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We use Krein formula and the S-matrix formalism to give formulas for the zeta-regularized determinant of non-Friedrichs extensions of the Laplacian on Euclidean surfaces with Conical Singularities. Th...
This paper studies formality of the differential graded algebra $RHom(E,E)$, where $E$ is a semistable sheaf on a K3 surface. The main tool is Kaledin's theorem on formality in families. For a large ...
The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the...
We give an affirmative answer to Nash Problem for quotient surface singularities, in particular for the icosahedral singularity $E_8$.
In a previous work, the authors gave a definition of `front bundles'. Using this, we give a realization theorem for wave fronts in space forms, like as in the fundamental theorem of surface theory. A...
Given a rational homology sphere M, whose splice diagram satisfy the semigroup condition, Neumann and Wahl were able to define a complete intersection surface singularity called splice diagram singul...
We prove that the asymptotic completion of a developable M\"obius strip in Euclidean three-space must have at least one singular point other than cuspidal edge singularities. Moreover, if the strip co...
In 1978 Lipman presented a proof of the existence of a desingularization for any excellent surface. The strategy of Lipman's proof is based on the finiteness of the number H(R) defined as the supreme...
The geometric motivic Poincar\'e series of a variety, which was introduced by Denef and Loeser, takes into account the classes in the Grothendieck ring of the sequence of jets of arcs in the variety. ...
Let $k$ be \emph{any} algebraically closed field in any characteristic, let $R$ be any regular local ring such that $R$ contains $k$ as a subring, the residue field of $R$ is isomorphic to $k$ as $k$...
The geometric motivic Poincar\'e series of a germ $(S,0)$ of complex algebraic variety takes into account the classes in the Grothendieck ring of the jets of arcs through $(S,0)$. Denef and Loeser pro...
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are differen...
A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by usi...
Given a prime q and a negative discriminant D, the CM method constructs an elliptic curve E/Fq by obtaining a root of the Hilbert class polynomial HD(X) modulo q.
The motivation for this paper are computer calculations of complete lists of weight systems of quasihomogeneous polynomials with isolated singularity at 0 up to rather large Milnor numbers.

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