Mathematics
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Will Feldman - Math Theory Meets Physical Intuition
Will Feldman, Assistant
modeling assumptions used to derive the equations.
“I like to work out these kinds of questions because
Other times, they explain the behavior of all the solutions
I get to use both physical intuition and theoretical
of the equation without relying on special formulae.
mathematical tools,” he said.
of Mathematics in 2020.
“And sometimes, the results are used to justify numerical
He studies mathematical
computations, which are meant to approximate solutions
an undergraduate, he thought he wanted to study physics
models of physics and
of these equations,” he said.
or history. He started taking math classes because math
was useful in studying advanced physics. “I had a lot of
Professor of Mathematics, joined the Department
thinks about the things most of us take for granted,
is called “homogenization”—the study of the physical
amazing math professors, and I started to like math a lot,”
properties of complicated heterogeneous materials. The
he said. “Eventually, I realized I could maybe study math
droplets, and flame propagation. These models are
idea is to “average” or “homogenize” the complicated
and also bring in my interest in applications (especially
often developed by engineers or physicists using basic
small-scale inhomogeneities in the material to derive
physics). Basically, that’s how I ended up studying partial
assumptions, but the resulting equations can be difficult
simpler effective equations to describe properties at
differential equations.”
or impossible to solve exactly.
larger scales. For example, the ideas of homogenization
theory can be used to study the shapes of water droplets
was worried he would need a special talent to succeed
results for these models,” said Feldman. In his research,
on surfaces that have microscopic roughness, such as a
at math, but he had supportive and encouraging
the results sometimes show the limitations of the
plant leaf, a piece of glass, or a table top.
mentors, so he never got too discouraged. “I hope the
for example, fluid flow, water
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One particular type of problem Feldman has studied
Feldman wasn’t always interested in mathematics. As
“I’m interested in proving mathematically rigorous
Like many undergrads who study math, Feldman
