Pauli, Sabrina Wickelgren, Kirsten
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Research in the Mathematical Sciences

These are lecture notes from the conference Arithmetic Topology at the Pacific Institute of Mathematical Sciences on applications of Morel’s A1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6...

Fornerod, Jean Nguyen, Hoai-Minh
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Research in the Mathematical Sciences

Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreteness of the set of eigenvalues of the transmission eigenvalue problem and studied their locations. In this paper, we establish the completeness of the generalized eigenfunctions and derive an optimal upper boun...

Alcántara, Claudia R.
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Research in the Mathematical Sciences

In this work, we construct, for any d≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d \ge 2$$\end{document}, a new foliation on CP2\documentclass[12pt]{minimal} \use...

Huneke, Craig Maitra, Sarasij Mukundan, Vivek
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Research in the Mathematical Sciences

Let (R,m,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(R,{\mathfrak {m}},\mathbb {k})$$\end{document} be an equicharacteristic one-dimensional complete local domai...

Cutkosky, Steven Dale Sarkar, Parangama
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Research in the Mathematical Sciences

We develop a theory of multiplicities and mixed multiplicities of filtrations, extending the theory for filtrations of m-primary ideals to arbitrary (not necessarily Noetherian) filtrations. The mixed multiplicities of r filtrations on an analytically unramified local ring R come from the coefficients of a suitable homogeneous polynomial in r varia...

Grisalde, Gonzalo Seceleanu, Alexandra Villarreal, Rafael H.
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Research in the Mathematical Sciences

The aims of this work are to study Rees algebras of filtrations of monomial ideals associated with covering polyhedra of rational matrices with nonnegative entries and nonzero columns using combinatorial optimization and integer programming and to study powers of monomial ideals and their integral closures using irreducible decompositions and polyh...

Andruskiewitsch, N. Angiono, I. Pevtsova, J. Witherspoon, S.
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Research in the Mathematical Sciences

We show that the cohomology ring of a finite-dimensional complex pointed Hopf algebra with an abelian group of group-like elements is finitely generated. Our strategy has three major steps. We first reduce the problem to the finite generation of cohomology of finite dimensional Nichols algebras of diagonal type. For the Nichols algebras, we do a de...

Ambrose, David M. Cakoni, Fioralba Moskow, Shari
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Research in the Mathematical Sciences

In this paper, we consider a perturbation problem for real transmission eigenvalues. Real transmission eigenvalues are of particular interest in inverse scattering theory. They can be determined from scattering data and are related to injectivity of the related scattering operators. The goal of this paper is to provide examples of existence of real...

Sutthimat, Phiraphat Rujivan, Sanae Mekchay, Khamron Rakwongwan, Udomsak
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Research in the Mathematical Sciences

This paper proposes an analytical formula for the conditional expectations of path-dependent product of polynomial and exponential function in the form of ∑j=0nλj(l)rtlje∑k=1mαk(l)rtk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackag...

Bergvall, Olof
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Research in the Mathematical Sciences

We develop an algorithm for computing the cohomology of complements of toric arrangements. In the case a finite group Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\...