Related papers: Bounded integral and motivic Milnor fiber
We study continuous-wave light propagation through a twisted birefringent single-mode fiber amplifier with saturable nonlinearity. The corresponding coupled-mode system is isomorphic to a non-Hermitian nonlinear dimer, and gives rise to…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BPM…
We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.
Although there is no natural internal product for hermitian forms over an algebra with involution of the first kind, we describe how to multiply two $\varepsilon$-hermitian forms to obtain a quadratic form over the base field. This allows…
A short intrinsic proof is given for the Bourgain-Brezis-Mironescu theorem with an extension for higher-order gradient forms. This argument illustrates the role of functional geometry and Fourier analysis for obtaining embedding estimates.…
We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining "toric" roots. Instead of introducing new variables and new relations to saturate by the variable inverses, we propose a more…
Mellin transform of fibre integral is calculated for certain classes of non-degenerate affine complete intersections. The lattice structure of the poles of the Mellin transform is clarified by means of the mixed Hodge structure of the…
We study motivic Donaldson-Thomas invariants for a class of quivers with potentials using the strategy of Behrend, Bryan, and Szendroi. This class includes quivers with potentials arising from consistent brane tilings and quivers with zero…
We consider a quasi-regular Dirichlet form. We show that a bounded signed measure charges no set of zero capacity associated with the form if and only if the measure can be decomposed into the sum of an integrable function and a bounded…
We develop a new technique for computing higher limits of functors over filtered posets by constructing explicit fibrant replacements within a suitable model category structure. We apply this procedure to develop two systematic vanishing…
We describe how to formulate Khovanov's functor-valued invariant of tangles in the language of bordered Heegaard Floer homology. We then give an alternate construction of Lawrence Roberts' Type D and Type A structures in Khovanov homology,…
In this survey one discusses the notion of the Poincar\'e series of multi-index filtrations, an alternative approach to the definition, a method of computation of the Poincar\'e series based on the notion of integration with respect to the…
Path integrals similar to those describing stiff polymers arise in the Helfrich model for membranes. We show how these types of path integrals can be evaluated and apply our results to study the thermodynamics of a minority stripe phase in…
We associate to any element in the Milnor K-theory of a field $k$ modulo 2 an invertible Morava K-theory motive over $k$. Specifically, for $\alpha$ in $\mathrm{K}^{\mathrm{M}}_{n+1}(k)/2$ we construct an invertible $\mathrm{K}(n)$-motive…
This note contains some results related to the definitions of toroidal embeddings and toroidal morphisms over non-closed fields of characteristic zero.
This paper extends the decorated Teichm\"uller theory developed before for punctured surfaces to the setting of ``bordered'' surfaces, i.e., surfaces with boundary, and there is non-trivial new structure discovered. The main new result…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
We study the scheme of formal arcs on a singular algebraic variety and its images under truncations. We prove a rationality result for the Poincare series of these images which is an analogue of the rationality of the Poincare series…
We develop the motivic integration theory over formal Deligne-Mumford stacks over a power series ring of arbitrary characteristic. This is a generalization of the corresponding theory for tame and smooth Deligne-Mumford stacks constructed…