24 research outputs found
Tautological relations and integrable systems
No full textWe present a family of conjectural relations in the tautological cohomologyof the moduli spaces of stable algebraic curves of genus with markedpoints. A large part of these relations has a surprisingly simple form: thetautological classes involved in the relations are given by stable graphs thatare trees and that are decorated only by powers of the psi-classes athalf-edges. We show that the proposed conjectural relations imply certainfundamental properties of the Dubrovin-Zhang (DZ) and the double ramification(DR) hierarchies associated to F-cohomological field theories. Our relationsnaturally extend a similar system of conjectural relations, which were proposedin an earlier work of the first author together with Gu\'er\'e and Rossi andwhich are responsible for the normal Miura equivalence of the DZ and the DRhierarchy associated to an arbitrary cohomological field theory. Finally, weprove all the above mentioned relations in the case and arbitrary using a variation of the method from a paper by Liu and Pandharipande, this canbe of independent interest. In particular, this proves the main conjecture fromour previous joined work together with Hern\'andez Iglesias. We also prove allthe above mentioned relations in the case and arbitrary .Comment: v3: final journal version, 44 page
Double Ramification Cycles and the n-Point Function for the Moduli Space of Curves
No full textIn this paper, using the formula for the integrals of the ψ-classes over the double ramification cycles found by S. Shadrin, L. Spitz, D. Zvonkine and the author, we derive a new explicit formula for the n-point function of the intersection numbers on the moduli space of curves
A conjectural formula for
No full textInternational audienceWe propose a conjectural formula for and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Gu\'er\'e and Rossi, and we prove that the two conjectures are in fact equivalent, though in a quite non-trivial way
Buryak–Okounkov Formula for the n-Point Function and a New Proof of the Witten Conjecture
No full text© The Author(s) 2020. We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous Witten conjecture/Kontsevich theorem, where the link between the intersection theory of the moduli spaces and integrable systems is established via the geometry of double ramification cycles.11Nsciescopu
Intersection numbers with Witten's top Chern class
No full textWitten’s top Chern class is a particular cohomology class on the moduli space of Riemann surfaces endowed with r-spin structures. It plays a key role in Witten’s conjecture relating to the intersection theory on these moduli spaces.Our first goal is to compute the integral of Witten’s class over the so-called double ramification cycles in genus 1. We obtain a simple closed formula for these integrals.This allows us, using the methods of the first author [Int. Math. Res. Not. 38 (2003) 2051-2094], to find an algorithm for computing the intersection numbers of the Witten class with powers of the ψ-classes over any moduli space of r-spin structures, in short, all numbers involved in Witten’s conjecture
Gamification as a Tool of Personnel Marketing
No full textEmployees are a key and important resource of any company, which means a growing demand for innovative tools of improving motivation, adaptability, and productivity. Gamification, originally applied in marketing and education, is gaining popularity in corporate environment. It increases employees’ motivation by using slot elements to stimulate their performance. The author studied the benefits, problems, and challenges of personnel gamification in corporate management. The analysis involved case studies and public data. Gamification proved quite effective in work engagement. However, it required certain conditions, e.g., technical equipment, particular psychophysical and cultural staff profile, etc. The main indicators that show the effectiveness of gamification were defined as follows: 1) engagement level; 2) labor productivity; 3) low staff turnover; 4) good work satisfaction level; 5) teamwork; 6) return on investment. The most popular gamification elements included leaderboards, grade systems, and corporate currency
Linking Indigenous Knowledge and Observed Climate Change Studies
No full textWe present indigenous knowledge narratives and explore their connections to documented temperature and other climate changes and observed climate change impact studies. We then propose a framework for enhancing integration of these indigenous narratives of observed climate change with global assessments. Our aim is to contribute to the thoughtful and respectful integration of indigenous knowledge with scientific data and analysis, so that this rich body of knowledge can inform science, and so that indigenous and traditional peoples can use the tools and methods of science for the benefit of their communities if they choose to do so. Enhancing ways of understanding such connections are critical as the Intergovernmental Panel on Climate Change Fifth Assessment process gets underway
Synthesis of 2-((3-(ethoxycarbonyl)-4,5,6,7-tetrahydrobenzo [b] thiophen-2-yl)amino)-4-(4-methoxyphenyl)-4-oxobut-2-enoate
No full text2-((3-(Ethoxycarbonyl)-4,5,6,7-tetrahydrobenzo[b]thiophen-2-yl)amino)-4-(4-methoxyphenyl)-4-oxobut-2-enoate has been synthesized by the reaction of ethyl (E)-2-((5-(4-methoxyphenyl)-2-oxofuran-3(2H)-ylidene)amino)-4,5,6,7-tetrahydrobenzo[b]thiophene-3-carboxylate or 2-((3-(ethoxycarbonyl)-4,5,6,7-tetrahydrobenzo[b]thiophen-2-yl)amino)-4-(4-methoxyphenyl)-4-oxobut-2-enoate with potassium tert-butoxide. © 2022 Author(s).The work was done with the financial support of the Russian Foundation for Basic Research (project no. 19-43-590023)
