Abstract
These are some reflections on the great algebraic geometer Shreeram Abhyankar given at the Banquet at the International Conference on Lattice Path Combinatorics and Applications, California Polytechnic University, Pomona, on Thursday, August 20, 2015.
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Notes
- 1.
Abhyankar classified algebra into three types: (i) high school algebra (polynomials, power series): Bhaskara (1114), Cardano (1530), Ferrari (1540), Newton (1680), Tschirnhausen (1683), Euler (1748), Sylvester (1840), Cayley (1870), Kronecker (1882), Mertens (1886), König (1903), Perron (1905), Hurwitz (1913), Macaulay (1916), Zariski (1941), Hironaka (1964); (ii) college algebra (rings, fields, and ideals): Dedekind (1882), Noether (1925), Krull (1930), Zariski (1941), Chevalley (1943), Cohen (1946), Nagata (1960); and (iii) university algebra (functors): Serre (1955), Cartan (1956), Eilenberg (1956), Grothendieck (1960), Mumford (1965).
References
Abhyankar, S.S.: The contributions of Ramanujan to mathematics. In: Ramakrishnan, Alladi (ed.) Symposia on Theoretical Physics and Mathematics, vol. 10, pp. 1–6. Plenum, New York (1970)
Abhyankar, S.S.: Historical ramblings in algebraic geometry and related algebra. Am. Math. Mon. 83, 409–448 (1976)
Abhyankar, S.S.: Inversion and invariance of characteristic terms: Part I. In: Alladi, K., Klauder, J.R., Rao, C.R. (eds.) The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, pp. 93–168. Springer, New York (2010)
Acknowledgements
I am thankful to the organizers of the International Conference on Lattice Paths Combinatorics and Applications and in particular to Alan Krinik, for not only inviting me to speak in one of the technical sessions, but also to be the Banquet Speaker at this conference which honored the memory of Shreeram Abhyankar and Philippe Flajolet.
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Alladi, K. (2019). Reflections on Shreeram Abhyankar. In: Andrews, G., Krattenthaler, C., Krinik, A. (eds) Lattice Path Combinatorics and Applications. Developments in Mathematics, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-030-11102-1_3
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