductory manner.

Baker and Richter's $A_\infty$ analog of the complex cobordism spectrum provides characteristic numbers for complex-oriented toric manifolds, which generalize to define similar invariants for Hamiltonian toric dynamical systems: roughly, the `completely integrable' systems of classical mechanics which (by KAM theory) possess remarkable stability properties. arXiv:1910.12609

Introduction to Ising model; review spin-1/2 and matrix representation of states  and operators; programming basics

https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020

We investigate putting 2+1 free and holographic theories on a product of time with a curved compact 2-d space. We then vary the geometry of the space, keeping the area fixed, at zero/finite temperature, and measure the Casimir/free energy respectively. I will begin by discussing the free theory for a Dirac fermion or scalar field on deformations of the round 2-sphere. I will discuss how the Dirac theory may arise in physical systems such as monolayer graphene. For small deformations we solve analytically using perturbation theory. For large deformations we use novel numerical methods to compute these energies for specific deformations, including ones that drive the space to become singular. I will give evidence that the round sphere globally maximises the Casimir/free energy, which may imply geometric instabilities for spheres of such mono layer materials, although probably not graphene. We then discuss the analog for a holographic theory by studying its gravity dual. Here we use gravity techniques to analytically prove at zero temperature the round sphere maximises the Casimir energy. We discuss attempts to show the same for free energy at finite temperature. And finally I will report on on-going numerical gravity calculations of the Casimir energy for specific  deformations of the round sphere which yield an unexpected result.

 

I'll discuss elliptic cohomology from a physical perspective, indicating the importance of the Segal-Stolz-Teichner conjecture and joint work with D. Berwick-Evans on rigorously proving some of these physical predictions.

Thirteen years ago, Lurie has sketched a way to obtain equivariant elliptic cohomology and equivariant topological modular forms without the need to restrict to rational or complex coefficients. Recently, David Gepner and I have found one way to flesh out the details and and provide computations in the U(1)-equivariant case. On this work I will report.

Introduction to path integrals and the semi-classical limit

https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020

Overview/definition of symmetry, elements of group theory
https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020