Claudio Meneses

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

4. Linear phase space deformations with angular momentum symmetry. J. Geom. Mech. 11 no. 1 (2019) 45–58.

DOI:10.3934/jgm.2019003 arXiv

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

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

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:

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

  arXiv

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

arXiv

 

 


 

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.