Geodesic
Hilbert Schemes and Multiple $q$-Zeta Values
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 2, pp. 79-87.

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We present several conjectures on multiple $q$-zeta values and on the role which they play in certain problems of enumerative geometry.
Mots-clés : multiple $q$-zeta value, $q$-deformation
Keywords: Hilbert scheme, GW/DT correspondence. 
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A. Yu. Okounkov. Hilbert Schemes and Multiple $q$-Zeta Values. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 2, pp. 79-87. http://geodesic.mathdoc.fr/item/FAA_2014_48_2_a4/

[1] Y. André, Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Panoramas et Synthèses, 17, Société Math. de France, Paris, 2004 | MR | Zbl

[2] D. Bradley, “Multiple q-zeta values”, J. Algebra, 283:2 (2005), 752–798 | DOI | MR | Zbl

[3] F. Brown, “Mixed Tate motives over $\mathbb{Z}$”, Ann. of Math. (2), 175:2 (2012), 949–976 | DOI | MR | Zbl

[4] E. Carlsson, A. Okounkov, “Exts and vertex operators”, Duke Math. J., 161:9 (2012), 1797–1815 | DOI | MR | Zbl

[5] P. Etingof, O. Schiffmann, Lectures on quantum groups, Lectures in Mathematical Physics, International Press, Somerville, MA, 2002 | MR | Zbl

[6] L. Göttsche, “Hilbert schemes of points on surfaces”, Proceedings of the International Congress of Mathematicians, v. II, Higher Ed. Press, Beijing, 2002, 483–494 | MR | Zbl

[7] M. E. Hoffman, “The algebra of multiple harmonic series”, J. Algebra, 194:2 (1997), 477–495 | DOI | MR | Zbl

[8] M. Kaneko, D. Zagier, “A generalized Jacobi theta function and quasimodular forms”, The moduli space of curves (Texel Island, 1994), Progr. Math., 129, Birkhäuser, Boston, 1995, 165–172 | MR | Zbl

[9] M. Kool, V. Shende, R. Thomas, “A short proof of the Göttsche conjecture”, Geom. Topol., 15:1 (2011), 397–406 | DOI | MR | Zbl

[10] M. Lehn, “Lectures on Hilbert schemes”, Algebraic Structures and Moduli Spaces (Montreal, 2003), CRM Proc. Lecture Notes, 38, Amer. Math. Soc., Providence, 2004, 1–30 | DOI | MR | Zbl

[11] M. Levine, R. Pandharipande, “Algebraic cobordism revisited”, Invent. Math., 176:1 (2009), 63–130 | DOI | MR | Zbl

[12] D. Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande, “Gromov–Witten theory and Donaldson-Thomas theory. I; II”, Compos. Math., 142:5 (2006), 1263–1304 | DOI | MR

[13] H. Nakajima, Lectures on Hilbert Schemes of Points on Surfaces, Univ. Lecture Series, 18, Amer. Math. Soc., Providence, RI, 1999 | DOI | MR | Zbl

[14] N. Nekrasov, “Seiberg–Witten prepotential from instanton counting”, Adv. Theor. Math. Phys., 7:5 (2003), 831–864 | DOI | MR | Zbl

[15] A. Oblomkov, A. Okounkov, R. Pandharipande, The GW/DT correspondence for descendents, ne opublikovano

[16] A. Okounkov, R. Pandharipande, “The local Donaldson–Thomas theory of curves”, Geom. Topol., 14:3 (2010), 1503–1567 | DOI | MR | Zbl

[17] J. Okuda, Y. Takeyama, “On relations for the multiple $q$-zeta values”, Ramanujan J., 14:3 (2007), 379–387 | DOI | MR | Zbl

[18] A. Smirnov, On the instanton $R$-matrix, arXiv: 1302.0799

[19] R. Thomas, “A holomorphic Casson invariant for Calabi–Yau $3$-folds and bundles on K3 fibrations”, J. Differential Geom., 54:2 (2000), 367–438 | DOI | MR | Zbl

[20] D. Zagier, “Values of zeta functions and their applications”, First European Congress of Mathematics (Paris, 1992), v. II, Progr. Math., 120, Birkhäuser, Basel, 1994, 497–512 | MR | Zbl

[21] V. Zudilin, “Algebraicheskie sootnosheniya dlya kratnykh dzeta-funktsii”, UMN, 58:1 (2003), 3–32 | DOI | MR | Zbl