• Research Group Geometry

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

4. Linear phase space deformations with angular momentum symmetry. To appear in the Journal of Geometric Mechanics.

3. 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

2. Remarks on groups of bundle automorphisms over the Riemann sphere. Geom. Dedicata (2017) pp. 1–28. DOI: 10.1007/s10711-017-0309-y

1. On vector-valued Poincaré series of weight 2. J. Geom. Phys. (2017) pp. 317–329. DOI: 10.1016/j.geomphys.2017.06.004

Preprints

On a functional of Kobayashi for Higgs bundles. (with Sergio A. H. Cardona)

Optimum weight chamber examples of moduli spaces of stable parabolic bundles in genus 0.

Homotopy classes of gauge fields and the lattice. (with José A. Zapata)

Singular connections, WZNW action, and moduli of parabolic bundles on the sphere. (with Leon A. Takhtajan)

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:

3. Differentiation matrices for meromorphic functions. (with Rafael G. Campos) Bol. Soc. Mat. Mexicana (3) 12, no. 1, (2006) 121-131.

2. Geometry of effective gauge fields. (with Jorge Martínez) J. Phys. Conf. Ser. 24 (2005), no. 1, p. 39.

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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Teaching

During the spring semester I will be teaching a graduate course on vector bundles on Riemann surfaces. You can find the syllabus here.