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Reed Math Prof Wins NSF Grant

A punctured torus being turned inside out. Topologists study these and similar vexing problems.

Prof. Kyle Ormsby [mathematics 2014–], who is set to start his tenure-track position at Reed this fall, is already bringing in the accolades. In May, Reed received a $172,146 research grant from the National Science Foundation for a project under Ormsby’s direction. The project “Structure and computations in motivic and chromatic homotopy” begins in September and continues through August 2017.

If the title leaves you scratching your head, Ormsby explains that the grant will provide support for his study of “some pieces of mathematics that lie at the intersection of topology and algebraic geometry.” Algebraic geometry, as you undoubtedly know, “narrows the focus of geometry, only studying shapes that are defined by polynomial equations.” Topology is the study of geometric properties that are unchanged by the continuous deformation of figures. For example, topologists consider doughnuts and coffee cups to belong to the same class (single-holed objects) because one could be stretched to resemble another.

“If topology’s objects are made out of saltwater taffy,” says Ormsby, “then algebraic geometry’s objects are constructed from peanut brittle—far more rigid and inflexible.”

Because of this, he says that the two fields "don’t communicate much." But recently mathematicians have found that they can apply tools and theorems from algebraic geometry to problems of homotopy (a subfield of topology) and vice versa.

According to the abstract of the project, the research will work at the intersection of these fields, using algebraic geometry and homotopy theory to inform each other.

Ormsby earned a PhD from the University of Michigan in 2010. Since then, he has been a National Science Foundation fellow and an instructor at MIT. 

More good news for math majors: part of the grant will go to fund undergrad research over the summer.

Tags: math, doughnuts,

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