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Department of Mathematics

Analysis and geometry

Analysis and geometry are two of the core areas of mathematics. Modern research is fundamental to the structures of mathematical physics.

Analysis and geometry are two of the oldest and richest areas of mathematics, with many intersections and interactions with other disciplines and with each other. Roughly speaking analysis describes functions and their properties such as differentiability, while geometry studies abstractions of spatial structures. These come together in topics such as differential geometry.

Despite its ancient antecedents, analysis and geometry continue to develop in modern directions, partly driven by theories in mathematical physics. Special structures such as symplectic geometry lead to novel differential operators.

Current research areas include:

  • Berezinians
  • Geometry of differential operators
  • Homotopy algebras
  • Poisson brackets
  • Quantization and quantum groups
  • Supermanifolds
  • Symplectic structures

More information about our research, and some papers, can be found by browsing the webpages of the staff members. Potential PhD students may email staff directly to discuss possible projects.