Dr Fabrizio Del Monte PhD

School of Mathematics
Assistant Professor

Contact details

Email
f.delmonte@bham.ac.uk
View my research portal
Address
School of Mathematics
Watson Buiiding
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Dr Fabrizio Del Monte is a mathematical physicist working at the interface of integrable systems, string theory, and algebraic geometry. Fabrizio obtained his PhD from SISSA, Italy, in 2020 under the supervision of Giulio Bonelli and Alessandro Tanzini. Following this, he was a CRM-ISM postdoctoral fellow at the Centre de Recherches Mathématiques in Montréal and a research associate at the University of Sheffield, before joining University of Birmingham in 2024 as an assistant professor.

Personal website.

Qualifications

  • PhD in Theoretical Particle Physics, SISSA Trieste, 2020
  • MSci in Theoretical Physics, Università di Pisa, 2016

Biography

CRM-ISM Postdoctoral Fellow (CRM Montréal, 2021-2023), Research Associate (University of Sheffield, 2023-2024).

Research

Research themes

  • Integrable Systems
  • Tau Functions
  • q-Difference Equations
  • String Theory
  • Stability Conditions
  • Mirror Symmetry

Research activity

Dr Del Monte's research develops rigorous methods to understand nonperturbative String Theory through Integrable Systems. Recently, he expanded its scope to include Bridgeland Stability conditions and Donaldson-Thomas invariants in Algebraic Geometry. Specifically, he investigates integrable systems related to supersymmetric quantum field theories (QFTs) derived from geometric constructions in M-theory: isomonodromic deformations for four-dimensional 'class S' theories and their q-deformations for five-dimensional 'geometrically engineered' theories.

In 4d, he studied isomonodromic tau functions on elliptic curves through analytic Fredholm determinant formulas, relating them to non-perturbative partition functions. He also characterised these tau functions via the symplectic geometry of flat connections, which he is leveraging to study their modular transformations, physically corresponding to electromagnetic duality in the QFT.

In 5d, he introduced a novel correspondence with discrete integrable systems, enabling exact computations of BPS spectra and solutions to the associated Riemann-Hilbert problem. This work addressed longstanding problems in the algebraic geometry of stable sheaves. He also studies monodromy spaces of q-difference equations, parametrising moduli spaces of vacua and line operators in 5d QFTs. He is developing a new approach to this growing subject, through a systematic study of WKB approximation for q-difference equations.

Publications

Recent publications

Article

Del Monte, F 2024, 'BPS Spectra and Algebraic Solutions of Discrete Integrable Systems', Communications in Mathematical Physics, vol. 405, no. 6, 147. https://doi.org/10.1007/s00220-024-05016-4

Bertola, M, Korotkin, D & Del Monte, F 2023, 'Generating Function of Monodromy Symplectomorphism for 2 × 2 Fuchsian Systems and Its WKB Expansion', Journal of mathematical physics, analysis, geometry, vol. 19, no. 2, pp. 301-338. https://doi.org/10.15407/mag19.02.301

Del Monte, F, Desiraju, H & Gavrylenko, P 2023, 'Isomonodromic Tau Functions on a Torus as Fredholm Determinants, and Charged Partitions', Communications in Mathematical Physics, vol. 398, no. 3, pp. 1029-1084. https://doi.org/10.1007/s00220-022-04458-y

Del Monte, F, Desiraju, H & Gavrylenko, P 2023, 'Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus', Journal of Physics A: Mathematical and Theoretical, vol. 56, no. 29, 294002. https://doi.org/10.1088/1751-8121/acdc6c

Monte, FD & Longhi, P 2023, 'Quiver Symmetries and Wall-Crossing Invariance', Communications in Mathematical Physics, vol. 398, no. 1, pp. 89-132. https://doi.org/10.1007/s00220-022-04515-6

Monte, FD & Longhi, P 2023, 'The threefold way to quantum periods: Wkb, tba equations and q-painlevé', SciPost Physics, vol. 15, no. 3, 112. https://doi.org/10.21468/scipostphys.15.3.112

Bertola, M, Del Monte, F & Harnad, J 2022, 'Fredholm Pfaffian τ -Functions for Orthogonal Isospectral and Isomonodromic Systems', Annales Henri Poincare, vol. 23, no. 12, pp. 4521-4554. https://doi.org/10.1007/s00023-022-01204-x

Bonelli, G, Del Monte, F & Tanzini, A 2021, 'BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations', Annales Henri Poincare, vol. 22, no. 8, pp. 2721-2773. https://doi.org/10.1007/s00023-021-01034-3

Bonelli, G, Del Monte, F, Gavrylenko, P & Tanzini, A 2021, 'Circular quiver gauge theories, isomonodromic deformations and WN fermions on the torus', Letters in Mathematical Physics, vol. 111, no. 3, 83. https://doi.org/10.1007/s11005-020-01343-4

Bonelli, G, Del Monte, F, Gavrylenko, P & Tanzini, A 2020, 'N = 2 ∗ Gauge Theory, Free Fermions on the Torus and Painlevé VI', Communications in Mathematical Physics, vol. 377, no. 2, pp. 1381-1419. https://doi.org/10.1007/s00220-020-03743-y

Del Monte, F, Francia, D & Grassi, PA 2016, 'Multimetric supergravities', Journal of High Energy Physics, vol. 2016, no. 9, 64. https://doi.org/10.1007/JHEP09(2016)064

Doctoral Thesis

Del Monte, F 2020, 'Supersymmetric Field Theories and Isomonodromic Deformations'.

Preprint

Monte, FD & Longhi, P 2024 'Monodromies of Second Order q-difference Equations from the WKB Approximation' arXiv. https://doi.org/10.48550/arXiv.2406.00175

Barnich, G & Monte, FD 2018 'Introduction to Classical Gauge Field Theory and to Batalin-Vilkovisky Quantization'.

View all publications in research portal