Professor Adjunto A1
Departamento de Matemática
Centro de Ciências Exatas e da Natureza (CCEN)
Universidade Federal de Pernambuco (UFPE)
alan.nmuniz@ufpe.br
Research interests:
I'm a researcher in Algebraic and Complex geometries focusing on distributions and foliations, moduli of (parabolic) sheaves and tensors. Some of my topics of interest are the following:
Automorphism groups of holomorphic distributions and foliations;
Parabolic vector bundles over Riemann surfaces and moduli spaces of logarithmic connections;
Moduli spaces of holomorphic distributions and foliations;
Moduli spaces of sheaves and related topics;
Varieties of tensors and Euclidean Distance Degree;
Publications:
Appendix to "Logarithmic sheaves of complete intersections" (by Daniele Faenzi, Marcos Jardim, and Jean Vallès) to appear in Ann. SNS
Codimension one foliations on homogeneous varieties. (Daniele Faenzi and Vladimiro Benedetti) to appear in Adv. in Math. DOI:10.1016/j.aim.2023.109332
On the Moduli of Logarithmic Connections on Elliptic Curves. (with Thiago Fassarella and Frank Loray) Math. Z. 301, 4079–4118 (2022). DOI:10.1007/s00209-022-03041-4
Moduli of Distributions via Singular Schemes. (with Maurício Corrêa and Marcos Jardim) Math. Z. 301, pages 2709–2731 (2022). DOI:10.1007/s00209-022-03001-y
Codimension one distributions of degree 2 on the three-dimensional projective space. (with Marcos Jardim and Hugo Galeano) J. Pure Appl. Algebra 226, No. 2, Article ID 106840, 32 p. (2022) DOI:10.1016/j.jpaa.2021.106840
Foliations on the projective plane with finite group of symmetries. (with Rudy Rosas) Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXII (2021), 871-902. DOI: 10.2422/2036-2145.201906_011.
Polynomial bounds for automorphisms groups of foliations. (with Maurício Corrêa) Rev. Mat. Iberoam. 35 (2019), 1153-1194. DOI: 10.4171/rmi/1081
Preprints:
Rank-two reflexive sheaves on the projective space with second Chern class equal to four. (2023) (with Marcos Jardim)
On the minimal algebraic complexity of the rank-one approximation problem for general inner products. (2023) (with K. Kozhasov, Y. Qi, and L. Sodomaco)
Holomorphic foliations of degree two and arbitrary dimension. (2023) (with Maurício Corrêa)
p-Forms from Syzygies. (2022)
PhD Thesis:
Polynomial bounds for automorphism groups of foliations (under the supervision of Mauricio Corrêa at UFMG).
Presentations:
Symmetries of foliations on the projective plane. Slides
On moduli spaces of rank two logarithmic connections over an elliptic curve. Slides, Video from BRAG .
Moduli of Distributions via Singular Schemes. Slides , Video from 33CBM.
Symmetries of foliations on surfaces. Slides from DBE-Seminar 29/11/21