# Irregular connections on algebraic curves and quantum field theory (QuantumG)

PTDC/MAT-PUR/30234/2017

## Members

- Carlos Florentino (Co PI)
- Davide Masoero (PI)
- Stefano Negro
- Andrea Raimondo
- Roberto Tateo
- Miguel Tierz Parra

## PhD Students

## Description

The general aim of the project is to create a fertile research and training environment for senior and junior scientists working in the fields of Geometry, Mathematical Physics, and Theoretical Physics. The scientific questions we plan to address are mainly two: 1. We plan to achieve a complete analytic and geometric understanding of the ODE/IM correspondence for the g-Quantum KdV model, and of its massive deformations. 2. We aim at making a distinct impact in the understanding of supersymmetric and topological gauge theories, bringing together results from random matrix theory, statistical mechanics and integrable systems. With these methods we expect to obtain a complete description of the phase diagram of quantum electrodynamics and quantum chromodynamics theories in three dimensions, with different types of supersymmetric matter.

The host institution is the Group of Mathematical Physics of
the University of Lisbon. This is
a research centre in Mathematics funded by the Portuguese Science Foundation (FCT). The
project includes funding for **two postdoctoral
positions**. The call for the first one can be found at http://fciencias-id.pt/node/48
(2548 - PhD Scientific Researcher Recruitment; PTDC/MAT-PUR/30234/2017;
Project QuantumG)

Time span: 16/09/2018-15/09/2021

## Relevant publications

- D. Masoero, A. Raimondo, and D. Valeri
- Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued
connections I. The simply-laced case

*Commun. Math. Phys.*(2016) 344: 719. - D. Masoero, A. Raimondo, and D. Valeri
- Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued
connections II. The non simply-laced case

*Commun. Math. Phys.*(2017) 349: 1063. - J. Russo, G.Silva, and M. Tierz
- Supersymmetric U(N) Chern–Simons-Matter Theory and Phase
Transitions

*Commun. Math. Phys.*(2015) 338: 1411. - C. Florentino and S. Lawton
- The topology of moduli spaces of free group representations

*Math. Annalen*345 (2009) 453-489. - D. Bombardelli, Fioravanti and R. Tateo
- Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal.

*Journal of Physics A: Mathematical and Theoretical*42, no. 37 (2009): 375401.