Dr. Mihaela Vajiac
Program Director for Mathematics
- Scholarly Works:
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Digital Commons
- Education:
- University of Bucharest, Bachelor of Science
Boston University, Ph.D.
Biography
Dr. Mihaeila Vajiac is the Director of the Center of Excellence in Complex and Hypercomplex Analysis (CHECHA). She is also the organizer of the Math/Physics/Computation Seminar at Chapman, and one of the organizers of the Special Session on Geometric Methods in Hypercomplex Analysis at the AMS Fall Western Sectional Meeting in late 2018.
Some of her research interests include:
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.
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.
Differential Geometry, Symplectic Geometry, Integrable Sustems
Learn more about each of these on her website.
Recent Creative, Scholarly Work and Publications
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D. Alpay, I. Lewkowicz and M. Vajiac. Discrete Wiener algebra in the bicomplex setting, spectral factorization with symmetry, and superoscillations. Analysis and Mathematical Physics,13, No. 3, Paper No. 54, 32 p. (2023).
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D. Alpay, I. Lewkowicz and M. Vajiac. Interpolation with symmetry and a Herglotz Theorem in the bicomplex setting. Journal of Mathematical Analysis and Applications, vol. 524 (2023), no. 2, Paper No. 127201
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D. Alpay, K. Diki and M. Vajiac: A note on the complex and bicomplex neural networks. Applied Mathematics and Computation, vol. 445 (2023) Paper No. 127864, 12pp.
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D. Alpay, K. Diki and M. Vajiac: An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications. Mathematische Nachrichten
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A note on the complex and bicomplex valued neural networks with D. Alpay and K.Diki in Applied Mathematics and Computation 445, 127864
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Ternary Complex Analysis and Applications, Vajiac, M.B., in "New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative", Birkhauser 2021
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The infinity is the chasm in which our thoughts are lost: Reflections on Sophie Germain's Essay, A. Glesser, A., Suceava, B., Vajiac, M.B., in Memoirs of the Scientific Sections of the Romanian Academy AND in The Best Writing on Mathematics 2021
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"Differential Geometry and Global Analysis: in honor of Tadashi Nagano" Publisher: Contemporary Mathematics, volume 777, American Mathematical Society ISBN: 978-147-04-6015-0 Editors: Chen, B.Y., Brubaker, N., Sakai, T., Suceava, B.D., Tanaka, M.S., Tamaru, H., Vajiac, M.B.
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"New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative", Birkhauser 2021. Editors: D. Alpay, R. Peretz, D. Shoikhet, and M.B. Vajiac
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Ternary Clifford Algebras, Cerejeiras, P., Vajiac, M.B., Advances in Applied Clifford Algebras 31(1) , 1-18
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Birkhauser: Linear Systems and Operator Theory: Linear Systems, Signal Processing and Hypercomplex Analysis, Editors: Alpay, D., Vajiac, M.B.
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Estimates of B.-Y. Chen's \delta^\hat-Invariant in Terms of Casorati Curvature and Mean Curvature for Convex Euclidean Hypersurfaces, Suceava, B., Vajiac, M., in International Electronic Journal of Geometry, vol.12, No. 1 (2019)
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A primer on Script Geometry, Cerejeiras, P., Kaehler, U., Mertens, T., Sommen, F., Vajiac, A., Vajiac, M, arxiv.org/abs/1911.07102.
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Gleason's Problem Associated to a Real Ternary Algebra and Applications, D. Alpay, A. Vajiac, M.B. Vajiac, in Adv. Appl. Clifford Algebras (2018) 28: 43
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Norms and Moduli on Multicomplex Spaces, M.B. Vajiac, in Clifford Analysis and Related Topics, In Honor of Paul A. M. Dirac, CART 2014, Tallahassee, Florida, Springer, 2018