Combinatorial geometry investigates the arrangement and interaction of discrete geometric objects, such as points, lines and higher-dimensional shapes, and quantifies their combinatorial properties.

The geometry of finite classical polar spaces arises from vector spaces over finite fields equipped with nondegenerate reflexive sesquilinear or quadratic forms. Points correspond to one-dimensional ...

The universe’s geometry determines whether the cosmos is spatially finite or infinite. The geometry could be flat, open (meaning negatively curved), or closed (meaning positively curved). In two ...

Discrete mathematics is the study of finite or countable discrete structures; it spans such topics as graph theory, coding theory, design theory, and enumeration. The faculty at Michigan Tech ...

It has been an exhilarating year in combinatorics research. In early 2023, mathematicians were stunned when two of the biggest problems in the field were solved in as many months. Now, a third major ...