# IRTG-Seminar Summer Term 2019

This semester we meet again with the IRTG-Seminar. The meeting will take place in Kaiserslautern.

#### Meeting: Tuesday, 9th July 2019, Kaiserslautern, 48-210. We start at 15:30. At 17:00 we have to change the room to 48-438.

TimeNameTitle
15:30-16:15Sogo Pierre SanonArithmetic of abelian varieties
16:30-17:15Miguel PlumaThe SYK model and q-Gaussians
17:30-18:15Lukas Ristau
Massively parallel methods in algebraic geometry using Singular and GPI-Space

#### Abstracts of the meeting

• Miguel’s talk: In this talk we will see the construction of q-Gaussian variables, and we will show the connection with the so called SYK model. The q-Gaussian variables were introduced by Bozejko and Speicher in 1991, in the context of non-commutative probability. Starting with a real Hilbert space H and the natural action of the symmetric group on the n-fold tensor product of H, we define a deformed inner product on the tensor algebra T(H). The q-Gaussian variables are defined as “creation” plus “annihilation” in the completion of T(H). The SYK model was introduced by Sachdev and Ye in 1993 as a model for quantum random spin systems, later in 2015 it was promoted by Kitaev as a simple model for quantum holografy. The SYK model is a random matrix model and has the remarkable property that its eigenvalue distribution converges towards the distribution of the q-Gaussian variable. Recently we showed that this property can be extended to the multivariate situation.