Related papers: Recent developments of the DDVV Conjecture

In This paper, we survey recent progress on the theory of Gromov- Witten invariants on Hilbert schemes of points mainly on elliptic surfaces and simply connected minimal surface of general type. In particular, we focus on the aspects of…

We survey the classical results of the Dirichlet Approximation Theorem.

This is a survey on Sarnak's Conjecture

We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…

This is an extended abstract for a survey talk given in Oberwolfach on 1st December 2022, slightly updated in June 2023. I survey some work around the notion of quasiminimality and some of the progress towards Zilber's conjecture from the…

I review recent progress in defining probability distributions in the inflationary multiverse.

These brief notes record our puzzles and findings surrounding Givental's recent conjecture which expresses higher genus Gromov-Witten invariants in terms of the genus-0 data. We limit our considerations to the case of a projective line,…

We prove Dejean's conjecture. Specifically, we show that Dejean's conjecture holds for the last remaining open values of n, namely 15 <= n <= 26.

In this short note we give counterexamples to several results related to extension theorems published recently.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…

We highlight recent developments in neutrino astrophysics. We discuss some of the connections with nuclear physics.

In this paper, we give a new discovery of conversion of generalized singular values. New formulation is proposed.

The method for solving the KdV are considered.

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.

The article presents the proof of Casas-Alvero conjecture.

We obtain some new inequalities of Chebyshev Type.