Genival F. F. 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

I'm interested in nonlinear elliptic problems, in particular, variational equations and topics 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 a fully nonlinear k-Hessian system of Lane-Emden type. Preprint 2024
  2. Radially symmetric solutions to a Lane-Emden type system. Preprint 2024
  3. The Complexity of Higher Chow Groups, Canadian Math. Bull. , 2023, DOI: 10.4153/S0008439522000509
    with James Lewis
  4. The Chow motive of a Fano variety of k-planes, Communications in Algebra , 2023, DOI: 10.1080/00927872.2023.2252078
    with James Lewis
  5. Lyapunov exponents for G2 variations of Hodge structures. Preprint
  6. The Hodge-D conjecture for a product of elliptic curves. Preprint
    with James Lewis, Karim Mansour and Alex Ghitza
  7. On the topology of Fano smoothings Interactions with Lattice Polytopes, Springer, 2022, DOI: 978-3-030-98327-7
    with Tom Coates and Alessio Corti
  8. On the monodromy of elliptic surfaces, Israel Journal of Mathematics, 2022, DOI: s11856-022-2458-4
  9. Notes on the Hodge Conjecture for Fermat Varieties, Experimental Results , Volume 2 , 2021 , e22, DOI: 10.1017/exp.2021.14
  10. 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
  11. 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
Expository Papers
  1. The classical Dirichlet problem
  2. Known cases of the Hodge conjecture
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