Zhang Receives NSF Career Award

May 25, 2017

Headshot of Harry (Hui) ZhangExplaining higher-dimensional space is in many ways an expression of the inexpressible, and exactly the kind of work that Dr. Hui Zhang is engaged in. A professor in the department of Computer Engineering and Computer Science since the Fall of 2015, Zhang was recently awarded an NSF Career Award for his work, “CAREER:  Visualizing Mathematical Structures in High-Dimensional Space.”

Higher Dimensional Space
It’s a heady topic to reduce to layman’s terms, although a challenge that Zhang is more than eager to engage. His work materializes a theoretical space that is neither a destination or physically reproducible place, but a mathematical construct used in higher level equations and formulas.

“In the mathematical world, 4th dimensional, 5th dimensional, etc. Human beings can only perceive 3d space. But when the computation is about xyzabc. It’s about equivalence, how one entity is equivalent to another one in high dimensional space,” explains Zhang.

He continues adding, “This is purely mathematical. The 4th dimensional world is the fourth axis. We use a lot of very interesting phenomena. In our 3-dimensional space a ribbon can go into a ring and lift up the ring. In 4-dimensional space, this is not possible. A ring would fall through the ribbon. This kind of analogy from 1-dimensional to 2 dimensional to 3-dimensional… many of these phenomena that I’m trying to visualize already existed in a mathematical book (on the page).”

Applications
Zhang’s ambitious project is meant to help negotiate a logical puzzle impossible for many to perceive. His visualizations offer new opportunities for mathematicians, educators, and students to engage daunting hypothetical research.

He explains, “From a computer science perspective, many of the techniques that we use for visualization can be used for a lot of other areas. Within mathematical areas, it has two applications. First it helps mathematicians with their hypotheses. Second, it helps with students to visual interface, to try for things without theory, how to navigate 4-dimensional space.”