Speaker
Description
In this talk, I will present a brief introduction to matrix models[2], which
naturally arise if we work in the context of interacting QFT, as $\phi^{4}_{4}$ model, constructing graphs we make perturbation expansion, where arise graphs made of vertexes and edges [1]. The goal of talk to show how combinatoric factors of graphs and maps could be calculated using Gaussian integrals or it's generalization. Matrix models arise in different fields of Quantum gravity, string theory, and different CFT-s, and have deep geometric background.
References
[1] D Bessis, C Itzykson, J.B Zuber “Quantum field theory techniques in graphical enumeration”. In: Advances in Applied Mathematics 1 (1980), pp. 109–
157. doi: 10.1016/0196-8858(80)90008-1.
[2] A. Zvonkin. “Matrix integrals and map enumeration: An accessible introduction”. In: Mathematical and Computer Modelling 26 (1997), pp. 281–
304. doi: 10.1016/S0895-7177(97)00210-0
| Field | Mathematics |
|---|---|
| Length | Long 20 min |
