Cédric Villani, Of triangles, gases, prices and men (lecture)

Content

The Lady of Shalott
- can only see thing through a mirror
Riemann Hypothesis
- relation to prime numbers
- and also eigenvector of matrix describing large atoms (similar with bus drivers)
- in practice it’s true (not proof, cf physics, economics (joke))
how to become famous mathematician
- prove great theorem
- find great problem
- find great concepts
  - Riemannian geometry
  - curvature
hyperbolic stitching
- constant negative curvature
Poincaré: the art of giving same name to different things
Ricci curvature (cf general relativity)

Boltzmann
- sect of people visiting Boltzmann’s grave
- connection to statistics
Bernoulli
- law of large numbers
Abraham de Moivre
- exp(-x* *2)
Buffon’s needle
Laplace
- the Law of Errors
Adolphe Quetelet – popularized law of random causes
Francis Galton (if Greeks had known that law, they’d have personified it)
Claude Shannon
- draft: information or uncertainty
- rework by von Neumann: entropy
entropy
- number of combinations is out of this world, so logarithmize it
- vacuum doesn’t suck, it’s power of statistics
- “Disorder and information is better than order and disinformation” (about a broadcasting company)
partial differential equations
- Navier-Stokes equations are popular in Holywood industry
maximum entropy – law of errors
- a Boltzmann’s equation for homogenous gas (is not homogenous)

Cercignani Conjecture
- Toscani, Villani
- “Simple to state, difficult to prove. As you like it.”
- this idea was completely naïve and could never work but he found an interesting identity
Leonid Kantorovich
- very real-life problems (A-bomb, taxi fares, Petrograd siege)
- book: The best uses of economic resources
- operational research, plywood
  - linear programming used to be in French high school curriculum
- Monge-Kantorovich
  - min-max flow theorem?
  - the theorem looks like maximization of capitalistic profit

conclusion of topics
- prices (optimization)
- shapes of triangles (geometry)
- entropy (statistics)
coworkers
- Felix Otto, John Lott
- visiting in USA, no duties, just going to lunch and socialize – it cost him fortune
the lazy gas experiment
- initial and final state of gas
- optimize the way it transitions
- similar to movement in curved space
Optimal transport, old and new (1000 pages book by him)
new theorem every month
importance of random encounters for research