Higher-dimensional obstructions for star reductions

Obstructions to dimensional reduction in hot QCD

I describe results on screening masses in hot gauge theories. Wilsonian effective long distance theories called dimensionally reduced (DR) theories describe very well the longest screening length in pure gauge theories. In the presence of fermions, meson-like screening lengths dominate the long-distance physics for 3Tc/2 ≤ T < 3Tc, and thus obstruct perturbative DR. Extrapolation of our results...

Differential reductions of the Kadomtsev - Petviashvili equation and associated higher dimensional nonlinear PDEs

We represent an algorithm allowing one to construct new classes of partially integrable multidimensional nonlinear partial differential equations (PDEs) starting with the special type of solutions to the (1+1)-dimensional hierarchy of nonlinear PDEs linearizable by the matrix Hopf-Cole substitution (the Bürgers hierarchy). We derive examples of four-dimensional nonlinear matrix PDEs together wi...

Lie Cylinders and Higher Obstructions to Deforming Submanifolds

To every morphism χ : L → M of differential graded Lie algebras we associate a functors of artin rings Defχ whose tangent and obstruction spaces are respectively the first and second cohomology group of the cylinder of χ. Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kähler manifo...

Lie Description of Higher Obstructions to Deforming Submanifolds

To every morphism χ : L → M of differential graded Lie algebras we associate a functors of artin rings Defχ whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of χ. Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanif...

Higher Dimensional