The workshop «Secondary and delocalized index invariants» was held in Copenhagen, Denmark

The workshop «Secondary and delocalized index invariants» was held in Copenhagen, Denmark

Professor of the Nilkolskii Mathematical Institute, gave a plenary talk: «On the index of elliptic problems in plane compound domains».

11- 15 June 2018   the workshop «Secondary and delocalized index invariants» was held in Copenhagen, Denmark. The organizer of the event was University of Copenhagen (QS 79). Savin A. Yu., Doctor of Physics and Mathematics, professor of the Nilkolskii Mathematical Institute, gave a plenary talk: «On the index of elliptic problems in plane compound domains». The following problem was considered there. Let D be a compact plane domain with piecewise smooth boundary and we are also given a finite system of cuts of this domain by smooth curves. We consider differential equations in D with boundary conditions imposed along the boundary of D and transmission conditions along the cuts. Under appropriate ellipticity conditions, such problems have Fredholm property in weighted Sobolev spaces (with weights prescribed at the singular points on the boundary and inside the domain). In this talk, we address the index problem in this setting. The focus is on the contributions of the singular points to the index formula. It turns out that these contributions can be described as η-invariants of conormal symbols at the singular points and to define these η-invariants, we extend the definition of η-invariant due to Melrose to parameter-dependent boundary value problems.

News
All news
Science
27 Jun
RUDN Mathematicians: 5G will cope with traffic when using WiGig

RUDN mathematicians investigated the possibility of combining 5 GNR technology and WiGig — a high-frequency range that allows you to transfer data at speeds up to 10 Gbps. This will smooth traffic fluctuations in 5Gnetworks and cope with user requests.

Science
23 Jun
Scientists Reveal the Water Column of the Yamal Lakes Can Be a Microbial Filter

Scientists from the Winogradsky Institute of Microbiology RAS, RUDN University, St. Petersburg State University and the Tyumen Scientific Centre SB RAS studied the microbial communities from several lakes of the Yamal Peninsula. It turned out that methanotrophs (bacteria that use methane as a source of energy) consume methane more actively in the deep mature lakes of the peninsula than in small thermokarst lakes. In this regard, methane emissions into the atmosphere from the surface of deep lakes are low, and only small (relatively younger thermokarst lakes with constitutional ground ice) can make a significant contribution to methane emissions in the north of Western Siberia. Thus, bacteria perform an important function for the climate balance — they reduce the emission of methane into the atmosphere.

Science
20 Jun
RUDN University Physicists Determine the Optimal Conditions for Holding High-Energy Plasma Clouds in Pyrotron

RUDN University physicists have described the conditions for the most efficient operation of long mirror-based variant of cyclotron in the autoresonance mode. These data will bring better understanding of plasma processes in magnetic traps.