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Geometry is concerned with the shape, size, and orientation of objects in space, and indeed such properties of space itself. The particular objects studied and the tools used in investigating their properties create subfields of geometry, such as algebraic geometry (which generally uses tools from algebra to study objects called algebraic varieties that are solution sets to algebraic equations) and differential geometry (which generally uses tools from analysis to study objects called manifolds that generalize Euclidean space). Another example is analytic geometry (which generalizes algebraic geometry by considering spaces and maps defined locally by analytic functions). Other subfields of geometry represented in our Department include discrete geometry (which studies combinatorial properties of finite or discrete objects) and symplectic geometry (which studies objects with structure generalizing that of the phase space of certain dynamical systems).

Algebraic Geometry
Anthony Iarrobino
Alina Marian
Alex Suciu
Ana-Maria Castravet
Emanuele Macri

Differential Geometry
Chris Beasley
Maxim Braverman
Robert McOwen
Peter Topalov

Singularities in Analytic Geometry
Terence Gaffney
David Massey

Discrete/Combinatorial Geometry
Egon Schulte

Symplectic Geometry
Jonathan Weitsman