Algebra, Combinatorics, and Complexity
Complexity theory concerns theoretical limits on how fast computers can solve a problem, such as deciding if 282,589,933 - 1 is prime (it is). From a practical perspective, the presumed hardness of factoring a large integer is critical to internet security. Philosophically speaking, the famous P vs NP problem essentially asks: can creativity be automated? There are many deep connections between complexity and combinatorics, but traditionally through graph theory and optimization. Recent pure mathematics work with his Illinois research group brings Professor Yong’s own core competency of algebraic combinatorics into the conversation in a novel way:through the study of Newton polytopes. These geometric objects trace back to 1676 correspondence from Isaac Newton to Henry Oldenburg (the creator of scientific peer review).
During his Spring 2021 CAS Release Time appointment, Professor Yong will participate in the program on Combinatorial Algebraic Geometry at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University.