Related papers: Problems related to isoparametric theory

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

We survey the field of nonparametric inference under shape constraints, providing a historical overview and a perspective on its current state. An outlook and some open problems offer thoughts on future directions.

We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…

In this note, we discuss the interactions between differential topology and isoparametric foliations, surveying some recent progress and open problems.

This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.

In this paper we provide an application to the Neumann problem of a recent three critical points theorem.

We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

We prove existence results for nodal solutions of the Yamabe equation that are constant along the level sets of an isoparametric function.

We identify and study a simple combinatorial problem that is derived from submodularity issues encountered in the theory of tangles of graphs and abstract separation systems.

Presented is a new method yielding parameterized solution to an interval parametric linear system. Some properties of this method are discussed. The solution enclosure it provides is compared to the enclosures by other methods. It is shown…

Some notes and questions about the concept of time are exposed. Particular reference is given to the problem in quantum mechanics, in connection with the indeterminacy principle.

I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…

We obtain simple proofs of certain inequalites for bivariate means.

A selection of open problems in the theory of composites is presented. Particular attention is drawn to the question of whether two-dimensional, two-phase, composites with general geometries have the same set of possible effective tensors…

Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories,…

Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…

This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.

This paper collects polynomial Diophantine equations that are simple to state but apparently difficult to solve.

Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.