Exts and the AGT Relations

We prove the connection between the Nekrasov partition function of N= 2 super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday–Gaiotto–Tachikawa relations. Mathematically, this is achieved by relating the Carlsson–Okounkov Ext vector bundle on the moduli space of rank 2 sheaves with Liouville vertex operators. Our approach is geometric in nature, and uses a new method for intersection-theoretic computations of the Ext operator. Keywords: Nekrasov partition function, AGT relations, Ext operators, shuffle algebr

Yangians and cohomology rings of Laumon spaces

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of $GL_n$. We construct the action of the Yangian of $sl_n$ in the cohomology of Laumon spaces by certain natural correspondences. We construct the action of the affine Yangian (two-parametric deformation of the universal enveloping algebra of the universal central extension of $sl_n[s^{\pm1},t]$) in the cohomology of the affine version of Laumon spaces. We compute the matrix coefficients of the generators of the affine Yangian in the fixed point basis of cohomology. This basis is an affine analogue of the Gelfand-Tsetlin basis. The affine analogue of the Gelfand-Tsetlin algebra surjects onto the equivariant cohomology rings of the affine Laumon spaces. The cohomology ring of the moduli space $M_{n,d}$ of torsion free sheaves on the plane, of rank $n$ and second Chern class $d$, trivialized at infinity, is naturally embedded into the cohomology ring of certain affine Laumon space. It is the image of the center $Z$ of the Yangian of $gl_n$ naturally embedded into the affine Yangian. In particular, the first Chern class of the determinant line bundle on $M_{n,d}$ is the image of a noncommutative power sum in $Z$.Comment: final version, to appear in Selecta Mat

European Union’s Dependency on Russian Energy. Geopolitical Considerations

Russia is not a military or economic superpower anymore, but is still an energy superpower. It’s advantage? Russia controls the access to the energy resources on its own territory and the ones in its “close vicinity”. Considering the geostrategic energy resources, the Caspian Sea is a “Russian lake” or a “mare nostrum”. Bearing in mind that the Middle East is under “American control” and in conflict for thirty years, and China became a “black hole” in this field, absorbing anything it can, the Caspian area appeared for the European consumers “the promised land” of energy, especially after the implosion of the communist system. Now, here we find the most important international actors: Russia, USA, European Union and China. Will the Caspian area become a new “Middle East”?geostrategic energy resources; European Union; Russia; energy resources geopolitics

The Dynamic of Foreign Visitors in Romania since 1990. Current Challenges of Romanian Tourism

This study represents a quantitative and qualitative analysis of the Romanian tourism phenomenon that focuses on the current challenges to which it has to adapt in order to become competitive on the European market and to overcome its current stage of subsistence tourism. One of the selected criteria for highlighting the main dysfunctions of the Romanian tourism and that also represents the goal of this research is one of the indicators that quantify the annual flow of international tourists that come to Romania. In Romania's post-communist economic development (a negative evolution, of course), tourism remains a real lever for national and regional economic development that can bring Romania numerous competitive advantages on the European Union market

Ultra Short Multiband AM/FM/DAB Active Antennas for Automotive Application

The length reduction of rod antennas is nowadays a major concern in the automotive industry. The need for new shorter rods stems from the desire to fulfil the design aesthetics of modern cars and to alleviate the mechanical issues the longer rods have. However, despite the severe length reduction, the short rods have to perform at least as good as the 40 cm long active monopoles usually met nowadays. In this context, the present thesis investigates the possibilities to use for AM, FM and DAB broadcast reception in an automotive environment 20 cm long active monopole antennas and 14 cm long active helical elements. Electrically very short active antennas are challenging because the very low effective height of the antenna element and its inconvenient antenna impedance with a highly reactive character pose important constrains upon the antenna amplifier. The amplifier has to have high input impedance, which has to be increasingly higher, as the antenna impedance gets also higher. At the same time, the amplifier has to exhibit enough gain and low noise character, in order to achieve good sensitivity. There are also important requirements to be fulfilled concerning its linearity