Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Zograf, Peter"'
A meander can be seen as a pair of transversally intersecting simple closed curves on a 2-sphere. We consider pairs of transversally intersecting simple closed curves on a closed oriented surface of arbitrary genus g. The number of such higher genus
Externí odkaz:
http://arxiv.org/abs/2304.02567
Autor:
Korotkin, Dmitry, Zograf, Peter
We study the moduli space of meromorphic 1-forms on complex algebraic curves having at most simple poles with fixed nonzero residues. We interpret the Bergman tau function on this moduli space as a section of a line bundle and study its asymptotic be
Externí odkaz:
http://arxiv.org/abs/2303.12244
Autor:
Korotkin, Dmitry, Zograf, Peter
Publikováno v:
SIGMA 18 (2022), 001, 10 pages
The Bergman tau functions are applied to the study of the Picard group of moduli spaces of quadratic differentials with at most $n$ simple poles on genus $g$ complex algebraic curves. This generalizes our previous results on moduli spaces of holomorp
Externí odkaz:
http://arxiv.org/abs/2108.01419
If a bulk gravitational path integral can be identified with an average of partition functions over an ensemble of boundary quantum theories, then a corresponding moment problem can be solved. We review existence and uniqueness criteria for the Stiel
Externí odkaz:
http://arxiv.org/abs/2103.12078
Autor:
Zograf, Peter
Publikováno v:
Journal of Mathematical Sciences 240 (2019), 535-538
An explicit closed form expression for 2-correlators of Witten's two dimensional topological gravity is derived in arbitrary genus.
Comment: Some typos in the published version corrected
Comment: Some typos in the published version corrected
Externí odkaz:
http://arxiv.org/abs/2012.03268
Publikováno v:
Duke Mathematical Journal, 170 no. 12 (2021), 2633-2718
We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space $\mathcal{Q}_{g,n}$ of genus $g$ meromorphic quadratic differentials with $n$ simple poles as polynomials in the intersection numbers of $\psi$-classes with expl
Externí odkaz:
http://arxiv.org/abs/2011.05306
Publikováno v:
Inventiones mathematicae, 230:1 (2022), 123-224
We study the combinatorial geometry of a random closed multicurve on a surface of large genus and of a random square-tiled surface of large genus. We prove that primitive components of a random multicurve represent linearly independent homology cycle
Externí odkaz:
http://arxiv.org/abs/2007.04740
Publikováno v:
SIGMA 16 (2020), 086, 13 pages
We approximate intersection numbers $\big\langle \psi_1^{d_1}\cdots \psi_n^{d_n}\big\rangle_{g,n}$ on Deligne-Mumford's moduli space $\overline{\mathcal M}_{g,n}$ of genus $g$ stable complex curves with $n$ marked points by certain closed-form expres
Externí odkaz:
http://arxiv.org/abs/2004.02749
Publikováno v:
Arnold Math. Journal, 6:2 (2020), 149-161
We state conjectures on the asymptotic behavior of the Masur-Veech volumes of strata in the moduli spaces of meromorphic quadratic differentials and on the asymptotics of their area Siegel-Veech constants as the genus tends to infinity.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/1912.11702
We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space of meromorphic quadratic differential with simple poles as polynomials in the intersection numbers of psi-classes supported on the boundary cycles of the Deligne
Externí odkaz:
http://arxiv.org/abs/1908.08611