Off-critical lattice models and massive SLEs

We suggest how versions of Schramm’s SLE can be used to describe the scaling limit of some off-critical 2D lattice models. Many open questions remain

Topology of quadrature domains

We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.Comment: 37 pages, 11 figures in J. Amer. Math. Soc., Published electronically: May 11, 201

Russian economic thought on agricultural issues

The author of this article, the remarkable Russian economist Nikolai Makarov (1886-1980), is one of the brightest representatives of Chayanov's organization-production school, who had a long and dramatic life. After graduating from the Faculty of Economics of the Moscow University, he conducted economic-statistical studies of the Russian peasantry and cooperation, and taught a number of agrarian-economic disciplines at the universities of Moscow and Voronezh. Makarov took an active part in the preparation of agrarian reforms during the 1917 Revolution. During the Civil War, he emigrated to the United States and wrote books about American agriculture. In 1924, at the invitation of Alexander Chayanov, Makarov returned to Soviet Russia - as a wellknown professor and influential expert in the comparative studies of rural development in various regions of the world. The fruitful scientific work of Makarov and his colleagues from the organization-production school was stopped in 1930 - when Stalin accused Chayanov and Makarov of sabotaging collectivization and preparing a counter-revolutionary coup in the USSR. Makarov spent several years in prison, and in the mid-1930s, he was sent to work as an economist at the state farms of the Black-Earth region. In the late 1940s, he was allowed to return to research and teaching, and in old age, he published a number of books on the Soviet agricultural economy. The article presents the emigrant period of Makarov's life, when he collaborated with the editorial board of the Peasant Russia journal published in Czechoslovakia in the 1920s. Makarov conducts a political-economic analysis of the main issues and topics in the Russian agrarian thought of the late 19th - early 20th centuries. First, he describes the features of the Narodnik and Marxist theoretical-methodological approaches to the study of the Russian rural evolution. Then, in the spirit of the Chayanov school, Makarov looks for a fruitful compromise between these two ideologies. He notes the important impact on Russian agrarians of the international, primarily German, studies of the agricultural organization and evolution. The final sections of the article explain Makarov's original classifications and typologies of the forms and directions of the agricultural evolution. Today, a hundred years later, this Makarov's work helps us to better understand the debatable roots of the Russian and global agrarian ideologies in the early 20th century

Berezin transform in polynomial Bergman spaces

We study the reproducing kernel for weighted polynomial Bergman spaces and consider applications to the Berezin transform. Some of our results have applications in random matrix theory, a topic which we discuss in a separate (companion) paper

Fluctuations of eigenvalues of random normal matrices

In this note, we prove Gaussian field convergence of fluctuations of eigenvalues of random normal matrices in the interior of a quantum droplet