Professor Gerd Schmalz

Professor , Mathematics - Academic Board; School of Science and Technology

Phone: +61 2 6773 3182

Biography

Gerd Schmalz is a Professor of Mathematics. His research interest is in CR geometry, which is an interdisciplinary field that uses methods from Several complex variables, Differential geometry, Lie group theory and Differential equations. Applications of recent results include General relativity. Gerd has previously worked at Karl-Weierstrass-Institute, Bonn University, University of California at San Diego, Max-Planck-Institute for Mathematics and since 2005 for UNE. He was the Leading Chief Investigator of an ARC grant on “Symmetries in Real and Complex Geometry”. His research network includes colleagues from Australia, Italy, South Korea, Czech Republic, Russia and New Zealand. He has published more than 50 research papers and has been regularly invited to deliver talks at international conferences.

Qualifications

MA (Diploma, Moscow State), PhD (Acad Sci (GDR), Berlin), Habilitation (Bonn University)

Teaching Areas

I have been teaching units at all levels in various fields of pure and applied mathematics at Bonn University, the University of California at San Diego, and at UNE. Currently I am teaching MTHS120, MTHS130 and PMTH339.

Primary Research Area/s

Mathematics; Complex Analysis; Geometry

Research Interests

My research focuses on Complex Analysis and Geometry with applications in mathematical physics. I enjoy collaboration with my students and colleagues from various countries. I have published more than 50 research articles, cited 233 times by 87 authors. I have received various grants and scholarships, including an ARC discovery grant with V. Ejov (Flinders), G. Cairns (LaTrobe), Y. Nikolayevsky (LaTrobe) and D. Alekseevsky (Russia) in 2013-2018 and scholarships at the Max-Planck-Institute Bonn.

Currently I am working on constructions of higher-dimensional space times related to Sasakian manifolds.

Publications

Selected publications

Sykes, D.; Schmalz, G.; Ezhov, V. V.; The moduli space of spherical rigid hypersurfaces in ℂ². Izv. Ross. Akad. Nauk Ser. Mat. 85 (2021), no. 3, 191–202.

Alekseevsky, Dmitri V.; Ganji, Masoud; Schmalz, Gerd; Spiro, Andrea: Lorentzian manifolds with shearfree congruences and Kähler-Sasaki geometry. Differential Geom. Appl. 75 (2021), Paper No. 101724, 32 pp.

Medvedev, Alexandr; Schmalz, Gerd; Ezhov, Vladimir; On the classification of homogeneous affine tube domains with large automorphism groups in arbitrary dimensions. Adv. Math. 364 (2020)

Schmalz, Gerd; Ganji, Masoud: A criterion for local embeddability of three-dimensional CR structures. Ann. Mat. Pura Appl. (4) 198 (2019), no. 2, 491–503.

Ezhov, Vladimir; Kolář, Martin; Schmalz, Gerd: Rigid embeddings of Sasakian hyperquadrics in ℂⁿ⁺¹. J. Geom. Anal. 28 (2018), no. 3, 2185–2205.

Ottazzi, Alessandro; Schmalz, Gerd: Normal forms of para-CR hypersurfaces. Differential Geom. Appl. 52 (2017), 78–93.

Joo, Jae-Cheon; Kim, Kang-Tae; Schmalz, Gerd: On the generalization of Forelli's theorem. Math. Ann. 365 (2016), no. 3-4, 1187–1200.

Ezhov, Vladimir; Schmalz, Gerd: Explicit description of spherical rigid hypersurfaces in ℂ². Complex Anal. Synerg. 1 (2015), no. 1, Paper No. 2, 10 pp.

de Hoog, Frank; Schmalz, Gerd; Gureyev, Timur E.: An uncertainty inequality. Appl. Math. Lett. 38 (2014), 84–86. 94A15 (26D15 94A08)

V. Beloshapka, V. Ejov and G. Schmalz, Canonical Cartan connection and holomorphic invariants on Engel CR manifolds, Russian Journal of Mathematical Physics, 14, n. 2, 2007.

V. Ezhov and G. Schmalz, Non-linearizable CR-automorphisms, torsion-free elliptic CR-manifolds and second order ODE, J. Reine Angew. Math., 584, pp. 215-236, 2005.

Memberships

Australian Mathematical Society

American Mathematical Society

Deutsche Mathematiker-Vereinigung