The study of geometry dates back to the ancient Greeks. A few hundred years ago, mathematicians realized that certain properties of geometric spaces do not depend on their precise shape but only on global characteristics. Thus, they discovered the field of topology. In the 19th century, mathematicians began to apply analysis to the study of curved spaces. The theory of non-linear PDE has led to major advances in geometry and topology in the last several decades. Another approach to the study of curved spaces involves realizing them as solution sets of polynomial equations. From this perspective, commutative algebra is the main technical tool. Topology led to the invention of homological algebra and category theory. There is a rich interplay between geometry and topology on the one hand, and the theory of discrete groups, Lie groups and representation theory on the other. Since the 1980's, ideas from high-energy physics have led to striking developments in geometry and topology. Geometry and topology also play an important role in applied mathematics and material science.
Faculty members in Geometry & Topology:
- Karim Adiprasito: Relations between combinatorics, algebra, topology and geometry.
- Emmanuel Dror Farjoun (emeritus): Homotopy theory, Algebraic topology.
- Raz Kupferman: Analysis, geometry and their applications in physics and material science; variational calculus; numerical analysis.
- Ruth Lawrence-Naimark: Quantum Topology, Knot Theory, Quantum Groups, DGLAs.
- Dan Mangoubi: Spectral Geometry, Geometry of Eigenfunctions, Harmonic functions - continuous and discrete, Analysis & PDEs.
- Chloe Perin: Geometric group theory.
- Tomer Schlank: Arithmetic geometry, Algebraic topology.
- Zlil Sela: Low dimensional topology, Group theory.
- Jake Solomon: Differential geometry, Symplectic geometry and related aspects of physics.
- Michael Temkin: Non-archimedean geometry, Birational geometry, Resolution of singularities.