Carlos Perez-Sanchez math-phys

Carlos I. Perez-Sanchez

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  • I am a postdoc (Wissenschaftlicher Mitarbeiter) in the group of Răzvan Gurău. Before, I was a postdoc (adiunkt naukowy) in the group of Piotr Sułkowski at the Institute of Theoretical Physics, University of Warsaw, Poland. Prior to that, I did my Ph.D. in mathematics at the WWU-Münster, under supervision of Raimar Wulkenhaar.

    Generally, I'm interested in mathematical physics, specially if this has applications in quantum gravity. Without being a probabilist, roughly speaking, I work with random geometry ("the Euclidean quantum theory of geometry"). In order to define the gravity partition function, regulating procedures are commonly applied (this procedure is not only present in quantum gravity but often preformed in quantum field theory) The approaches I have worked on come in two flavours: first, simplicial or PL-approximations of manifolds, which precisely are generated by theory of random tensors (whose large-N was an essential finding by Gurău); the second is an algebraic approach based on finite-dimensional approximations in Connes' noncommutative geometry (NCG).

    On the random tensors side, I am interested in topological and geometric problems. Before, I worked on combinatorial and QFT aspects of random tensors, like loop equations (Dyson-Schwinger) equations and a Ward-Takahashi Identity, and on the geometric interpretation of their correlation functions.

    In random (finite) noncommutative geometry, 'geometry' (since our aim is gravitation, then also physics) is encoded in the spectrum of a Dirac operator. Regulating the path integral over Dirac operators means a spectral truncation. This, in turn, leads to a ubiquitous topic in mathematical physics: random matrix theory. Interestingly, the models that NCG gives us come with multiple matrices and with multitraces (the latter feature is not well-studied in the random matrix literature). These geometries are also then referred to as matrix (or fuzzy) geometries. Here I worked computing the spectral action and derived Yang-Mills(-Higgs) theory on a matrix geometry.

    Lately I'm also interested in functional renormalization, which helps to connect the quantum gravity models with low energy theories (formulated on smooth manifolds). I focused first on multimatrix models motivated by NCG.

    I am teaching Theoretical Statistical Mechanics (Übungsleitung, master course, WiSe 21/22).

    Albert-Ueberle-Str. 3-5, Büro 111. Tel. +49-6221-54-9457

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