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Natural sciences
- Commutative rings and algebras
- Order, lattices, ordered algebraic structures
- Combinatorics
- Applied discrete mathematics
We will develop novel tools to solve several important real-world
problems: (i) Proving safety of programs (Computer Science), (ii)
Computing network reliability (Industrial Engineering), (iii) Causality
(Statistics), and (iv) Geometry of particle interactions (Physics).
These problems are all traditionally modeled as polynomial systems.
However, given that solving a general system is very difficult, they all
lack scalable algorithms. The main idea is that our applications’
systems tend to have additional structural properties. Our vision is to
exploit these specific properties to sidestep the difficulty of solving
general systems, and obtain dedicated solution methods for realworld cases.
The most profound impact is in program verification, focusing on
proving the presence/absence of bugs or vulnerabilities in code.
Given the ever-increasing role of software in safety-critical
operations, e.g. avionics and healthcare, it is vital to perform software
verification reliably and exactly. Our results will have a huge
downstream effect on every aspect of verification, ultimately leading
to more secure and trustworthy software in all sorts of applications.
Another focus is Network Reliability with significant applications in
economics and epidemiology. We will develop novel methods to
compute the reliability. Finally, we will study the Amplituhedron: a
geometric object that dramatically simplifies calculations of particle
interactions in Physics