Genival
da Silva.

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

I'm interested in nonlinear elliptic PDEs and elliptic systems, problems related to existence and regularity of solutions.

Hodge theory & Complex Algebraic Geometry

I'm interested in Algebraic cyles and its connections. Topics include cycle class maps, Hodge-D and Hodge conjectures, higher Chow groups, real regulators and related topics.

Research Papers
  1. On an elliptic system with singular nonlinearity. Under peer review
  2. An elliptic equation with power nonlinearity and degenerate coercivity. Under peer review
  3. An inhomogeneous p-laplacian equation with a Hardy potential. Under peer review
  4. Quasilinear elliptic equations with superlinear convection. Under peer review
  5. Radially symmetric solutions to a Lane-Emden type system. Under peer review
  6. On a fully nonlinear k-Hessian system of Lane-Emden type. Preprint
  7. Lyapunov exponents for G2 variations of Hodge structures. Preprint
  8. The Complexity of Higher Chow Groups, Canadian Math. Bull. , 2023, DOI: 10.4153/S0008439522000509
    with James Lewis
  9. The Chow motive of a Fano variety of k-planes, Communications in Algebra , 2023, DOI: 10.1080/00927872.2023.2252078
    with James Lewis
  10. Known cases of the Hodge conjecture (expository) arXiv
  11. On the topology of Fano smoothings Interactions with Lattice Polytopes, Springer, 2022, DOI: 978-3-030-98327-7
    with Tom Coates and Alessio Corti
  12. On the monodromy of elliptic surfaces, Israel Journal of Mathematics, 2022, DOI: s11856-022-2458-4
  13. Notes on the Hodge Conjecture for Fermat Varieties, Experimental Results , Volume 2 , 2021 , e22, DOI: 10.1017/exp.2021.14
  14. 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
  15. 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/Class notes
  1. Real Analysis: Functions of a real variable.
Teaching
Expository