This is the second of two volumes that showcase young scientists who are continuing the outstanding tradition of Russian mathematics in their home country. There remain numerous strong research groups, particularly in Moscow and St. Petersburg, despite the familiar difficulties: academic salaries in Russia remain low, many leading figures have departed and there are plentiful opportunities for employment in university positions abroad or in sectors in Russia that offer a living wage. It is hoped that the articles in this book give a picture of the interests and achievements of mathematicians that participate in some of the active seminars in the country. Seven have something of the character of a survey, but also contain many original results and give extensive bibliographies; the eighth is a revised and expanded version of a 2002 research article.

The first of the two volumes (LMS Lecture Notes 338) was entitled Surveys in Geomety and Number Theory; this one is mainly on combinatorial and algebraic geometry and topology. Both volumes contain papers based on courses of lectures given at British universities by the authors under the ‘Young Russian Mathematicians’ scheme, which the London Mathematical Society set up to help such mathematicians visit the UK and to provide them with financial support.

In the nineties sheer subsistence was difficult for Russian academics. Over the last five years things have improved, and the salaries of university employees, though not generous, are closer to sufficing for the necessities of life.