Some more amplituhedra are contractible

The amplituhedra arise as images of the totally nonnegative Grassmannians by projections that are induced by linear maps. They were introduced in Physics by Arkani-Hamed \& Trnka (Journal of High Energy Physics, 2014) as model spaces that should provide a better understanding of the scattering amplitudes of quantum field theories. The topology of the amplituhedra has been known only in a few special cases, where they turned out to be homeomorphic to balls. The amplituhedra are special cases of Grassmann polytopes introduced by Lam (Current Developments in Mathematics 2014, Int.\ Press). In this paper we show that that some further amplituhedra are homeomorphic to balls, and that some more Grassmann polytopes and amplituhedra are contractible.Comment: 7 pages, to appear in Selecta Mathematic

Asymmetric function theory

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.Comment: 36 pages, 8 figures, 1 table. Written for the proceedings of the Schubert calculus conference in Guangzhou, Nov. 201

Teamwork Efficiency and Company Size

We study how ownership structure and management objectives interact in determining the company size without assuming information constraints or any explicit costs of management. In symmetric agent economies, the optimal company size balances the returns to scale of the production function and the returns to collaboration efficiency. For a general class of payoff functions, we characterize the optimal company size, and we compare the optimal company size across different managerial objectives. We demonstrate the restrictiveness of common assumptions on effort aggregation (e.g., constant elasticity of effort substitution), and we show that common intuition (e.g., that corporate companies are more efficient and therefore will be larger than equal-share partnerships) might not hold in general

Transactions

ალექსი გორგიძის დაბადებიდან 105 წლისთავისადმი მიძღვნილი შრომათა კრებული. Сборник трудов посвященный к 150 летию со дня рождения Алексея Горгидзе. The collection of works devoted to the 105th anniversary of the birth of the Alexi Gorgidz