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Leonardo Abbrescia was born in Bogotá, Colombia and lived there until he was 7 years old. His family
then moved to New York City where he lived in one of the most culturally diverse neighborhoods in the
country –Jackson Heights, Queens -- for 11 years. He would go on to become a first-generation college
student at Columbia University. His path to Columbia was made possible by the STEM Institute at the City
College of New York. The STEM Institute provides high school students across NYC a *free* summer
program where they could take courses for high school credit. Taking Pre-Calc and Calculus from the
incredible Mr. Cardenas and Ms. Pichardo at the Stem Institute was the most important factor in
Leonardo's admission to Columbia University.
His advisor at Columbia was Professor Daniela De Silva who patiently exposed him to the beauty of
Partial Differential Equations (PDEs). He was awarded a National Science Foundation (NSF) Graduate
Research Fellowship to pursue his Ph.D. in mathematics at Michigan State University. His advisor there
was Professor Willie Wong, from whom he learned even more about PDEs. He was then awarded an
NSF Postdoctoral Fellowship and completed a postdoc at Vanderbilt University under the mentorship of
Professor Jared Speck. When they were not talking about their children, Leonardo and Professor Speck
worked on (you guessed it) PDEs. He is currently an Assistant Professor at the Georgia Institute of
Technology and has never been more excited to work even more on PDEs.
When he is not learning about PDEs, he is learning about autism and how to better support his autistic
child.
Partial Differential Equations have consistently been at the forefront of the most important mathematical
achievements for the past 300 years. This is because physical (fluid dynamics, black holes, etc) or
biological (population growth, predator-prey, etc) phenomena have been proven to be well-approximated
by solutions to PDEs. One of the deepest sources of richness in the area is that solutions to PDEs can
develop catastrophic singularities in finite time -- even from perfect initial conditions. For compressible
fluids following the laws of thermodynamics, the most famous singularities are shock waves (think sonic
booms from supersonic flight or volcanic eruptions). Leonardo's joint work with Professor Speck has shed
new light on the formation and the geometry of these singularities. The field is at a particularly exciting
spot and Leonardo expects a burst of new exciting developments in the next few decades.
“To me, Hispanic Heritage Month is partly a reminder to celebrate the things that make us, us: our food,
our music, our culture. It is also a reminder that we can push ourselves to new heights by supporting
each other. I often think back to my time at the STEM Institute during Hispanic Heritage Month, where all
of my instructors were Hispanic.”