Teaching  Spring 2016:
Math 21001 Multi Variable Calculus
Math 39001: Differential Geometry of Curves and Surfaces
Research Interests:
 Complex and Hypercomplex Analysis
Complex Analysis is a classical branch of mathematics,
having its roots in late 18th and early 19th centuries,
which investigates functions of one and several complex
variables. It has applications in many branches of
mathematics, including Number Theory and Applied
Mathematics, as well as in physics, including Hydrodynamics,
Thermodynamics, Electrical Engineering, and Quantum Physics.
Clifford Analysis is the study of Dirac and Dirac type
operators in Analysis and Geometry, together with their
applications. In 3 and 4 dimensions Clifford Analysis is
referred to as Quaternionic Analysis. Furthermore, methods
and tools of Clifford Analysis are extended to the field of
Hypercomplex Analysis.
Publications:

"Holomorphy in Multicomplex Spaces",
D.C. Struppa, A. Vajiac, M.B. Vajiac,
Spectral Theory, Mathematical System Theory, Evolution
Equations, Differential and Difference Equations, Volume
221, ISBN 9783034802970, p. 617634, Springer (2012).

"Hyperbolic Numbers and their Functions",
M. Shapiro, D.C Struppa, A. Vajiac, M.B. Vajiac,
Analele Universitatii Oradea, Fasc. Matematica, Tom XIX,
Issue No. 1, p. 265283, (2012).

"The CauchyKowalewski product for bicomplex holomorphic
functions",
H. De Bie, D.C. Struppa, A. Vajiac, M.B. Vajiac,
Mathematische Nachrichten, Volume 285, Issue 10, p. 12301242, July (2012).

"Multicomplex hyperfunctions",
A. Vajiac, M.B. Vajiac,
Complex Variables and Elliptic Equations, Volume 57, Issue 78, p. 751762, (2012).

"Bicomplex hyperfunctions",
F. Colombo, I. Sabadini, D.C. Struppa, A. Vajiac, M.B. Vajiac,
Ann. Mat. Pura Appl. (4) 190, no.2, pg. 247261, (2011).

"Remarks on Holomorphicity in three settings: Complex,
Quaternionic, and Bicomplex",
D.C. Struppa, A. Vajiac, M.B. Vajiac,
Hypercomplex Analysis and Applications, Trends in Mathematics, pg. 261274,
Birkauser Verlag Basel/Switzerland (2011).
 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 CauchyFueter, the MosilTheodorescu, 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:

"Singularities of functions of one and several bicomplex variables",
F. Colombo, I. Sabadini, D.C. Struppa, A. Vajiac, M.B. Vajiac,
Arkiv for Matematik, Volume 49, Issue 2 (2011), pg. 277294.

"Hartogs Phenomena and Antisyzygies for Systems of Differential Equations",
A. Damiano, D.C. Struppa, A. Vajiac, M. Vajiac,
Journal of Geometric Analysis, Volume 19, Issue 2, p. 288300 (2009).

"Computational Algebra Techniques in Electromagnetism",
F. Colombo, I. Sabadini, D.C. Struppa, A. Vajiac, M.B. Vajiac,
Journal of Mathematical Sciences: Advances and Applications, Volume 3, No. 1, p. 7788 (2009).
 Differential Geometry, Symplectic Geometry, Integrable Sustems
Publications:

"Quantum type Products in Symplectic Geometry",
Houston Mathematics Journal, Vol. 35, No. 3, 2009

"Virasoro Actions and Harmonic Maps",
K. Uhlenbeck, M. Vajiac Journal of Differential Geometry p. 327341, Volume 8, number 2, October 2008
 "Remarks on the Curvature of Totally Umbillical Submanidfolds In Riemannian Spaces ", B. Suceava,M. Vajiac
in The Annals of the Al.I.Cuza University, Iasi, Tomul IV, 2008 f.1
 "Gauge Theory Techniques in Quantum Cohomology ",S. Rosenberg, M.Vajiac
in Advances in Algebraic Geometry Motivated by Physics
(Proceedings of the 952nd AMS Meeting Lowell, Massachusetts, April 12, 2000,
Special Session: Enumerative Geometry in Physics).
 "Gauge Theory Techniques in Quantum Cohomology",
Ph.D. Thesis,UMI Dissertation Services, Boston University (2000).
 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 nonEuclidean
geometries using purely geometric axioms, without using numbers,
distances, and/or continuity properties.
Publications:

"The power of a point for some real algebraic curves",
B. Suceava, A. Vajiac, M.B. Vajiac,
The Mathematical Gazette, London, March 2008, p. 2228 (2008).
 Mathematics Education
My interests lie in methodological aspects of introducing
research ideas and modern results in Mathematics and Physics
to undergraduate students and future teachers. My goal is to
raise scientific awareness and interest among college and
university students, and to prepare them for active
research.
Publications:

"A Polynomial Game",
B. Suceava, M. Vajiac,
Math Communicator.
Mihaela Vajiac
