# Geometry

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