# Mikhail Basok's research while affiliated with Saint Petersburg State University and other places

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## Publications (7)

For a non-cyclic free group $F$, the second homology of its pronilpotent completion $H_2(\widehat F)$ is not a cotorsion group.

We continue the study of the rational Picard group of the moduli space of Hitchin spectral covers started in Korotkin and Zograf (J Math Phys 59(9):091412, 2018). In the first part of the paper we expand the “boundary”, “Maxwell stratum” and “caustic” divisors introduced in Korotkin and Zograf (2018) via the set of standard generators of the ration...

We continue the study of the rational Picard group of the moduli space of Hitchin's spectral covers started in P. Zograf's and D. Korotkin's work [11]. In the first part of the paper we expand the ``boundary'', ``Maxwell stratum'' and ``caustic'' divisors introduced in [11] via the set of standard generators of the rational Picard group. This gener...

Building upon recent results of Dub\'edat (see arXiv:1403.6076) on the convergence of topological correlators in the double-dimer model considered on Temperleyan approximations $\Omega^\delta$ to a simply connected domain $\Omega\subset\mathbb C$ we prove the convergence of probabilities of cylindrical events for the \emph{double-dimer loop ensembl...

In this paper we introduce a divisor in the moduli space of odd spin curves
parametrizing spin curves such that some meromorphic function naturally
associated with the spin structure has less number of branch points then
maximal. We express the class of this divisor in the rational Picard group via
the set standards generators.

The goal of the paper is to give an analytic proof of the formula of G.
Farkas for the divisor class of spinors with multiple zeros in the moduli space
of odd spin curves. We make use of the technique developed by Korotkin and
Zograf that is based on properties of the Bergman tau function. We also show
how the Farkas formula for the {\it theta-null...

## Citations

... Cardy and Peschel [5] conjectured that the asymptotic of the partition function of any critical 2D lattice model on a Riemann surface should take a form similar to (1.1). Since the determinants of the discrete Laplacian and its vector bundle versions are partition functions of a number of lattice models, such as dimers and double dimers, discrete GFF, spanning trees and cycle-rooted spanning forests [3,11,24,25,27,28,30,31,37], our results can be viewed as a rigorous proof of a particular case of the Cardy-Peschel conjecture. Duplantier and David [13] computed the asymptotics of the determinant of the discrete square lattice Laplacian on a torus and a rectangle; their results were extended to cylinder, Möbius strip and Klein bottle by Brankov-Priezzhev and Izmailyan-Oganesyan-Hu [4,23]. ...

... There is a natural forgetful map h : P M [1]), albeit one of rather high codimension. Pulling back the Hodge class λ ∈ Pic(M g ) along the map h, we obtain a class on P M Sp(2n) g which we also denote by λ. ...

... Arguments of Hodge and Prym tau functions give sections of circle line bundles which are combinations of tautological classes; computation of monodromy of these arguments around Witten's cycle and Kontsevich's boundary of the combinatorial model gives combinatorial analogs of Mumford's relations in Picard group of M g,n . In section 8 we briefly describe the application of tau-functions to spaces of holomorphic N -differentials and spin moduli spaces following [55,4]. In particular we show how the analytical properties of tau-functions on spin moduli spaces imply the Farkas-Verra formula for divisor of degenerate odd spinors. ...