A5102856234- Algebraic structures and combinatorial models
- Nonlinear Waves and Solitons
- Advanced Algebra and Geometry
- Random Matrices and Applications
- Advanced Combinatorial Mathematics
- Nonlinear Photonic Systems
- Advanced Topics in Algebra
- Molecular spectroscopy and chirality
- Spine and Intervertebral Disc Pathology
- Black Holes and Theoretical Physics
- Mathematical functions and polynomials
- Stochastic processes and statistical mechanics
- Neurofibromatosis and Schwannoma Cases
- Polynomial and algebraic computation
- Spinal Fractures and Fixation Techniques
- Anesthesia and Pain Management
- Theoretical and Computational Physics
- Quantum chaos and dynamical systems
- Intraoperative Neuromonitoring and Anesthetic Effects
- Pelvic and Acetabular Injuries
- Geometry and complex manifolds
- Myofascial pain diagnosis and treatment
- X-ray Spectroscopy and Fluorescence Analysis
- Particle accelerators and beam dynamics
- Advanced Fiber Laser Technologies
Federal Almazov North-West Medical Research Centre
2019-2024
Russian Scientific Research Neurosurgical Institute
2018-2024
Kurchatov Institute
2016-2024
Institute for Information Transmission Problems
2023-2024
Ministry of Health of the Russian Federation
2023-2024
Institute of Oceanology. PP Shirshov Russian Academy of Sciences
2006-2023
Moscow Aviation Institute
2023
Gazprom (Russia)
2023
Institute for Theoretical and Experimental Physics
2019-2021
Université de Montréal
1997-2007
We generalize the Harish-Chandra-Itzykson-Zuber and certain other integrals (the Gross-Witten integral, over complex matrices rectangle matrices) using a notion of tau function matrix argument. In this case one can reduce multi-matrix to eigenvalues, which in turn are functions. also consider generalization Kontsevich integral.
A new representation of the 2N fold integrals appearing in various two-matrix models that admit reductions to over their eigenvalues is given terms vacuum state expectation values operator products formed from two-component free fermions. This used derive perturbation series for these under deformations induced by exponential weight factors measure, expressed as double and quadruple Schur function expansions, generalizing results obtained earlier certain models. Links with coupled KP...
We present the fermionic representation for q-deformed hypergeometric functions related to Schur polynomials considered by S.Milne \cite{Milne}. For $q=1$ these are also known as of matrix argument which zonal spherical $GL(N,C)/U(N)$ symmetric space. show that multivariable tau-functions KP hierarchy. At same time they ratios Toda lattice Takasaki in \cite{Tinit}, \cite{T} evaluated at certain values higher times. The variables times those hierarchies via Miwa change variables. discrete...
We introduce a useful and rather simple class of BKP tau functions which we shall call "easy functions". consider two versions hierarchy, one will "small hierarchy" (sBKP) related to $O(\infty)$ introduced in Date et al "large (lBKP) $O(2\infty +1)$ Kac van de Leur (which is closely the large $O(2\infty)$ DKP hierarchy (lDKP) Jimbo Miwa). Actually functions" sBKP were already considered Harnad al, here are more interested lBKP case also mixed small-large (Kac Leur). Tau under consideration...
We recall Krichever's construction of additional flows to Benney's hierarchy, attached poles at finite distance the Lax operator. Then we construct a `dispersionful' analogue this in which role is played by Miura fields. connect hierarchy with N-wave systems, and prove several facts about latter (Lax representation, Chern - Simons-type Lagrangian, connection Liouville equation, -functions).
We derive a bilinear expansion expressing elements of lattice KP $\tau$-functions, labelled by partitions, as sum over products pairs an associated BKP strict partitions. This generalizes earlier results relating determinants and Pfaffians minors skew symmetric matrices, with applications to Schur functions $Q$-functions. It is deduced using the representations $\tau$-functions vacuum expectation values (VEV's) fermionic operators charged neutral type, respectively. The generated insertion...
Point symmetries are obtained for all equations in the KP hierarchy. The Lie algebra each equation is infinite dimensional and involves several arbitrary functions of corresponding time tN. symmetry a semidirect sum Virasoro Kac–Moody one. “positive” part this embedded into known W∞ free fermion ĝl(∞). action on tau-function presented. negative point does not fit algebra, but P∞ based pseudodifferential operators.