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Of all publications in the section: 323
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Working paper
Cheltsov I., Shramov K., Przyjalkowski V. math. arxive. Cornell University, 2019
We classify smooth Fano threefolds with infinite automorphism groups.
Working paper
Shramov K., Przyjalkowski V. math. arxive. Cornell University, 2019
We classify smooth Fano weighted complete intersections of large codimension.
Working paper
Mazzucchi S., Moretti V., Remizov I. et al. math. arxive. Cornell University, 2020
Feynman formulas are representations of solutions to initial value problems, for some parabolic and Schrödinger equations, by the limits of integrals over finite Cartesian powers of some spaces. Two versions of these formulas which were suggested by Feynman himself are associated with names of Trotter and Chernoff respectively. These formulas can be interpreted as approximations for path integrals over spaces of functions of a real variable; the corresponding representations of the solutions to the said equations are usually known as Feynman-Kac formulas. This work presents some new Feynman type formulas, related to the Chernoff theorem, on Riemannian manifolds. The used manifolds are of boundend geometry which include all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a generally non-compact manifold of bounded geometry. A construction of Chernoff approximations is presented for those Feller semigroups in terms of shift operators. This provides approximations for solutions to initial-value problems for parabolic equations with variable coefficients on the manifold. It also yields the weak convergence of a sequence of random walks on the manifold to the diffusion process associated with the elliptic generator. For parallelizable manifolds this result is applied to the Brownian motion
Working paper
Cheltsov I., Przyjalkowski V. math. arxive. Cornell University, 2020
We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety X equals the dimension of the anticanonical system of X. We verify this conjecture for log Calabi--Yau compactifications of toric Landau--Ginzburg models for smooth Fano threefolds, complete intersections, and some toric varieties.
Working paper
Shramov K. math. arxive. Cornell University, 2019
Given a holomorphic conic bundle without sections, we show that finite groups acting by its fiberwise bimeromorphic transformations are bounded. This provides an analog of a similar result obtained by T.Bandman and Yu.Zarhin for quasi-projective conic bundles.
Working paper
A. V. Romanov. math. arxive. Cornell University, 2020. No. 2011.01822.
We consider the class of dissipative reaction-diffusion-convection systems on the circle and obtain conditions under which the final (at large times) phase dynamicsof a system can be described by an ODE with Lipschitz vector field in RN. Precisely in this class, the first example of a parabolic problem of mathematical physics without the indicated property was recently constructed.
Working paper
Shramov K. math. arxive. Cornell University, 2019
We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration.
Working paper
Shramov K. math. arxive. Cornell University, 2020
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero.
Working paper
Shramov K., Prokhorov Y. math. arxive. Cornell University, 2019
We classify uniruled compact Kähler threefolds whose groups of bimeromorphic selfmaps do not have Jordan property.
Working paper
Gorsky E., Negut A., Rasmussen J. math. arxive. Cornell University, 2016
We construct a categorification of the maximal commutative subalgebra of the type A Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal category of coherent sheaves on the flag Hilbert scheme to the (non-symmetric) monoidal category of Soergel bimodules. The adjoint of this functor allows one to match the Hochschild homology of any braid with the Euler characteristic of a sheaf on the flag Hilbert scheme. The categorified Jones-Wenzl projectors studied by Abel, Elias and Hogancamp are idempotents in the category of Soergel bimodules, and they correspond to the renormalized Koszul complexes of the torus fixed points on the flag Hilbert scheme. As a consequence, we conjecture that the endomorphism algebras of the categorified projectors correspond to the dg algebras of functions on affine charts of the flag Hilbert schemes. We define a family of differentials d_N on these dg algebras and conjecture that their homology matches that of the  gl_N projectors, generalizing earlier conjectures of the first and third authors with Oblomkov and Shende.
Working paper
Verbitsky M., Vuletescu V., Ornea L. math. arxive. Cornell University, 2018
The Oeljeklaus-Toma (OT-) manifolds are compact, complex, non-Kahler manifolds constructed by Oeljeklaus and Toma, and generalizing the Inoue surfaces. Their construction uses the number-theoretic data: a number field K and a torsion-free subgroup U in the group of units of the ring of integers of K, with rank of U equal to the number of real embeddings of K. We prove that any complex subvariety of smallest possible positive dimension in an OT-manifold is also flat affine. This is used to show that if all non-trivial elements in U are primitive in K, then X contains no proper complex subvarieties.
Working paper
Gayfullin S., Шафаревич А. А. math. arxive. Cornell University, 2018. No. arXiv:1805.05024.
Working paper
Gayfullin S. math. arxive. Cornell University, 2018
We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a locally transitive action of a reductive group is proved. Also we show that a normal affine complexity-zero horospherical variety is flexible.
Working paper
Levando D. V. math. arxive. Cornell University, 2017. No. 1702.06922.
The paper defines a family of nested non-cooperative simultaneous finite games to study coalition structure formation with intra and inter-coalition externalities. Every game has two outcomes - an allocation of players over coalitions and a payoff profile for every player.  Every game in the family has an equilibrium in mixed strategies. The equilibrium can generate more than one coalition with a presence of intra and inter group externalities. These properties make it different from the Shapley value, strong Nash, coalition-proof equilibrium, core, kernel, nucleolus. The paper demonstrates some applications: non-cooperative cooperation, Bayesian game, stochastic games and construction of a non-cooperative criterion of coalition structure stability for studying focal points. An example demonstrates that a payoff profile in the Prisoners' Dilemma is non-informative to deduce a cooperation of players.
Working paper
Levando D. V. math. arxive. Cornell University, 2016. No. arXiv:1612.02344.
The paper defines a non-cooperative simultaneous finite game to study coalition structure formation with intra and inter-coalition externalities. The novelty of the game is that the game definition embeds a \textit{coalition structure formation mechanism}. This mechanism portions a set of strategies of the game into partition-specific strategy domains, what makes every partition to be a non-cooperative game with partition-specific payoffs for every player. The mechanism includes a maximum coalition size, a set of eligible partitions with coalitions sizes no greater than this number (which also serves as a restriction for a maximum number of deviators) and a coalition structure formation rule. The paper defines a family of nested non-cooperative games parametrized by a size of a maximum coalition size. Every game in the family has an equilibrium in mixed strategies. The equilibrium can generate more than one coalition and encompasses intra and inter group externalities, what makes it different from the Shapley value. Presence of individual payoff allocation makes it different from a strong Nash, coalition-proof equilibrium, and some other equilibrium concepts. The accompanying papers demonstrate applications of the proposed toolkit.
Working paper
Levando D. V. math. arxive. Cornell University, 2016. No. 1612.03742.
The paper uses a non-cooperative simultaneous game for coalition structure formation (Levando, 2016) to demonstrate some applications of the introduced game: a cooperation, a Bayesian game within a coalition with intra-coalition externalities, a stochastic game, where states are coalition structures; self-enforcement properties of a non-cooperative equilibrium and a construction of a non-cooperative stability criterion.
Working paper
Finkelberg M. V., Kapranov M., Schechtman V. math. arxive. Cornell University, 2018
We consider the category of perverse sheaves on a complex vector space smooth with respect to a stratification given by an arrangement of hyperplanes with real equations. As shown in an earlier wotk of two of the authors, this category can be described in terms of certain diagrams of vector spaces labelled by all the faces of the real arrangement (we call such diagrams hyperbolic sheaves). In this paper we calculate, in these terms, several fundamental operations of sheaf theory such as forming the space of vanishing cycles, specialization and the Fourier-Sato transform.
Working paper
Kroshnin A., Sobolevski A. math. arxive. Cornell University, 2015. No. 1512.08421.
Endow the space P(R) of probability measures on R with a transportation cost J(mu, nu) generated by a translation-invariant convex cost function. For a probability distribution on P(R) we formulate a notion of average with respect to this transportation cost, called here the Fréchet barycenter, prove a version of the law of large numbers for Fréchet barycenters, and discuss the structure of P(R) related to the transportation cost J.