Jonathan Kress

Associate Professor Jonathan Kress serves as Associate Director of Science in the School of Mathematics & Statistics at the University of New South Wales (UNSW). His academic profile highlights expertise in Mathematical Physics with a specialized focus on Superintegrable Systems.

His research interests encompass:

• Mathematical Physics
• Superintegrable Systems
• Differential Geometry
• Quantum Mechanics
• Algebraic Geometry

Professor Kress's scholarly work demonstrates a consistent trajectory of advancing theoretical frameworks for understanding superintegrable systems. His recent publications reveal a sophisticated integration of algebraic geometry with differential geometry to develop classification schemes for superintegrable systems in arbitrary dimensions. His research particularly emphasizes conformal properties, separation of variables, and quantum mechanical applications of these highly symmetric systems.

Notable contributions include:

• Co-authoring the seminal book "Separation Variables Superintegrability" (2018) with Kalnins and Miller
• Developing algebraic conditions for conformal superintegrability across dimensions
• Establishing geometric foundations for classifying second-order superintegrable systems

Professor Kress maintains productive long-term collaborations, particularly with E.G. Kalnins and W. Miller, as evidenced by their co-authorship spanning over two decades. His work bridges pure mathematics with theoretical physics applications, appearing in prestigious journals including Communications in Mathematical Physics, Journal of Geometric Analysis, and Journal of Physics A: Mathematical and Theoretical. His research continues to shape the theoretical understanding of symmetry properties in physical systems.