Related papers: Some problems and conjectures about $L^2$-invarian…
We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional…
The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models…
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.
This paper extends the construction of invariants for virtual knots to virtual long knots and introduces two new invariant modules of virtual long knots. Several interesting features are described that distinguish virtual long knots from…
The paper deals with the cohomological invariants of smooth and connected linear algebraic groups over an arbitrary field. More precisely, we study degree $2$ invariants with coefficients $\mathbb{Q}/\mathbb{Z}(1)$, that is invariants…
This survey presents some combinatorial problems with number-theoretic flavor. Our journey starts from a simple graph coloring question, but at some point gets close to a dangerous territory of the Riemann Hypothesis. We will mostly focus…
The paper deals with second order abstract linear partial differential equations (LPDE) over a partial differential field with two commuting differential operators. In terms of usual differential equations the main content can be presented…
We construct an open enumerative theory for the Landau-Ginzburg (LG) model $(\mathbb{C}^2, \mu_r\times \mu_s, x^r+y^s)$. The invariants are defined as integrals of multisections of a Witten bundle with descendents over a moduli space that…
The $c_2$-invariant is an arithmetic graph invariant useful for understanding Feynman periods. Brown and Schnetz conjectured that the $c_2$-invariant has a particular symmetry known as completion invariance. This paper will prove completion…
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
We describe a correspondence between GL_n-invariant tensors and graphs, and show how this correspondence accomodates various types of symmetries and orientations.
We propose here selected actual features of measurement problems based on our concerns in our respective fields of research. Their technical similarity in apparently disconnected fields motivate this common communication. Problems of…
Let $G$ be a Lie group acting on a vector space $V$. Given a set of $G$-invariants, one can ask the question : does this set of invariants characterize the group $G$ ? We recall here some known results, ask questions and state some…
In this paper, we study the $L_p$ dual Minkowski problem for all $q, p \in \mathbb{R}$ from an algebraic perspective. We establish the existence of solutions for group-invariant convex bodies (not necessarily origin-symmetric), thereby…
We construct a new set of combinations from the mass matrices of the charged leptons and neutrinos that are invariant under basis transformation, hereafter {\it the} invariants. We use these invariants to study various symmetries and…
This article surveys invariants of four-manifolds and their relation to Donaldson-Witten theory, and other topologically twisted Yang-Mills theories. The article is written for the second edition of the Encyclopedia of Mathematical Physics,…
We present some questions and suggestion on the second part of the Hilbert 16th problem
This is a survey of results on the Hilbert property of algebraic varieties, and variants of it.
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…