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

## Content

### Curvature of spaces

- 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)

## Slow mastering of chance

- 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 Channon
- 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)

### Optimization problems

- 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

### Synthesis

- 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

## Meta

- sponsored by K. Janeček
- LibreOffice on MacOS
- use of French quotes in presentation
- Hilbert pronunciation [ilbert]
- Bolzano Lectures series (not in France)
- Bičák boasts about Bolzano
- how Bolzano read Euclid’s Foundations and was cured
- also A. Lincoln read Euclides