"So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality.
"
Albert Einstein
Mathematics and Research
Research Interests
My current interests lie in Symplectic Geometry, the
Theory of Integrable Systems, Riemann-Hilbert Problems, Riemannian Geometry,
Harmonic Maps in Lie Groups, Algebraic Methods in Mathematical Physics, and recently,
financial mathematics.
Algebraic Computational Methods in Geometric and Physics
PDEs
In recent years, techniques from computational algebra have
become important to render effective general results in the
theory of Partial Differential Equations. My research is
following the work of D.C. Struppa, I. Sabadini, F. Colombo,
F. Sommen, etc., authors which have shown how these tools can
be used to discover and identify important properties of
several systems of interest, such as the Cauchy-Fueter, the
Mosil-Theodorescu, the Maxwell, the Proca system, as well as
the systems which naturally arise from the work of the Belgian
school of Brackx, Delanghe and Sommen. Publications:
"Algebraic Analysis of Abelian Instantons and
Singularities of the Yang-Mills Equations", in
collaboration with D.C. Struppa, I. Sabadini, F. Colombo,
and A. Vajiac, submitted to journal.
"Hartogs Phenomena and Antisyzygies for Systems of
Differential Equations", in collaboration with
D.C. Struppa, A. Damiano, and A. Vajiac, submitted to
journal.
Integrable Systems, Quantum Cohomology, Harmonic Maps into Lie Groups
Publications:
"Quantum Products and ", to appear in Houston Math Journal.
"Virasoro Actions on Harmonic Maps in Lie Groups", to appear inthe Journal of Differential Geometry.
Foundations of Geometry
I am interested mostly in the Hilbertian axiomatic approach to
Geometry. Far from being an expert in this field, I am studying
especially the constructions of Euclidean and non-Euclidean
geometries using purely geometric axioms, without using numbers,
distances, and/or continuity properties. Publications:
"The power of a point for some real algebraic curves",
(in collaboration with M. Vajiac, B. Suceava), The
Mathematical Gazette, London, March 2008.
Financial Mathematics and Operations Research
My interests lie in Publications:
" ", (in
collaboration with Jian Li Hu), submitted to journal.
