This series is a crash course introduction to a handful of advanced topics designed to tackle the general problem of how to engineer Positive Operator-Valued Measures (POVMs) using observable building blocks, the so-called Instrument Manifold Program. This program emerged from a recent fundamental breakthrough: how to realize the measurement of a spin’s direction, a.k.a. the spin-coherent-state POVM, a spherical set of outcomes analogous to the well known coherent-state POVM of the standard phase plane.
**Outline:**
Oct 27: Introduction: The Planimeter and the ``Spherimeter''
Oct 30: Indirect Measurement and System-Meter Interaction
Nov 03: POVMs and Decoherence
Nov 06: Generalized Observables: Phase-Point and Spin-Direction
Nov 10: Transformation Groups and Enveloping Algebras
Nov 13: Frame Operators and Quasi-Probability Distributions
Nov 17: The Arthurs-Kelly (1965) and D’Ariano (2002) Measurements
Nov 20: Optical Homodyne and Heterodyne
Nov 24: Continuous Measurement and the Kraus-Operator Density
Nov 27: Simultaneous Measurements of Non-Commuting Observables
Dec 01: Instrumental Groups and Universal Markov Processes
Dec 04: Universal Instrument Navigation
Dec 08: Non-Euclidean Geometry
Dec 11: Non-Euclidean POVMs
**Location & Building Access:**
Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo
(Exception - November 27 in Space Room, 4th Floor)
**Registration:**
Please sign-up here: https://forms.office.com/r/dEA4EUq0CU
Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact academic@perimeterinstitute.ca.
*Scroll down to Registration and Enrollment to participate.*
**Structure:**
We will discuss 8 papers which had huge impact in physics. One week Instructor Pedro Vieira will discuss a paper; students should read it beforehand. One week later students discuss recent papers referring to that paper (20 min each student, ~ 3 presentations; at the end of the class Pedro will grade the presentations based on “Physics”, “Presentation”, “Question handling”; and give comments).
By the end of the course, students will have explored a vast set of topics in theoretical physics — spotting potential gaps to be fixed — sharpened their presentation skills through steady practice, and sparked cross-disciplinary conversations through our shared physics language.
*Familiarity with Quantum Field Theory and General Relativity is assumed.*
**The papers:**
Sept 12 & 19: On the Quantum Correction for Thermodynamic Equilibrium, Wigner, 1932
Topic: Quantum Mechanics
Sept 22 & 29: Existence theorem for certain systems of nonlinear PDEs, Foures-Bruhat, 1952
Topic: General relativity
Oct 3 & 10: The Renormalization Group and the Epsilon Expansion, Wilson and Kogut, 1973
Topic: Quantum Field Theory
**Oct 10 (EXTRA)** & 17: More about the Massive Schwinger Model, Coleman, 1976
Topic: 2D Quantum Field Theory
Oct 20 & 27: A sequence of approximated solutions to the S-K model for spin glasses, Parisi, 1980
Topic: Statistical Mechanics
Oct 31 & Nov 7: Quantum Field Theory and the Jones Polynomial, Witten, 1988
Topic: Topological Quantum Field Theory
Nov 10 & 17: Exactly Solvable Field Theories of Closed Strings, Brezin, Kazakov, 1989
Topic: 2D Quantum Gravity
Nov 21 & Nov 28: Unpaired Majorana fermions in quantum wires, Kitaev, 2000
Topic: Quantum Matter/Quantum Information
**Schedule:**
This is a Friday / Monday alternating week schedule from 915am-1045am.
**Exceptions:**
There will be an afternoon session at 130pm on Friday October 10 to avoid the Thanksgiving holiday.
**Location & Building Access:**
Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo
Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact academic@perimeterinstitute.ca.
**Registration and Enrollment:**
Please sign-up here: https://forms.office.com/r/nDQ6SDxSR4
Quantum field theory intertwines continuous and discrete structures. On the discrete side, combinatorics plays a central role in describing and understanding its expansions and models. This lecture series focuses on the combinatorial aspects of quantum field theory. In the first part, we explore analytic combinatorics techniques, inspired by QFT, for the
enumeration of graphs. These methods turn out to be surprisingly powerful in addressing deep questions in algebraic geometry, topology, and statistical models on graphs. In the second part, we turn to discrete structures arising in perturbative expansions of QFT. We study these from a modern combinatorics viewpoint, using tools such as Lorentzian polynomials and generalized permutahedra to better understand the mathematical objects at the heart of quantum field theory.
For updates visit: https://michaelborinsky.com/combqft.html
This course is offered by the University of Waterloo's Department of Combinatorics & Optimization; UW students can enroll through Quest.
Lectures will be held at Perimeter Institute, 31 Caroline St N, Waterloo. Students will need to sign in and out of Perimeter each day. Note room change on Sept 25 and Oct 2, and no classes week of October 13.
