# IGA mini Lecture series

## by Luis Alvarez-Gaume (Director, Simons Centre for Geometry and Physics
and Professor of Physics, SUNY, Stony Brook)

#
Lectures on Index Theory and Quantum Field Theory

## About the IGA Lecturer:

Luis Alvarez-Gaume is a theoretical physicist who works on string theory and quantum gravity.
He obtained his PhD in 1981 from Stony Brook University and worked from 1981 to 1984 at Harvard University as a Junior Fellow, before he moved to Boston University to work as a professor. From 1986 until 2016, he was a permanent member of the CERN Theoretical Physics unit. In 2016, he became the director of the Simons Center for Geometry and Physics at Stony Brook. He is renowned for his work on supersymmetry and QFT.

## Abstracts of lectures and venue:

Lectures 1 and 2: Index Theory, Quantum Field Theory and Supersymmetry

These two lectures will present a review of index theory as
it appears in the mathematics literature and the original proofs,
and then proceed to some aspects of QFT that involve
symmetry realization and symmetry breaking, and extend
these considerations to supersymmetry. We will then
present a general study of Witten's index in QFT, and
how it leads to a proof of the Atiyah-Singer index theorem
using loop space localization.

Level 7 conference room, 10am-12pm - Wednesday 14th November,
and Thursday 15th November 2018

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Lecture 3: Revisiting Goldstone's theorem

The last few years have seen an explosion of non-perturbative
techniques in QFT. Mostly due to the upgraded conformal
bootstrap, localization techniques, resurgence etcetera. We
have also learned that in theories with global symmetries,
we can access non-perturbative information in those sectors
of the Hilbert space describing states with high values of
the global charge. What is surprising is that the results
involve novel ways of understanding Goldstone's theorem
and breaking of Lorentz invariance. I will present some of
recent work on this subject.

Level 7 conference room, 10am-12pm - Friday 16th November 2018

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