Polynomial equations and systems of equations play a fundamental role in various fields of mathematics, science, and engineering. Despite being a mathematical pursuit for centuries, comprehending the intricate solutions (known as algebraic varieties) to these systems remains one of the most profound and central areas of contemporary mathematics.
Geometry is undergoing significant progress, and its impact is being felt across all areas of mathematics. Researchers are employing techniques from geometry to solve old problems (such as Perelman's resolution of the Poincaré conjecture) and explore new directions. In particular, the study of natural equations that arise in geometry has been a crucial theme, with advanced techniques from the theory of PDEs being employed. The Atiyah-Singer index theorem, developed in the 1960s, established a connection between the theory of linear PDEs, topology, and geometry. While the development of tools for nonlinear PDEs in geometry has been slower, it has resulted in some of the most extraordinary discoveries in mathematics, including Donaldson's breakthroughs in the theory of four-manifolds using the Yang-Mills equations from high-energy physics.”
Department Members in This Field
Faculty
- Dr Anton Asare-Tuah
- Dr John Boiquaye Homological Algebra, Category Theory, Hopf Algebras,Noncommutative Geometry
- Dr Benedict Vasco Normenyo Group Theory, Field Theory
- Dr Ralph Agyei Twum Representation Theory
- Mr Abdullah Abubakar Theory of Fusion Systems, Local Group Theory, Representation Theory of Finite Groups
- Dr Eugene Yaw Adade Adjei Geometric Analysis, Differential Geometry
Graduate Students
- TBA