Speaker: David Roberson, Tuesdays at 11:00 am EST, starting May 18.

News

Outline

This course will study quantum homomorphisms and isomorphisms and related topics. These concepts are based on quantum strategies for multiplayer interactive games, but we will view them more as quantum analogs of functions between the vertex sets of graphs. There are a surprising number of connections between these notions and other topics such as spectral bounds for graph parameters, conic optimization, and quantum groups. This course will explore such connections as well as related topics in quantum information.

Resources: pdfs

  1. Homework.
  2. arxiv.org/abs/1910.06958 Mancinska, Roberson. "Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs".
  3. arxiv.org/abs/2004.10893 Mancinska, Roberson, Varvitsiotis. "Graph isomorphism: Physical resources, optimization models, and algebraic characterizations".
  4. Variations on a Theme: Graph Homomorphisms. (David Roberson's Ph. D. thesis.)
  5. The sandwich theorem. Knuth's paper on Lovász theta.
  6. paper for last lecture. Mancinska, Roberson: Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs

Recordings of Lectures

  1. May 18: slides.
  2. May 25: slides.
  3. June 1: slides.
  4. June 8: slides.
  5. June 15: slides.
  6. June 22: slides.
  7. June 29: slides.
  8. July 6: slides.
  9. July 13: slides.
  10. July 20: slides.
  11. July 27: slides.
  12. August 3: slides.
  13. August 10: slides.
All videos

Contact

For further information, contact Chris Godsil.