Synopsis
Ten abandoned gold mines.- The Fubini Lectures.- Foreword.- The adventures of measure theory.- What is invariant theory, really?.- Twelve problems in probability no one likes to bring up.- Recurrent Themes of Gian-Carlo Rota's Mathematical Thought.- Resolution of Weyl modules: the Rota touch.- Circulant recursive matrices.- Remarks on Invariant geometric calculus. Cayley-Grassmann algebras and geometric Clifford algebras.- Grassmann geometric calculus, invariant theory and superalgebras.- Rota-Metropolis cubic logic and Ulam-Rényi games.- Umbral nature of the Poisson random variables.- A formal theory of resultants (I): an algorithm in invariant theory.- A formal theory of resultants (II): a constructive definition of the resultant.- Focus on Catalan Numbers and Combinatorics on Words.- Foreword to the surveys by Aigner and Perrin.- Catalan and other numbers: a recurrent theme.- Enumerative combinatorics on words.- Algebraic Combinatorics and Theoretical Computer Science.- Alphabet splitting.- Some operations on the family of equivalence relations.- Solving linear recurrences using functionals.- Polynomiality of the q, t-Kostka revisited.- A combinatorial approach to the theory of Pi-algebras and exponential growth.- On the permanent of certain circulant matrices.- Episturmian words and morphisms (results and conjectures).- A curious characteristic property of standard Sturmian words.
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