Home | Talks | Lecture notes | Codes | Publications@INSPIRE-HEP | Academic CV (PDF) |

**Lattice theory of condensed matter**, [pdf, 19Mb], [pptx, 12Mb].

Lectures given at the 2017 Helmholtz International Summer School Helmholtz International Summer School "Hadron Structure, Hadronic Matter, and Lattice QCD", 20 August - 2 September 2017, Dubna, Russia.**On the tensor of inertia,**Lecture notes [pdf, 0.1Mb], [tex, 0.0Mb], Classroom slides [pdf, 0.5Mb], [pptx, 0.3Mb].**Graphene, topological insulators and Weyl semimetals.**

Lectures given at the 2014 International Parma School on Theoretical Physics, 14-20 September 2014, Parma, Italy.- Graphene [pdf, 8Mb][pptx, 4Mb]
- Topological Insulators [pdf, 9Mb][pptx, 11Mb]
- Weyl Semimetals [pdf, 10Mb][pptx,5 Mb]

**Anomalous transport on the lattice**, [pdf, 15Mb], [pptx, 28Mb].

Lectures given at the 2014 Helmholtz International Summer School "Lattice QCD, Hadron Structure and Hadronic Matter", 25 August - 6 September 2014, Dubna, Russia.**Noether theorem**(5 pages, 1 figure) [pdf] [source]**Conjugate Gradient method for solving linear systems**(4 pages) [pdf] [source]**Methods for generating random numbers with arbitrary probability distribution**(5 pages, 2 figures) [pdf] [source]- Functional inversion
- Rejection sampling
- biased Metropolis

**Linear response theory**(7 pages) [pdf] [source]- Green-Kubo relation
- Kramers-Kronig relations
- Euclidean correlators

**Large-N quantum field theories**(lecture course read in winter semester 2012 in Regensburg University)__Short outline of the lecture course__[pdf] [source]__Large-N φ__(15 pages) [pdf] [source]^{4}theory and large-N O(N) nonlinear σ-model: analytic solutions in terms of collective field variables and lagrange multipliers- Generalized radial coordinates for M vectors in N-dimensional space with N ≥ M
- Collective field variables for large-N φ
^{4}field theory - Collective field variables for large-N O(N) σ model
- A solution of the large-N φ
^{4}field theory in terms of Lagrange multiplier field - A solution of the large-N O(N) σ-model in terms of Lagrange multiplier field

__Large-N φ__[Scanned script as PDF, 5 pages, 2.5 MB]^{4}theory: diagrammatic interpretation of saddle-point approximation and the next-to-leading order correction in 1/N- Integrating over Gaussian fluctuations of the collective fields around the saddle point
- Saddle point approximation as a sum over chain diagrams
- 1/N corrections as one-loop corrections with dressed propagators

__Large-N matrix models__[Scanned script as PDF, 15 pages, 13.5 MB]- Perturbative expansions of matrix models and random polygonations of surfaces
- Van der Monde determinant
- Coulomb gas interpretation of matrix models
- Solutions of resolvent equations and eigenvalue density
- Gross-Witten phase transition for the U(N) matrix model