Members

Alberto S. Cattaneo, professor.

My fields of interest are in mathematical physics, differential geometry and algebraic topology. In particular, my research activity includes deformation quantization, symplectic and Poisson geometry, topological quantum field theories, and the mathematical aspects of perturbative quantization of gauge theories.

On the arXiv.

Giovanni Canepa, PhD student.

My research interests are between field theory, differential geometry and general relativity. More precisely I'm interested in the mathematical aspects of General Relativity viewed as a field theory. Currently I'm working on gravity in the BV-BFV formalism, in collaboration with Alberto Cattaneo and Michele Schiavina.

On the arXiv.

Nicola Capacci, PhD student.

My research interests are in geometric approaches to mathematical physics, specifically in the interplay between quantum field theory, Poisson geometry and algebraic topology. In particular, I'm currently doing some reading about the BV formalism, deformation quantization and factorization algebras, which are possible approaches to axiomatize QTFs. In the near future I hope to use these theories to study generic aspects of observable's algebras of quantum theories.

Artem Kalmykov, PhD student.

My research interests lie on the intersection of representation theory and geometry, especially the one related to elliptic curves.

Nima Moshayedi, PhD student.

I am a PhD student at the Institute for Mathematics at the University of Zurich under the supervision of Prof. Dr. Alberto S. Cattaneo. My subject is Mathematical Physics from the geometric and algebraic point of view, where I am studying the behavior of Deformation Quantization, BV-BFV formalism, Topological Quantum Field Theories and several aspects of Path integrals and Gauge invariants.

On the arXiv.

Ödül Tetik, PhD student.

On the arXiv.

Past Members

Jonathan Lorand, PhD student.

Currently I am working on topics at the intersection of symplectic/Poisson geometry and representation theory, such as symplectic poset representations. I am also exploring categorifications of geometric algebra, e.g. studying symplectic structures in a category-theoretic setting. Generally, I am interested in topics which connect conceptual mathematics with applications - whether these be in physics, life sciences, or elsewhere.

My personal webpage is here.

On the arXiv.

Pavel Safronov, lecturer.

My research lies at the intersection of mathematical physics, algebraic geometry and representation theory. This involves topological field theories, derived algebraic geometry, higher (shifted) Poisson structures, geometric and deformation quantization of shifted symplectic structures and supersymmetric gauge theories.

On the arXiv.

Alessandro Valentino, postdoc.

My research area is at the intersection of topology, higher category theory and mathematical physics. I am generally interested in Topological Quantum Field Theory in the categorical setting, which means I spend time with cobordism categories, oo-categories, module categories, etc.. Recently I have been thinking about homotopy actions of groups on higher categories, 2-Segal spaces à la Dyckerhoff-Kapranov, and modular functors. I am also interested in nonperturbative aspects of QFT in the framework of factorization algebras.

On the arXiv.

Konstantin Wernli, PhD student.

My main research interests lie in the perturbative quantization of gauge theories, especially Chern-Simons theory and other AKSZ theories. Through the BV-BFV formalism developed by Cattaneo, Mnev and Reshetikhin I try to understand the behaviour of the perturbative expansion under the cutting and gluing of manifolds - also into pieces of higher codimension, using methods from algebraic topology. One of the big challenges is to understand the compatibility of boundary conditions with gauge fixings. One of the main goals is to connect this with the theory of (extended) TQFTs.
I am also interested in various related aspects of gauge theories, such as moduli space of solutions to the Euler-Lagrange equations, the combinatorics of Feynman graphs, and the problem of multiplying distributions according to Feynman graphs (Regularisation and Renormalisation), and the various connections between gauge-theory and low-dimensional topology.
Recently I have also become more interested in "holographic" and other bulk-boundary correspondences appearing in various area of physics, and their connection to gauge (and string) theories on manifolds with boundary (or corners).

On the arXiv.

Past members

(Last update 20.10.2020)

Camilo Arias Abad

Profesor Asistente, Universidad Nacional de Colombia en Medellín

Cattaneo group