Teacher-Researcher at Université Savoie Mont Blanc – LAPTh, France.
Assist. Prof. Dr. Frank Thuillier is a distinguished researcher in mathematical physics, specializing in the topological aspects of quantum field theories. His work delves into the intricate structures of TQFTs, employing cohomological methods to explore gauge theories and manifold invariants. Through his affiliation with LAPTh and Université Savoie Mont Blanc, Dr. Thuillier contributes significantly to the theoretical understanding of topological invariants and their applications in physics.
Professional Profile
Orcid
🎓 Education
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Habilitation à Diriger des Recherches (HDR): Université Savoie Mont Blanc
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Ph.D. in Theoretical Physics: Specific details not publicly available; inferred from his extensive publication record in mathematical physics.
💼 Experience
Dr. Frank Thuillier is an Assistant Professor and researcher at the Laboratoire d’Annecy-le-Vieux de Physique Théorique (LAPTh), affiliated with the CNRS and Université Savoie Mont Blanc in France. His work lies at the intersection of mathematical physics and topology, focusing on the cohomological structures underlying topological quantum field theories (TQFTs). He has significantly contributed to the understanding of abelian gauge theories, particularly through the lens of Deligne–Beilinson cohomology. Dr. Thuillier collaborates internationally and has co-authored over 35 peer-reviewed publications.
📊 Author Metrics
🔬 Research Interests
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Topological Quantum Field Theories (TQFTs) of cohomological type
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BRST symmetry and equivariant cohomology
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Abelian knot invariants and manifold invariants via Deligne–Beilinson cohomology
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Gauge theories and topological invariants in 3-manifolds
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Functional integration in abelian Chern–Simons and BF theories
Top Noted Publications:
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“U(1)ⁿ Chern–Simons Theory: Partition Function, Reciprocity Formula, and Chern–Simons Duality”
Journal of Mathematical Physics, April 2025.
DOI: 10.1063/5.0239253
This paper extends the U(1) Chern–Simons theory to a U(1)ⁿ framework by combining Chern–Simons and BF actions with integer coupling constants. Utilizing Deligne–Beilinson cohomology, the authors compute a partition function that serves as a topological invariant of closed oriented 3-manifolds. They derive a reciprocity formula leading to a new expression of this invariant, potentially aligning with Reshetikhin–Turaev invariants, and demonstrate a duality between U(1)ⁿ Chern–Simons theories.
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“The U(1) BF Functional Measure and the Dirac Distribution on the Space of Quantum Fields”
Journal of Mathematical Physics, November 2023.
DOI: 10.1063/5.0166948
In this letter, Dr. Thuillier explores the relationship between the U(1) BF measure and the Fourier transform of a Dirac distribution defined on the ℤ-module of quantum fields. He revisits the U(1) BF partition function using this Dirac distribution and elucidates a natural connection between U(1) BF and Chern–Simons theories.
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“Gauge Fixing and Metric Independence in Topological Quantum Theories”
Modern Physics Letters A, May 2022.
DOI: 10.1142/S0217732322500882
Co-authored with Enore Guadagnini and Federico Rottoli, this paper addresses the claim that functional integration in topological gauge theories depends nontrivially on the gauge-fixing metric. The authors demonstrate that both the partition function and the mean values of gauge-invariant observables are, in fact, independent of the gauge-fixing metric.
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“3D Topological Models and Heegaard Splitting II: Pontryagin Duality and Observables”
Journal of Mathematical Physics, November 2020.
DOI: 10.1063/5.0027779
This work continues the study of smooth Deligne–Beilinson cohomology groups on closed 3-manifolds represented by Heegaard splittings. Dr. Thuillier defines Deligne–Beilinson 1-currents forming elements of the Pontryagin dual of H¹_D(M) and uses singular fields to recover partition functions of U(1) Chern–Simons and BF quantum field theories, as well as to determine the link invariants defined by these theories.
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“3D Topological Models and Heegaard Splitting I: Partition Function”
Journal of Mathematical Physics, April 2019.
DOI: 10.1063/1.5079618
In this initial study, Dr. Thuillier constructs smooth Deligne–Beilinson cohomology groups on closed 3-manifolds using Heegaard splittings and derives partition functions for U(1) Chern–Simons and BF quantum field theories from this construction.
Conclusion:
Assist. Prof. Dr. Frank Thuillier is an outstanding candidate for the Research for Best Researcher Award in Mathematical Physics. His contributions to topological quantum field theory, particularly through the lens of Deligne–Beilinson cohomology, have broadened the foundational understanding of abelian gauge theories and advanced key mathematical techniques used in modern theoretical physics.