Related papers: Jet schemes, log discrepancies and Inversion of Ad…
We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie…
Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…
In this thesis new objects to the existing set of invariants of Lie algebras are added. These invariant characteristics are capable of describing the nilpotent parametric continuum of Lie algebras. The properties of these invariants, in…
We study a pair consisting of a smooth variety over a field of positive characteristic and a multi-ideal with a real exponent. We prove the finiteness of the set of minimal log discrepancies for a fixed exponent if the dimension is less…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
The goal of this work is to study the existence and properties of non constant entire curves f drawn in a complex irreducible n-dimensional variety X, and more specifically to show that they must satisfy certain global algebraic or…
We target multivariable series associated with resolutions of complex analytic normal surface singularities. In general, the equivariant multivariable analytical and topological Poincar\'e series are well-defined and have good properties…
Let $X$ be an integral projective variety of codimension two, degree $d$ and dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the…
We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…
We present a short proof, relaying on the divergence theorem, verifying that minimal sets in the plane are trivial.
In this paper we consider the fragmentation of a parton into a jet with small jet radius $R$. Perturbatively, logarithms of $R$ can appear, which for narrow jets can lead to large corrections. Using soft-collinear effective theory, we…
Singularities of plane into plane mappings described by parabolic two-component systems of quasi-liner partial differential equations of the first order are studied. Impediments arising in the application of the original Whitney's approach…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in…
We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction…
Motivated by work of Dragt and Abell on accelerator physics, we study the completion of symplectic jets by polynomial maps of low degrees. We use Anders\'en-Lempert Theory to prove that symplectic completions always exist, and we prove the…
We introduce and study on examples a notion of the Artin shape for a motive related to a projective homogenous variety. We apply it to the problem of finding the complete motivic decomposition of the variety. Our examples cover unitary…
A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…