This project addresses mathematical structures in the space of all possible quantum theories. The space of all QFTs is infinite-dimensional, with CFT fixed-points linked by paths corresponding to RG flows. These CFTs are the building blocks of all possible quantum theories (including theories of quantum gravity and black holes). Our goal is to understand the space of all theories by first understanding some special subsets. We use complementary approaches, such as Resurgent Analysis, Bootstrap Techniques, and Localisation. These approaches solve quantum theories described by random matrix models, CFTs in diverse dimensions, and quantum theories with localisable observables. The very same theory may be approachable using these different techniques, leading to complementary information. By solving different special sets of quantum theories, we expect to describe geometrical and algebraic structures on local patches of the full space of quantum theories.

**5-6 September 2019***IST Lisbon*

**Vasilis Niarchos***(Durham University)*

"Deconstruction of 4d QFTs from 3d QFTs"**Costis Papageorgakis***(Queen Mary University of London)*

"Exact dimensional deconstruction of the 6D (2,0) theory"**Wolfger Peelaers***(Oxford University)*

VOAs and rank-two instanton SCFTs

Weil-Petersson, Kontsevich, Schwarzschild

**Paolo Gregori, Ricardo Schiappa**

Two remarkable facts about JT two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensemble is described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e., changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series)... read more

**3 October 2020**

*Explica-me como se tivesse 5 anos -* LINK (in Portuguese)