Teaching

Fall 2020: PHYS 57000(U) “Quantum Gravity and Black Holes”

Tue-Thu 4:30-5:45 pm; Room PHYS 338

Prerequisites: Basic familiarity with general relativity at the level of Carroll’s book (a free version is here) and basics of quantum field theory at the level of Peskin-Schroeder’s book.

Course description: We will discuss black hole thermodynamics, path integrals in quantum gravity, holography and gauge/gravity dualities, and connections to quantum information theory and entanglement.

References: We will follow the structure of Tom Hartman’s lectures notes: (Lectures on Quantum Gravity and Black Holes)

Combined with these lecture notes:

Jared Kaplan’s lecture notes: (Why Quantum Gravity?) (Lectures on AdS/CFT from the bottom up)

Hong Liu’s lecture notes and recorded videos form the course Holographic duality

We will use the application Slack to post course announcements, reports, discuss ideas and share interesting papers we have come across. If you are planning to attend the class please send me an email and I will add you to the course channel on Slack.

Homework:

The students should read the relevant section of the lecture notes before coming to class and submit two questions on slack. Every lecture will have homework problems that will be assigned in class and have to be submitted on Slack up to a week after the lecture.
There will be a term project and we will decide the groups in a few weeks.

Syllabus:

  • Lecture 1: Gravity in long distances (reading: Section 1 of Hartman’s lectures)
  • Lecture 2: Gravity in very short distances (reading: Lecture 1 of Hong Liu’s course)
  • Lecture 4: Black hole thermodynamics (reading: Section 2 of Hartman’s lectures)
  • Lecture 5: Gauge redundancy in gravity (reading: section 4 of Kaplan’s lectures)
  • Lecture 6: Rindler space and Hawking radiation (reading: section 3 of Hartman’s lectures
  • Lecture 7: Path integrals, states and operators (reading: section 4 of Hartman’s lectures)
  • Lecture 8: Path integrals, and Hawking radiation (reading: section 5 of Hartman’s lectures)
  • Lecture 9: Path integrals in gravity 1 (reading: section 6 of Hartman’s lectures)
  • Lecture 10: Path integrals in gravity 2
  • Lecture 11: Symmetries and the Hamiltonian in gravity (reading: section 8 of Hartman’s lectures)
  • Lecture 12: Preview of AdS/CFT correspondence (reading: section 10 of Hartman’s lectures)
  • Lecture 13: Free particles in AdS (reading: section 2 and 3 of Kaplan’s Lectures on AdS/CFT)
  • Lecture 14: Free fields in AdS (reading: section 4 of Kaplan’s Lectures on AdS/CFT)
  • Lecture 15: AdS from near horizon limits (reading: section 11 of Hartman’s notes)
  • Lecture 16: Absorption cross section from D1-D5-P (reading: section 12 of Hartman’s notes)
  • Lecture 17: Absorption cross section from the dual CFT (reading: section 13 of Hartman’s notes)
  • Lecture 18: The statement of AdS/CFT (reading: section 14 of Hartman’s notes)
  • Lecture 19: Generalized free fields and AdS/CFT (reading: section 6 of Kaplan’s lectures on AdS/CFT)
  • Lecture 20: Correlation functions in AdS/CFT (reading: section 15 of Hartman’s notes)
  • Lecture 21: Black hole thermodynamics in AdS (reading: section 16 of Hartman’s notes)
  • Lecture 22: Eternal black holes and entanglement (reading: section 17 of Hartman’s notes)
  • Lecture 23: Holographic entanglement entropy (reading: section 21 of Hartman’s notes)
  • Lecture 24:
  • Lecture 25:
  • Lecture 26:
  • Lecture 27:

If you have any questions/comments or suggestions please do not hesitate to send me a message.


Fall 2019: PHYS 57000(A) “Quantum Information and Geometry”

Tue-Thu 4:45-6:00 pm; Room PHYS 338

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Prerequisites: Quantum Mechanics and/or Operator Algebra, Statistical Mechanics, Classical Mechanics. Knowledge of Quantum Field Theory is not required; however, familiarity with the basics of General Relativity and Riemannian geometry will be assumed.

Course description: This course is an introduction to information-theoretic methods in fundamental physics. It is aimed at graduate students and advanced undergraduate students in Physics and Mathematics. I strongly encourage interested Mathematics students with knowledge of operator algebras to participate.

Topics that we will cover:

1)  Entanglement Theory and General Quantum Systems

2) Tensor Networks, Many-body Quantum Systems and Geometry

3) Quantum Fields and Entanglement

4) Basics of Conformal Field Theory

5) Towards the Emergence of Spacetime and Holography

If you have suggestions/comments regarding the course please do not hesitate to email me.

To keep the course interactive and the students can play a more active role in choosing the focus of the course, we will use the application Slack to post course announcements, reports, discuss ideas and share interesting papers we have come across. If you are planning to attend the class please send me an email and I will add you to the course channel on Slack.

Some books on the basics of quantum information theory:

Some references on quantum many-body quantum systems  and tensor networks:

Some references on von Neumann algebras and Modular Theory:

Some references on local algebras of quantum fields:

Some references on conformal field theory:

Some references on Quantum gravity, black holes:

Some references on AdS/CFT correspondence:

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