Daniel Galviz
Daniel Galviz
Postdoctoral ResearcherÂ
Yau Mathematical Science Center
Tsinghua University
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Welcome to my homepage!
I am a postdoctoral researcher in Mathematics and Mathematical Physics at Yau Mathematical Science Center (YMSC), Tsinghua University.  Â
My primary research interests lie at the intersection of geometry, topology, and mathematical physics, with a particular focus on TQFT, Chern–Simons theory, and categorical structures in low-dimensional topology.
I am the founder and lecturer of ICTP-PWF: Physics Latam.
On this website, I provide some information about my research interests, CV, lecture notes and seminars. I hope you find it useful!
I also organize the Math & HEP Seminar series.
Education
🎓 PhD in Mathematics, 2026
Education
🎓 PhD in Mathematics, 2026
        Advisor: Nicolai Reshetikhin.
        YMSC, Tsinghua University.
🎓 MSc in Theoretical Physics, 2020
    Advisor: Ulf-G. Meißner.
        Institute of Physics, University of Bonn.
🎓 BSc in Physics, 2017
    Advisor: Adel Khoudeir.
        Faculty of Science, University of Los Andes.
Research interests
Research interests
Mathematics
Mathematical Physics
Quantum Topology
Quantum Field Theory
String Theory
LATEST
LATEST
A Functorial Theory of Defects in
Abelian Chern-Simons Theory
Daniel Galviz
We develop a nonperturbative, functorial theory of defects in Abelian Chern–Simons theory on surfaces of arbitrary genus, showing that the finite quadratic module controls not only the bulk TQFT but also its boundaries, domain walls, condensations, and defects. We also establish an Alterfold/Chern–Simons dictionary. We further show that reciprocity does not generally define a TQFT duality, contrary to recent claims in the literature. Together, these results provide an explicit, unified realization of the Abelian defect structure, bringing previously separate gauge-theoretic and categorical descriptions into a single TQFT framework.
Torus Berry Data Determine
All-Genus Abelian Topological Orders
We show that Berry data measured on a torus are enough to determine the full all-genus Abelian topological theory, including its defects. This puts a long-standing piece of folklore in Abelian topological order on rigorous footing.
Equivalence of
Toral Chern-Simons and Reshetikhin-Turaev theories
We show that toral Chern–Simons theory and its Reshetikhin–Turaev counterpart are equivalent as TQFTs. Earlier work established relations only at the level of partition functions or mapping-class-group representations; to our knowledge, this is the first explicit proof of the expected equivalence at the level of the full, nonperturbative TQFT.
Toral Chern-Simons TQFTÂ
via Geometric Quantization in Real Polarization
We construct toral Chern–Simons theory through geometric quantization and show that it leads to a well-defined nonperturbative TQFT. This provides a rigorous mathematical foundation for describing Abelian topological order on surfaces of arbitrary genus.
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