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