Ten abandoned gold mines
I thank Domenico Senato and his fellow organizers for the kind invitation to participate in this gathering of friends of Gian-Carlo Rota — to grieve with you his passing and to search with you for a renewal of the work he laid out for us. Mimmo and Elvira have asked me to speak about Gian-Carlo’s mathematical work — and I do so in keen recollection of the happy evenings the four of us spent together at a café on the corso in Cortona just in the summer of 1998. Gian-Carlo had a way of creating order in his life, imposing patterns on time so as to be able to concentrate his energies, and to plan for discussions with innumerable people. I like to compare this practice with the establishment of rules in the monastic orders. That summer’s Regola Cortoniense starts, as usual, not with the angelus but with lunch (no pasta, but with a big bowl of fruit to take to his room in prospect of an evening and morning without supplies). Then the combinatorial seminars, followed by a carefully scheduled series of tête-àtêtes with individual students and visitors. At 17h30 sharp, we climb into la Macchina Senato, for the short drive uphill from the Palazzone to the town. There, always at that table just outside the door of his favorite café, Gian-Carlo orders his evening meal: three scoops of gelato al cioccolato covered with a rich chocolate sauce, topped off with those tiny but ubiquitous Japanese parasols, which are promptly distributed as offerings. Discussion begins immediately on the umbral calculus, and lasts until after dark. A few pleasantries off the subject, to relax in the evening calm, and Mimmo and Elvira head for their lodging. Gian-Carlo and I return on foot (downhill) to the Palazzone. The day is complete. These were such happy hours for us all.
KeywordsSample Space Invariant Theory Projective Geometry Symmetry Class Exterior Algebra
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- Chan, W., Rota, G.-C., Stein, J. (1995): The power of positive thinking. In: White, N.L. (ed.) Invariant Methods in Discrete and Computational Geometry. Kluwer, Dordrecht, pp. 1–36Google Scholar
- Chan, W. (1998): Classification of trivectors in 6D-space. In: Sagan, B.E., Stanley, R.P. (eds.) Mathematical Essays in Honor of Gian-Carlo Rota. Birkhäuser Boston, Boston, MA, pp. 63–110Google Scholar
- Grosshans, F.D., Rota, G.-C., Stein, J. (1987): Invariant theory and superalgebras. (CBMS Regional Conference Series in Mathematics, 69). American Mathematical Society, Providence, RIGoogle Scholar
- Huang, R.Q. (1990): Combinatorial methods in invariant theory. Ph.D. Thesis, Massachusetts Institute of TechnologyGoogle Scholar
- Kung, J.P.S. (ed.) (1995): Gian-Carlo Rota on Combinatorics. Birkhäuser Boston, Boston, MAGoogle Scholar
- Metropolis, N., Nicoletti, G., Rota, G.-C. (1981): A new class of symmetric functions. In: Mathematical Analysis and Applications. Part B. Academic Press, New York, pp. 563–575Google Scholar
- Rota, G.-C., Mullin, R. (1970): On the foundations of combinatorial theory: III. Theory of binomial enumeration. In: Harris, B. (ed.) Graph Theory and its Applications. Academic Press, New York. pp. 167–213Google Scholar
- Rota, G.-C. (1973): The valuation ring of a distributive lattice. In: Faitlowicz, S., Kaiser, K. (eds.) Proceedings of the University of Houston Lattice Theory Conference. Department of Mathematics, University of Houston, Houston, TX, pp. 574–632Google Scholar
- Rota, G.-C. (1998): Introduction to geometric probability. (AMS Colloquium Lectures, Baltimore, January 1998) American Mathematical Society, Providence, RI, videocasette; edited version: Math. Intelligencer 20(4), 11–16Google Scholar
- Rota, G.-C. (2001): Twelve problems in probability no one likes to bring up. In: Crapo, H. Senato, D. (eds.) Algebraic combinatorics and computer science. A tribute to Gian-Carlo Rota. Springer Milan, pp. 57Google Scholar