Guglielmo Fucci
Professor of Mathematics · East Carolina University

Guglielmo Fucci

My research focuses on mathematical physics, with particular emphasis on spectral theory and Sturm–Liouville theory, including the analysis of spectral functions and their applications to geometric analysis on manifolds, spectral geometry, quantum field theory, and quantum gravity.

Director of Undergraduate Studies, Department of Mathematics

Research
Interests

My work focuses on spectral functions and their applications across several areas of mathematical physics and analysis.

The interdisciplinary nature of these problems brings my research into contact with partial differential equations, complex analysis, special functions, and asymptotic analysis.

Spectral Theory

Spectral zeta functions, functional determinants, Sturm–Liouville operators, and spectral asymptotics.

Geometric Analysis

Spectral geometry, heat kernels, Laplace-type operators, and analysis on manifolds.

Quantum Field Theory

Casimir problems, one-loop effects, quantum fields in curved settings, and related models.

Special Functions & Asymptotics

Complex analytic and asymptotic methods arising in spectral and geometric problems.

Publications

Refereed publications in reverse chronological order.

G. Fucci and J. Stanfill, The spectral ζ-function of Sturm–Liouville operators with N generalized point potentials, arXiv:2609.19322.
1.G. Fucci, M. Piorkowski, and J. Stanfill, Complex analytic theory of Sturm-Liouville operators with Schatten p-class resolvents, arXiv:2604.10115.
2.G. Fucci, M. Piorkowski, and J. Stanfill, ζ-function via contour integrals and universal sum rules, arXiv:2508.15699.
3.G. Fucci and J. Stanfill, The exotic structure of the spectral ζ-function for the Schrödinger equation with Pöschl–Teller potential, Annales Henri Poincaré (2025), online first.
4.G. Fucci, M. Piorkowski, and J. Stanfill, The spectral ζ-function for quasi-regular Sturm–Liouville operators, Letters in Mathematical Physics 115, 8 (2025).
5.G. Fucci and C. Romaniega, Vacuum energy of scalar fields on spherical shells with general matching conditions, Journal of Physics A: Mathematical and Theoretical 57, 095401 (2024).
6.G. Fucci and C. Romaniega, Casimir energy for spinor fields with δ-shell potentials, Journal of Physics A: Mathematical and Theoretical 56, 265201 (2023).
7.G. Fucci, F. Gesztesy, K. Kirsten, L. L. Littlejohn, R. Nichols and J. Stanfill, The Krein-von Neumann extension revisited, Applicable Analysis 101, No. 5, 1593 (2022).
8.A. Flachi and G. Fucci, One-loop effective action of the CP^{N−1} model at large μβ, Physics Letters B 821, 136627 (2021).
9.G. Fucci, F. Gesztesy, K. Kirsten and J. Stanfill, Spectral zeta-Functions and zeta-Regularized Functional Determinants for Regular Sturm-Liouville Operators, Results in the Mathematical Sciences 8, No. 61 (2021).
10.G. Fucci, K. Kirsten and J. M. Muñoz-Castañeda, Casimir pistons with generalized boundary conditions: a step forward, Analysis and Mathematical Physics 11, 70 (2021).
11.A. Flachi, G. Fucci, M. Nitta, S. Takada and R. Yoshii, Ground state modulations in the CP^{N−1} model, Physical Review D 100, 085006 (2019).
12.G. Fucci, Asymptotic Expansion of the Heat Kernel Trace of Laplacians with Polynomial Potentials, Letters in Mathematical Physics 108, 2453 (2018).
13.G. Fucci, Vacuum Instability in Kaluza-Klein Manifolds, Journal of Physics A: Mathematical and Theoretical 51, 215202 (2018).
14.G. Fucci and K. Kirsten, Some New Results for the One-loop Mass Correction to the Compactified λϕ^4 Theory, Journal of Mathematical Physics 59, 033503 (2018).
15.G. Fucci, The Casimir Effect for Pistons with Transmittal Boundary Conditions, International Journal of Modern Physics A 32, 1750182 (2017).
16.G. Fucci and K. Kirsten, Functional determinants and Casimir energy in higher dimensional spherically symmetric background potentials, Journal of Physics A: Mathematical and Theoretical 49, 275203 (2016).
17.G. Fucci, The Casimir Effect for Thick Pistons, International Journal of Modern Physics A 31, 1650012 (2016).
18.G. Fucci and K. Kirsten, Expansion of Infinite Series Containing Modified Bessel Functions of the Second Kind, Journal of Physics A: Mathematical and Theoretical 48, 435203 (2015).
19.G. Fucci, Casimir Pistons with General Boundary Conditions, Nuclear Physics B 891, 676–699 (2015).
20.G. Fucci, C. Graham, and K. Kirsten, Spectral Functions for Regular Sturm-Liouville Problems, Journal of Mathematical Physics 56, 043503 (2015).
21.G. Fucci and K. Kirsten, Analytic Continuation of the Doubly-periodic Barnes Zeta Function, Applied Mathematics and Computation 221, 598 (2013).
22.M. Beauregard, G. Fucci, K. Kirsten and P. Morales, Casimir Effect in the Presence of External Fields, Journal of Physics A: Mathematical and Theoretical 46, 115401 (2013).
23.G. Fucci and K. Kirsten, The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the Type I ×_f N, Communications in Mathematical Physics 317, 635–665 (2013).
24.G. Esposito, G. Fucci, A. Y. Kamenshchik and K. Kirsten, Spectral Methods in Quantum Field Theory and Quantum Cosmology, Journal of Physics A: Mathematical and Theoretical 45, 374004 (2012).
25.G. Fucci and K. Kirsten, The Casimir Effect for Generalized Piston Geometries, International Journal of Modern Physics A 27, 1260008 (2012).
26.G. Fucci and K. Kirsten, Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension, Communications in Mathematical Physics 314, 483–507 (2012).
27.G. Fucci, On the Hurwitz Zeta Function of Imaginary Second Argument, Journal of Mathematical Physics 52, 113501 (2011).
28.G. Fucci and K. Kirsten, Bose-Einstein Condensation on Product Manifolds, Journal of Physics A: Mathematical and Theoretical 44, 332002 (2011).
29.G. Fucci and K. Kirsten, Conical Casimir Pistons with Hybrid Boundary Conditions, Journal of Physics A: Mathematical and Theoretical 44, 295403 (2011).
30.G. Fucci and K. Kirsten, The Casimir Effect for Conical Pistons, Journal of High Energy Physics 03, 016 (2011).
31.A. Flachi and G. Fucci, Zeta Determinant for Laplace Operators on Riemann Caps, Journal of Mathematical Physics 52, 023503 (2011).
32.G. Fucci, K. Kirsten and P. Morales, Pistons modelled by Potentials, in Cosmology, Quantum Vacuum, and Zeta Functions, Springer-Verlag (2011), p. 313.
33.G. Fucci and K. Kirsten, Small Mass Expansion of Functional Determinants on the Generalized Cone, Journal of Physics A: Mathematical and Theoretical 43, 365204 (2010).
34.G. Fucci and I. G. Avramidi, On the Gravitationally Induced Schwinger Mechanism, in Quantum Field Theory under the Influence of External Conditions (QFEXT09), World Scientific (2010), pp. 485–491.
35.G. Fucci, Non-Perturbative One-Loop Effective Action for Electrodynamics in Curved Spacetime, Journal of Mathematical Physics 50, 102301 (2009).
36.I. G. Avramidi and G. Fucci, Low-Energy Effective Action in Non-Perturbative Electrodynamics in Curved Spacetime, Journal of Mathematical Physics 50, 102302 (2009).
37.I. G. Avramidi and G. Fucci, A Model for the Pioneer Anomaly, Canadian Journal of Physics 87, 1089–1093 (2009).
38.I. G. Avramidi and G. Fucci, Non-perturbative Heat Kernel Asymptotics on Homogeneous Abelian Bundles, Communications in Mathematical Physics 291, 543–577 (2009).
39.G. Fucci and I. G. Avramidi, Non-commutative Corrections in Spectral Matrix Gravity, Classical and Quantum Gravity 26, 045019 (2009).
40.I. G. Avramidi and G. Fucci, Kinematics in Matrix Gravity, General Relativity and Gravitation 41, 1407–1435 (2009).
41.G. Fucci, B. Wang and P. Singh, Asymptotic Behavior of the Newton-Boussinesq Equation in a Two-Dimensional Channel, Nonlinear Analysis: Theory, Methods and Applications 70, 2000–2013 (2009).
42.G. Fucci and I. G. Avramidi, Noncommutative Einstein Equations, Classical and Quantum Gravity 25, 025005 (2008).
43.G. Esposito, G. Fucci, A. Y. Kamenshchik and K. Kirsten, New Developments in the Spectral Asymptotics of Quantum Gravity, Journal of Physics A: Mathematical and General 39, 6317–6322 (2006).
44.G. Esposito, G. Fucci, A. Y. Kamenshchik and K. Kirsten, A New Spectral Cancellation in Quantum Gravity, in Analysis, Geometry and Topology of Elliptic Operators, World Scientific (2006), pp. 467–492.
45.G. Esposito, G. Fucci, A. Y. Kamenshchik and K. Kirsten, A Non-Singular One-Loop Wave Function of the Universe from a New Eigenvalue Asymptotics in Quantum Gravity, Journal of High Energy Physics 09, 063 (2005).
46.G. Esposito, G. Fucci, A. Y. Kamenshchik and K. Kirsten, Spectral Asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions, Classical and Quantum Gravity 22, 957–974 (2005).

Contact

Department of Mathematics
East Carolina University
331 Austin Building
East Fifth Street
Greenville, NC 27858-4353
Phone: (252) 328-1885
Email: fuccig@ecu.edu