- Tuesday April 4: Preliminaries on Convexity
- Thursday April 6: Shannon Entropy and Khinchin Axioms, Kullback-Leibler divergence and Fisher-Rao metric
- Tuesday April 11: Thermodynamic semirings, Khinchin axioms and algebraic properties
- Thursday April 13: Thermodynamic semirings for Renyi and Tsallis entropy and Kullback-Leibler divergence, entropy operads
- Tuesday April 18: Mutual information and inclusion-exclusion, Hochschild complex, mutual information as Hochschild cocycles, finite field polylogarithms and Tsallis entropies
- Thursday April 20: Quantum versus classical probability: events, observables, probability distributions, expectation values, composite systems, dynamics
- Tuesday April 18: finite dimensional quantum mechanics as complex projective geometry, pure states and projective spaces, tensor products and Segre embeddings
- Thursday April 20: pure states and Bloch vectors, complex projective spaces as symmetric products, Fubini-Study metric and quantum information, Wigner's theorem
- Tuesday April 25: geometric structure of the space of density matrices (U(N) orbits, flag manifolds and simplexes), entropy in quantum information, von Neumann entropy
- Thursday April 27: relative entropy in quantum probability, completely positive maps and quantum channels, measurement postulate, entropy and channel capacity
- Tuesday May 2: thermodynamic semirings, tropical and entropical trace and von Neumann entropy, thermodynamic deformations of states on C* algebras, entropies of dynamical systems, quantum relative entropy and Fisher metric
- Thursday May 4: Classical codes, code parameters, rate and minimum distance, spoiling operations, existence of the asymptotic bound, singleton bound
- Tuesday May 9:
- Thursday May 11:
- Tuesday May 16:
- Thursday May 18:
- Tuesday May 23:
- Thursday May 25:
- Tuesday May 30:
- Thursday June 1: student presentations

- Quantum Statistical Mechanics, Kolmogorov Complexity, and the Asymptotic Bound for Error-correcting Codes
- Dyson-Schwinger Equations in the Theory of Computation
- Information Algebras and their Applications

- M.Mezard, A.Montanari, "Information, physics and computation", Oxford University Press, 2009.
- I.Bengtsson, K.Zyczkowski, "Geometry of quantum states", Cambridge University Press, 2006.
- K.R. Parthasarathy, "Quantum Computation, quantum error correcting codes and information theory", Narosa, 2006.
- Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter, "The Functional Analysis of Quantum Information Theory", Springer 2015.
- K. Fujii, "Quantum computation with topological codes" Springer, 2016.
- S.Amari, H.Nagaoka, "Methods of Information Geometry" AMS and Oxford, 2000

- Matilde Marcolli, Ryan Thorngren, "Thermodynamic semirings", arXiv:1108.2874
- Matilde Marcolli, Nicolas Tedeschi, "Entropy algebras and Birkhoff factorization", arXiv:1412.0247
- Yuri Manin, Matilde Marcolli, "Error-correcting codes and phase transitions", arXiv:0910.5135
- Yuri Manin, Matilde Marcolli, "Kolmogorov complexity and the asymptotic bound for error-correcting codes", arXiv:1203.0653
- Matilde Marcolli, Christopher Perez, "Codes as fractals and noncommutative spaces", arXiv:1107.5782
- Matilde Marcolli, John Napp, "Quantum computation and real multiplication", arXiv:1312.3590
- Yuri Manin, "Renormalization and computation I: motivation and background", arXiv:0904.4921,
- Yuri Manin, "Renormalization and Computation II: Time Cut-off and the Halting Problem", arXiv:0908.3430.
- Colleen Delaney, Matilde Marcolli, "Dyson-Schwinger equations in the theory of computation", arXiv:1302.5040
- Philippe Elbaz-Vincent, Herbert Gangl, "Finite polylogarithms, their multiple analogues, and the Shannon entropy", pdf

- John C. Baez, Mike Stay, "Physics, Topology, Logic and Computation: A Rosetta Stone", arXiv:0903.0340
- John C. Baez, Tobias Fritz, Tom Leinster, "A characterization of entropy in terms of information loss", arXiv:1106.1791
- Yuri Manin, "A computability challenge: asymptotic bounds and isolated error-correcting codes", arXiv:1107.4246
- Yuri Manin, "Complexity vs Energy: Theory of Computation and Theoretical Physics", arXiv:1302.6695
- Yuri Manin, "Zipf's law and L. Levin's probability distributions", arXiv:1301.0427
- Yuri Manin, "Classical computing, quantum computing, and Shor's factoring algorithm", arXiv:quant-ph/9903008
- S.Trebst, M.Troyer, Z.Wang, A.Ludwig, "A short introduction to Fibonacci anyon models, arXiv:0902.3275
- Michael H. Freedman, Alexei Kitaev, Michael J. Larsen, Zhenghan Wang, "Topological quantum computation", arXiv:quant-ph/0101025
- C.Nayak, S.Simon, A.Stern, M.Freedman, S.Sarma, "Non-Abelian Anyons and Topological Quantum Computation", arXiv:0707.1889
- M.Redei, S.J.Summers, "Quantum Probability Theory", arXiv:quant-ph/0601158
- P.Jizba, "Information theory and generalized statistics" pdf
- Pierre Baudot, Daniel Bennequin, "The Homological Nature of Entropy" pdf