Migliorini, Pagaria: I lavori di June Huh

Migliorini, Luca and Pagaria, Roberto:
I lavori di June Huh
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana Serie 1 8 (2023), fasc. n.2, p. 141-155, (Italian)
pdf (992 Kb), djvu (360 Kb). | Zbl 1535.01078

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Una delle quattro medaglie Fields assegnate nel 2022 è stata vinta dal matematico June Huh, per isuoi contributi altamente innovativi alla combinatoria. I lavori di June Huh, oltre a risolvere brillantemente varie congetture aperte da molto tempo, creano un nuovo ponte tra la combinatoria e settori della matematica in apparenza molto distanti quali la topologia e la geometria algebrica. In questo articolo ci proponiamo di dare una introduzione il più possibile elementare alla combinatoria e di spiegare alcuni tra i principali risultati di Huh dando anche un'idea dell'originalità dei suoi metodi.

Referenze Bibliografiche

[ADH23] FEDERICO ARDILA, GRAHAM DENHAM, and JUNE HUH, Lagrangian geometry of matroids, J. Amer. Math. Soc. 36 (2023), no. 3, 727-794. | fulltext (doi) | MR 4583774 | Zbl 1512.05068

[AHK18] KARIM ADIPRASITO, JUNE HUH, and ERIC KATZ, Hodge theory for combinatorial geometries, Ann. of Math.(2) 188 (2018), no. 2, 381-452. | fulltext (doi) | MR 3862944 | Zbl 1442.14194

[AZ18] MARTIN AIGNER and GÜNTER M. ZIEGLER, Proofs from The Book, sixth ed., Springer, Berlin, 2018. | fulltext (doi) | MR 3823190 | Zbl 1392.00001

[BH20] PETTER BRÄNDÉN and JUNE HUH, Lorentzian polynomials, Ann. Of Math. (2) 192 (2020), no. 3, 821-891. | fulltext (doi) | MR 4172622 | Zbl 1444.13038

[BHM+20] TOM BRADEN, JUNE HUH, JACOB P. MATHERNE, NICHOLAS PROUDFOOT, and BOTONG WANG, A semi-small decomposition of the chow ring of a matroid, 2020. | fulltext (doi) | MR 4477425 | Zbl 1509.14012

[BHM+23] TOM BRADEN, JUNE HUH, JACOB P. MATHERNE, NICHOLAS PROUDFOOT, and BOTONG WANG, Singular Hodge theory for combinatorial geometries, 2023. | Zbl 1535.05058

[Brä15] PETTER BRÄNDÉN, Unimodality, log-concavity, real-rootedness and beyond, Handbook of enumerative combinatorics, Discrete Math. Appl. (Boca Raton), CRC Press, Boca Raton, FL, 2015, pp. 437-483. | MR 3409348 | Zbl 1327.05051

[Bre94] FRANCESCO BRENTI, Log-concave and unimodal sequences in algebra, combinatorics, and geometry: an update, Jerusalem combinatorics '93, Contemp. Math., vol.178, Amer. Math. Soc., Providence, RI, 1994, pp. 71-89. | fulltext (doi) | MR 1310575 | Zbl 0813.05007

[DBE48] NICOLAAS G. DE BRUIJN and PAUL ERDÖS, On a combinatioral problem, Indagationes Mathematicae 10 (1948), 421-423. | Zbl 0032.24405

[DCP95] CORRADO DE CONCINI and CLAUDIO PROCESI, Wonderful models of subspace arrangements, Selecta Math. (N.S.) 1 (1995), no. 3, 459-494. | fulltext (doi) | MR 1366622 | Zbl 0842.14038

[DW74] THOMAS A. DOWLING and RICHARD M. WILSON, The slimmest geometric lattices, Trans. Amer. Math. Soc. 196 (1974), 203-215. | fulltext (doi) | MR 345849 | Zbl 0289.05020

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[EW14] BEN ELIAS and GEORDIE WILLIAMSON, The Hodge theory of Soergel bimodules, Ann. Of Math. (2) 180 (2014),no. 3, 1089-1136. | fulltext (doi) | MR 3245013 | Zbl 1326.20005

[FY04] EVA MARIA FEICHTNER and SERGEY YUZVINSKY, Chowrings of toric varieties defined by atomic lattices, Invent.Math. 155 (2004), no. 3, 515-536. | fulltext (doi) | MR 2038195 | Zbl 1083.14059

[GGW14] JIM GEELEN, BERT GERARDS, and GEOFF WHITTLE, Solving Rota's conjecture, Notices Amer. Math. Soc. 61 (2014), no. 7, 736-743. | fulltext (doi) | MR 3221124 | Zbl 1338.05039

[GKP94] RONALD L. GRAHAM, DONALD E. KNUTH, and OREN PATASHNIK, Concrete mathematics, second ed., Addison Wesley Publishing Company, Reading, MA, 1994, A foundation for computer science. | MR 1397498 | Zbl 0836.00001

[GM80] MARK GORESKY and ROBERT MAC-PHERSON, Intersection homology theory, Topology 19 (1980), no. 2, 135-162. | fulltext (doi) | MR 572580 | Zbl 0525.14010

[GM83] MARK GORESKY and ROBERT MAC-PHERSON, Intersection homology. II, Invent. Math. 72 (1983), no. 1, 77-129. | fulltext EuDML | fulltext (doi) | MR 696691 | Zbl 0529.55007

[HK12] JUNE HUH and ERIC KATZ, Log-concavity of characteristic polynomials and the Bergman fan of matroids, Math.Ann. 354 (2012), no. 3, 1103-1116. | fulltext (doi) | MR 2983081 | Zbl 1258.05021

[Huh12] JUNE HUH, Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs, J. Amer.Math. Soc. 25 (2012), no. 3, 907-927. | fulltext (doi) | MR 2904577 | Zbl 1243.14005

[Kal22] GIL KALAI, The work of June Huh, Proceedings of theInternational Congress of Mathematicians, vol. 28, 2022, https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/laudatio-jh.pdf. | Zbl 1423.14004

[Knu74] DONALD E. KNUTH, The asymptotic number of geometries, J. Combinatorial Theory Ser. A 16 (1974), 398-400. | fulltext (doi) | MR 335312 | Zbl 0278.05010

[Knu11] DONALD E. KNUTH, The art of computer programming, Addison-Wesley, Upper Saddle River, NJ, 1975-2011. | MR 378456 | Zbl 0895.68054

[Mor78] JOHN W. MORGAN, The algebraic topology of smooth algebraic varieties, Inst. Hautes Études Sci. Publ. Math. (1978), no. 48, 137-204. | fulltext EuDML | MR 516917 | Zbl 0401.14003

[Nel18] PETER NELSON, Almost all matroids are nonrepresentable, Bull. Lond. Math. Soc. 50 (2018), no. 2, 245-248. | fulltext (doi) | MR 3830117 | Zbl 1384.05065

[NK09] HIROKAZU NISHIMURA and SUSUMU KURODA (eds.), A lost mathematician, Takeo Nakasawa, Birkhäuser Verlag,Basel, 2009, The forgotten father of matroid theory. | fulltext (doi) | MR 2516551 | Zbl 1163.01001

[OS80] PETER ORLIK and LOUIS SOLOMON, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), no. 2, 167-189. | fulltext EuDML | fulltext (doi) | MR 558866 | Zbl 0432.14016

[OT92] PETER ORLIK and HIROAKI TERAO, Arrangements of hyperplanes, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 300, Springer-Verlag, Berlin, 1992. | fulltext (doi) | MR 1217488 | Zbl 0757.55001

[Oxl11] JAMES OXLEY, Matroid theory, second ed., Oxford Graduate Texts in Mathematics, vol. 21, Oxford University Press, Oxford, 2011. | fulltext (doi) | MR 2849819 | Zbl 1233.05080

[Rot97] GIAN-CARLO ROTA, Combinatorics, representation theory and invariant theory, pp. 39-54, Birkhäuser Boston,Boston, MA, 1997. | MR 1392963 | Zbl 0908.06001

[Sta89] RICHARD P. STANLEY, Log-concave and unimodal sequences in algebra, combinatorics, and geometry, Graph theory and its applications: East and West (Jinan, 1986), Ann. New York Acad. Sci., vol. 576, New York Acad. Sci., New York, 1989, pp. 500-535. | fulltext (doi) | MR 1110850 | Zbl 0792.05008

[Sta12] RICHARD P. STANLEY, Enumerative combinatorics. Volume 1, second ed., Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge,2012. | MR 2868112 | Zbl 1256.00015

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[Yuz99] SERGEY YUZVINSKY, Rational model of subspace complement on atomic complex, Publ. Inst. Math. (Beograd) (N.S.) 66 (1999), no. 80, 157-164, Geometric combinatorics(Kotor, 1998). 7 | fulltext EuDML | MR 1765044 | Zbl 0954.52024

[Yuz02] SERGEY YUZVINSKY, Small rational model of subspace complement, Trans. Amer. Math. Soc. 354 (2002), no. 5, 1921-1945. | fulltext (doi) | MR 1881024 | Zbl 0997.52015

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

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Referenze Bibliografiche