Hoon Hong: Research Overview

Goal

My current research goal is to develop

mathematical theories
algorithms
software libraries/packages

for efficiently solving algebraic constraints arising in mathematics, science and engineering.

A constraint is an expression (well formed formula) involving rational numbers, variables (ranging over real numbers), arithemetic functions such as +, -, * , /, relations such as =, >, >=, logical connectives such as and , or , not , quantifers such as forall and exists (formally a formula in the first order theory of real closef field).

A constraint defines a subset of the free variable space, we naturally calls it the solution set. Solving means to extract some useful information about the solution set such as

Emptiness
Finiteness
Dimension
Number of components
Topological type
Volume
A defining quantifier-free formula
An approximate simple defining formula.
Plotting
....

Motivation

The main motivation for tackling this problem comes from the observation that numerous problems in mathematics, science and engineering can be reduced to that of solving constraints. Thus, making progress in solving constraints will have a broad impact.

Approach

I try to achieve efficiency by

Developing new/better mathematical theories and more efficient algorithms.
Utilizing the structure (in particular composition).
Allowing approximate answers (but to a given precision).

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