Abstract
We present several conjectures on multiple q-zeta values and on the role which they play in certain problems of enumerative geometry.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Y. André, Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Panoramas et Synthèses, vol. 17, Société Math. de France, Paris, 2004.
D. Bradley, “Multiple q-zeta values,” J. Algebra, 283:2 (2005), 752–798.
F. Brown, “Mixed Tate motives over Z,” Ann. of Math. (2), 175:2 (2012), 949–976.
E. Carlsson and A. Okounkov, “Exts and vertex operators,” Duke Math. J., 161:9 (2012), 1797–1815.
P. Etingof and O. Schiffmann, Lectures on Quantum Groups, Lectures in Math. Physics, International Press, Somerville, MA, 2002.
L. Göttsche, “Hilbert schemes of points on surfaces,” in: Proceedings of the International Congress of Mathematicians, vol. II, Higher Ed. Press, Beijing, 2002, 483–494.
M. E. Hoffman, “The algebra of multiple harmonic series,” J. Algebra, 194:2 (1997), 477–495.
M. Kaneko and D. Zagier, “A generalized Jacobi theta function and quasimodular forms,” in: The Moduli Space of Curves (Texel Island, 1994), Progr. Math., vol. 129, Birkhäuser, Boston, 1995, 165–172.
M. Kool, V. Shende, and R. Thomas, “A short proof of the Göttsche conjecture,” Geom. Topol., 15:1 (2011), 397–406.
M. Lehn, “Lectures on Hilbert schemes,” in: Algebraic Structures and Moduli Spaces (Montreal, 2003), CRM Proc. Lecture Notes, vol. 38, Amer. Math. Soc., Providence, 2004, 1–30.
M. Levine and R. Pandharipande, “Algebraic cobordism revisited,” Invent. Math., 176:1 (2009), 63–130.
D. Maulik, N. Nekrasov, A. Okounkov, and R. Pandharipande, “Gromov-Witten theory and Donaldson-Thomas theory. I, II,” Compos. Math., 142:5 (2006), 1263–1304.
H. Nakajima, Lectures on Hilbert Schemes of Points on Surfaces, Univ. Lecture Series, vol. 18, Amer. Math. Soc., Providence, RI, 1999.
N. Nekrasov, “Seiberg-Witten prepotential from instanton counting,” Adv. Theor. Math. Phys., 7:5 (2003), 831–864.
A. Oblomkov, A. Okounkov, and R. Pandharipande, The GW/DT Correspondence for Descendents, unpublished.
A. Okounkov and R. Pandharipande, “The local Donaldson-Thomas theory of curves,” Geom. Topol., 14:3 (2010), 1503–1567.
J. Okuda and Y. Takeyama, “On relations for the multiple q-zeta values,” Ramanujan J., 14:3 (2007), 379–387.
A. Smirnov, On the Instanton R-Matrix, http://arxiv.org/abs/1302.0799.
R. Thomas, “A holomorphic Casson invariant for Calabi-Yau 3-folds and bundles on K3 fibrations,” J. Differential Geom., 54:2 (2000), 367–438.
D. Zagier, “Values of zeta functions and their applications,” in: First European Congress of Mathematics, Vol. II (Paris, 1992), Progr. Math., vol. 120, Birkhäuser, Basel, 1994, 497–512.
W. Zudilin, “Algebraic relations for multiple zeta values,” Uspekhi Mat. Nauk, 58:1 (2003), 3–32; English transl.: Russian Math. Surveys, 58:1 (2003), 1–29.
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 48, No. 2, pp. 79–87, 2014
Original Russian Text Copyright © by Andrei Okounkov
To the 100th birthday of I. M. Gelfand
Supported by NSF grant FRG 1159416.
Rights and permissions
About this article
Cite this article
Okounkov, A. Hilbert schemes and multiple q-zeta values. Funct Anal Its Appl 48, 138–144 (2014). https://doi.org/10.1007/s10688-014-0054-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10688-014-0054-z