Claudio Meneses

Dr. Claudio Meneses

Mathematisches Seminar
Christian-Albrechts-Universität Kiel
Ludewig-Meyn-Str. 4
D-24098 Kiel

DFG Principal Investigator

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, Mathematical Physics, and Lie Theory. My current work focuses on the study of analytic aspects in moduli theory, and more concretely, the study of natural Kähler structures of moduli spaces of  vector bundles on Riemann surfaces, and 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.

I am currently a Principal Investigator under the DFG priority programme  SPP 2026 Geometry at Infinity.

Here you may find further details on my project entitled Wall-crossing and hyperkähler geometry of moduli spaces

(during the funding period 2017-2020 I was a member of the project Asymptotic geometry of the Higgs bundle moduli space).

 

Research interests
Complex analytic geometry of moduli spaces, geometry and topology of gauge field theories, integrable systems.


Publications

10. "Thin homotopy and the holonomy approach to gauge theories. To appear in "Contributions of Mexican Mathematicians Abroad."

  arXiv

9. On a functional of Kobayashi for Higgs bundles. (with Sergio A. H. Cardona) Int. J. Geom. Methods Mod. Phys. 17 (2020) no. 13, art. no. 2050200 (16 pp.)

doi:10.1142/S021988782050200X arXiv

8. Homotopy classes of gauge fields and the lattice. (with José A. Zapata)  Adv. Theor. Math. Phys. 23 (2019) no. 8, pp. 2207–2254.

doi:10.4310/ATMP.2019.v23.n8.a7 arXiv

7. Macroscopic observables from the comparison of local reference systems. (with José A. Zapata) Class. Quantum Gravity 36 235011 (2019).

doi:10.1088/1361-6382/ab49a7 arXiv

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

doi:10.3934/jgm.2019003 arXiv

5. 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
4. 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

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

   

 

 

 

Conference proceedings and reports

2. Geometric models for moduli spaces of parabolic Higgs bundles in genus 0. Oberwolfach report, Geometry and Physics of Higgs Bundles (2019) pp. 23–25.

 doi:10.4171/OWR/2019/23
1. Geometry of effective gauge fields. (with Jorge Martínez) J. Phys. Conf. Ser. 24 no. 1 (2005) pp. 39. doi:10.1088/1742-6596/24/1/005                      

 

 

 

 

Preprints

Geometric models and variation of weights on moduli of parabolic Higgs bundles over the Riemann sphere: a case study.

arXiv

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

arXiv

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

arXiv

 

 

 

 

 

 

 

Notes

Notes on parabolic Higgs bundles.

                    

 

Ph.D. Thesis: Kähler potentials on the moduli space of stable parabolic bundles over the Riemann sphere. Stony Brook University (2013).

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).

 

 

Teaching

During the spring semester of 2018 I taught a graduate course on vector bundles on Riemann surfaces. You can find the syllabus here.