Related papers: Open problems in the wild McKay correspondence and…
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
We develop a quantitative framework for understanding the class of wicked problems that emerge at the intersections of natural, social, and technological complex systems. Wicked problems reflect our incomplete understanding of…
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for including a problem here; importance is ignored.
A minimal area problem imposing different length conditions on open and closed curves is shown to define a one parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable…
This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…
As an inverse relation, involution with an invariant sequence plays a key role in combinatorics and features prominently in some of Shapiro's open questions [L.W. Shapiro, Some open questions about random walks, involutions, limiting…
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
The basis for the field theory are properties of the closed exterior differential forms (skew-symmetric differential forms defined on manifolds with the closed metric forms), which reflect properties of the conservation laws for physical…
Let $k$ be a field, let $G$ be a reductive algebraic group over $k$, and let $V$ be a linear representation of $G$. Geometric invariant theory involves the study of the $k$-algebra of $G$-invariant polynomials on $V$, and the relation…
The purpose of this note is to study the existence of a nontrivial solution for an elliptic system which comes from a newly introduced mathematical problem so called Field-Road model. Specifically, it consists of coupled equations set in…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
The CHY scattering equations on the moduli space $M_{0,n}$ play a prominent role at the interface of particle physics and algebraic statistics. We study the scattering correspondence when the Mandelstam invariants are restricted to a fixed…
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…
Hypertoric varieties are quaternionic analogues of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
We obtain a global version and a twisted version (in the sense of \cite{bp05}) of the main theorem of \cite{bkr}.
In this survey we discuss some of the classical and modern methods in studying the (Riemann-)Schottky problem, the problem of characterizing Jacobians of curves among principally polarized abelian varieties. We present many of the recent…
I briefly review several important formal theory developments in quantum field theory and string theory that were reported at ICHEP conferences in past decades, and explain how they underlie a new research area referred to as physical or…
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…