Genival Francisco Fernandes
da Silva Jr.

Assistant Professor of Mathematics
Texas A&M University - San Antonio
Department of Mathematics
Classroom Hall, Room 314 U
Email: gdasilva@tamusa.edu
I completed my PhD in Mathematics at Washington University in St. Louis under direction of Prof. Matt Kerr, after that I was a postdoc at Imperial College London under supervision of Prof. Tom Coates and Prof. Alessio Corti.
Research Interests
Analysis of PDE

My research interests lie in nonlinear elliptic partial differential equations and elliptic systems, with a particular focus on the existence and regularity of solutions, approached through both variational and non-variational methods.

Below is a list of research subtopics I frequently consider:

I maintain a list of open question that come up during my research here: Open problems in Elliptic PDEs.

Research Papers
  1. Quasilinear elliptic equations with superlinear convection.
    Journal of Mathematical Analysis and Applications, 2025, DOI: 10.1016/j.jmaa.2025.130005
  2. An elliptic equation with power nonlinearity and degenerate coercivity.
    Journal of Elliptic and Parabolic Equations, 2025, DOI: 10.1007/s41808-025-00341-8
  3. On an elliptic system with singular nonlinearity.
    European Journal of Mathematics, 2025, DOI: 10.1007/s40879-025-00840-x
  4. A nonlinear problem related to optimal insulation.
    Under peer review - 2025
  5. A New proof of the p'-conjecture in the plane via a priori estimates.
    Under peer review - 2025
  6. Quasilinear Hardy-Hénon equation with power source.
    Under peer review - 2025
  7. An inhomogeneous p-laplacian equation with a Hardy potential.
    Under peer review - 2024
  8. Radially symmetric solutions to a Lane-Emden type system.
    Under peer review 2024
  9. Continuous weak solutions to the Ideal Hall equation
    Preprint - 2023
  10. The Complexity of Higher Chow Groups
    Canadian Math. Bull. , 2023, DOI: 10.4153/S0008439522000509
    with James Lewis
  11. On the Hodge conjecture for complete intersections
    Communications in Algebra , 2023, DOI: 10.1080/00927872.2023.2252078
    with James Lewis
  12. Known cases of the Hodge conjecture (expository)
    arXiv
  13. On the topology of Fano smoothings
    Interactions with Lattice Polytopes, Springer, 2022, DOI: 978-3-030-98327-7
    with Tom Coates and Alessio Corti
  14. On the monodromy of elliptic surfaces
    Israel Journal of Mathematics, 2022, DOI: s11856-022-2458-4
  15. Notes on the Hodge Conjecture for Fermat Varieties
    Experimental Results , Volume 2 , 2021 , e22, DOI: 10.1017/exp.2021.14
  16. On the arithmetic of Landau-Ginzburg model of a certain class of threefolds
    Communications in Number Theory and Physics 13, No. 1, 2019, DOI: 10.4310/cntp.2019.v13.n1.a5
  17. Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution,
    Canadian Journal of Mathematics 68, 2014, DOI: 10.4153/CJM-2015-020-4
    with Matt Kerr and Greg Pearstein
Books
Teaching
Expository