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The Ricci flow is a powerful tool in geometry to construct the canonical metric on a given manifold. It can be viewed as a nonlinear heat flow of the Riemannian metric and may develop finite time sing...
The aim of the symposium is to bring together specialists of various do- mains of singularity theory and mathematical foundation of complex systems representing very classical aspects of the Fields. W...
We give an example of a well posed, nite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce nite time sing...
In a previous paper, there was defined a multi-index filtration on the ring of functions on a hypersurface singularity corresponding to its Newton diagram generalizing (for a curve singularity) the di...
Abstract: This paper deals with the study of the behaviour of the value semigroup of a curve singularity define over a global field reduced modulo a maximal ideal. We also define a global zeta functio...
In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the corresponding...
This brief survey of some singularity invariants related to Milnor fibers should serve as a quick guide to references. We attempt to place things into a wide geometric context while leaving technicali...
We show that a homology plane of general type has at worst a single cyclic quotient singular point. An example of such a surface with a singular point does exist [MS, Theorem 3.1]. We also show that ...
Log del Pezzo surfaces play the role of the opposite of surfaces of general type. We will completely classify all the log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity.
Let A be an n×n random matrix with iid entries over a finite field of order q. Suppose that the entries do not take values in any additive coset of the field with probability greater than 1 − ...
In this article we study the 2-distributions in Rn satisfying everywhere the Goursat condition. We give the normal form at a neighborhood of a point where the small growth vector has a singularity of ...
We give a review of the theories of [FJR] and the theory of [JKV]and prove that for the singularity Ar−1 = xr (with the group G = μr), the stack of Ar−1-curves of [FJR] is canonically isom...
We study matrix factorizations of a section W of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with...
We apply the Painleve test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infi...
We prove an equivalence between the derived category of a variety and the equivariant/graded singularity category of a corresponding singular variety. The equivalence also holds at the dg level.

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