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.

Current Teaching
Research Papers
  1. An elliptic equation with power nonlinearity and degenerate coercivity. Under peer review (Journal of Differential Equations)
  2. An inhomogeneous p-laplacian equation with a Hardy potential. Under peer review (Advanced Nonlinear Studies)
  3. Quasilinear elliptic equations with superlinear convection. Under peer review (Calculus of Variations and Partial Differential Equations)
  4. On a fully nonlinear k-Hessian system of Lane-Emden type. Under peer review (Potential Analysis)
  5. Radially symmetric solutions to a Lane-Emden type system. Under peer review (Nonlinear Analysis)
  6. Lyapunov exponents for G2 variations of Hodge structures. Preprint
  7. The Complexity of Higher Chow Groups, Canadian Math. Bull. , 2023, DOI: 10.4153/S0008439522000509
    with James Lewis
  8. The Chow motive of a Fano variety of k-planes, Communications in Algebra , 2023, DOI: 10.1080/00927872.2023.2252078
    with James Lewis
  9. Known cases of the Hodge conjecture (arXiv)
  10. On the topology of Fano smoothings Interactions with Lattice Polytopes, Springer, 2022, DOI: 978-3-030-98327-7
    with Tom Coates and Alessio Corti
  11. On the monodromy of elliptic surfaces, Israel Journal of Mathematics, 2022, DOI: s11856-022-2458-4
  12. Notes on the Hodge Conjecture for Fermat Varieties, Experimental Results , Volume 2 , 2021 , e22, DOI: 10.1017/exp.2021.14
  13. On the arithmetic of Landau-Ginzburg model of a certain class of threefolds, CNTP Vol. 13, No. 1, 2019, DOI: 10.4310/cntp.2019.v13.n1.a5
  14. Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution,
    Canad. J. Math. 68, 2014, DOI: 10.4153/CJM-2015-020-4
    with Matt Kerr and Greg Pearstein
Books
  1. Real Analysis: Functions of a real variable. (In talks with Springer UTM)
Notes
Selected Past Teaching
Talks
Computer Code
A rank of my 10 favorite textbooks

With respect to the didatics (how easy it is to follow) of the author not the content of the book.

  1. Riemannian Geometry, M. do Carmo
  2. Differential Geometry of Curves and Surfaces, M. do Carmo
  3. Introduction to Real Analysis, E. Lages Lima
  4. Principles of Algebraic Geometry, P. Griffiths
  5. Algebraic Geometry, R. Hartshorne
  6. Fourier Analysis, E. Stein
  7. Complex Analysis, L. Ahlfors
  8. Partial Differential Equations, L. Evans
  9. Abstract Algebra, D. Dummit