Dr. Claudio Meneses
Mathematisches Seminar
Christian-Albrechts-Universität Kiel
Ludewig-Meyn-Str. 4
D-24098 Kiel
Postdoctoral Fellow
meneses (at) math.uni-kiel.de
Phone: ++49-(0)431-880-4583
Room 412a
Office Hours: by appointment
Welcome to my website. I am a mathematician interested in interactions between Complex and Symplectic Geometry, and Mathematical Physics. My current work focuses on the study of the natural Kähler structures of moduli spaces of vector bundles on Riemann surfaces, and on the way they may be reconstructed in terms of families of field theories. I am keen to explore any situation where these areas may benefit from tools and techniques of the others.
Research interests
Complex analytic geometry of moduli spaces, geometry and topology of gauge field theories, integrable systems.
Publications
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4. Linear phase space deformations with angular momentum symmetry. J. Geom. Mech. 11 no. 1 (2019) 45–58. |
DOI:10.3934/jgm.2019003 | arXiv |
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3. Remarks on groups of bundle automorphisms over the Riemann sphere. Geom. Dedicata 196 no. 1 (2018) pp. 63–90. |
DOI:10.1007/s10711-017-0309-y | arXiv |
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2. On Shimura's isomorphism and (Γ,G)-bundles on the upper-half plane. Contemp. Math. 709 (2018) pp. 101–113. |
DOI:10.1090/conm/709/14295 | arXiv |
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1. On vector-valued Poincaré series of weight 2. J. Geom. Phys. 120C (2017) pp. 317–329 |
DOI:10.1016/j.geomphys.2017.06.004 | arXiv |
Preprints
| On a functional of Kobayashi for Higgs bundles (with Sergio A. H. Cardona) | arXiv |
| Optimum weight chamber examples of moduli spaces of stable parabolic bundles in genus 0. | arXiv |
| Homotopy classes of gauge fields and the lattice (with José A. Zapata) | arXiv |
| Logarithmic connections, WZNW action, and moduli of parabolic bundles on the sphere (with Leon A. Takhtajan) | arXiv |
Ph.D. Thesis: Kähler potentials on the moduli space of stable parabolic bundles over the Riemann sphere. Stony Brook University (2013).
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Predoctoral:
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3. Differentiation matrices for meromorphic functions. (with Rafael G. Campos) Bol. Soc. Mat. Mexicana (3) 12, no. 1, (2006) 121-131. |
arXiv | |
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2. Geometry of effective gauge fields. (with Jorge Martínez) J. Phys. Conf. Ser. 24 (2005), no. 1, p. 39. |
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1. Geometry of C-flat connections, coarse graining and the continuum limit. (with Jorge Martínez and José A. Zapata) J. Math. Phys. 46 (2005), no. 10, 102301, 18 pp. |
DOI:10.1063/1.2037527 |
Master's thesis: Deformations of Poisson algebras. (in Spanish) UNAM, Mexico (2007).
Bachelor's thesis: Geometry of simplicial and C-flat connections. (in Spanish) UMSNH, Mexico (2005).
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Notes
Notes on parabolic Higgs bundles.
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Teaching
During the spring semester of 2018 I taught a graduate course on vector bundles on Riemann surfaces. You can find the syllabus here.