Matthias Kawski develops, and employs, tools from differential geometry and algebraic combinatorics to study nonlinear control systems.
Controlled dynamical systems are distinguished from classical ones by their input and output channels that allow one to interact with the systems. Prototypical is the difference between planetary motion and motion of a human-made satellite. Classically one asks: Where will the system go? When is the next eclipse? Is the solar system stable? Control theory asks inverse questions: Can I get there, and if so how? How optimally? Is the system stabilizable? Applications are ubiquitous, from mechanical and electrical systems, to finance, biomedicine and beyond.
Kawski employs diverse mathematical tools, from Lie algebras to combinatorial Hopf algebras, to uncover geometric properties of control systems on manifolds, and to design efficient algorithms suiting the inherently nonassociative nature of noncommuting flows (control actions).
Ph.D. University of Colorado-Boulder 1986
Nonlinear control theory -- using tools from differential geometry to combinatorial Hopf algebras.
Using technology, especially interactive dynamic visualization, in mathematics education.
Spring 2021 | |
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Course Number | Course Title |
MAT 371 | Advanced Calculus I |
MAT 412 | Differential Geometry |
MAT 493 | Honors Thesis |
MAT 591 | Seminar |
APM 792 | Research |
APM 799 | Dissertation |
Fall 2020 | |
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Course Number | Course Title |
MAT 371 | Advanced Calculus I |
MAT 492 | Honors Directed Study |
MAT 493 | Honors Thesis |
MAT 495 | Undergraduate Research |
APM 501 | Differential Equations I |
MAT 591 | Seminar |
APM 792 | Research |
MAT 792 | Research |
APM 799 | Dissertation |
Summer 2020 | |
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Course Number | Course Title |
APM 792 | Research |
MAT 792 | Research |
APM 795 | Continuing Registration |
MAT 799 | Dissertation |
Spring 2020 | |
---|---|
Course Number | Course Title |
MAT 412 | Differential Geometry |
MAT 492 | Honors Directed Study |
MAT 493 | Honors Thesis |
MAT 591 | Seminar |
APM 792 | Research |
APM 799 | Dissertation |
Fall 2019 | |
---|---|
Course Number | Course Title |
MAT 371 | Advanced Calculus I |
MAT 410 | Intro to General Topology |
MAT 492 | Honors Directed Study |
MAT 495 | Undergraduate Research |
MAT 591 | Seminar |
MAT 792 | Research |
APM 792 | Research |
APM 799 | Dissertation |
Summer 2019 | |
---|---|
Course Number | Course Title |
APM 792 | Research |
MAT 792 | Research |
APM 795 | Continuing Registration |
Spring 2019 | |
---|---|
Course Number | Course Title |
MAT 371 | Advanced Calculus I |
MAT 412 | Differential Geometry |
MAT 493 | Honors Thesis |
MAT 591 | Seminar |
APM 792 | Research |
APM 799 | Dissertation |
Fall 2018 | |
---|---|
Course Number | Course Title |
MAT 371 | Advanced Calculus I |
MAT 410 | Intro to General Topology |
MAT 492 | Honors Directed Study |
MAT 495 | Undergraduate Research |
MAT 591 | Seminar |
MAT 792 | Research |
APM 792 | Research |
APM 799 | Dissertation |
Summer 2018 | |
---|---|
Course Number | Course Title |
MAT 300 | Mathematical Structures |
MAT 371 | Advanced Calculus I |
MAT 792 | Research |
APM 792 | Research |
Spring 2018 | |
---|---|
Course Number | Course Title |
MAT 371 | Advanced Calculus I |
MAT 591 | Seminar |
APM 792 | Research |
Fall 2017 | |
---|---|
Course Number | Course Title |
MAT 371 | Advanced Calculus I |
MAT 495 | Undergraduate Research |
APM 501 | Differential Equations I |
MAT 792 | Research |
APM 792 | Research |
Summer 2017 | |
---|---|
Course Number | Course Title |
MAT 300 | Mathematical Structures |
STP 421 | Probability |
MAT 792 | Research |
APM 792 | Research |
Spring 2017 | |
---|---|
Course Number | Course Title |
MAT 300 | Mathematical Structures |
MAT 410 | Intro to General Topology |
MAT 591 | Seminar |
APM 792 | Research |
Fall 2016 | |
---|---|
Course Number | Course Title |
MAT 272 | Calc w/Analytic Geometry III |
MAT 342 | Linear Algebra |
MAT 495 | Undergraduate Research |
MAT 792 | Research |
APM 792 | Research |
Summer 2016 | |
---|---|
Course Number | Course Title |
MAT 300 | Mathematical Structures |
STP 421 | Probability |
MAT 792 | Research |
APM 792 | Research |
Charles Wexler Teaching Award (1994)
Associate editor (1995-1998): Systems and Control Letters
Managing editor (since 1995, responsible for the Americas): Journal of Dynamical and Control Systems
Executive editor (responsible for Computer Algebra): Electronic Journal of Mathematics and Technology
Section editor (Control and Dynamical Systems) for Springer Encyclopedia of Complexity and System Science
Reviewer for ( AMS) Mathematical Reviews (98).
Referee for Grant Proposals (NSF 41, NRF of RSA 1)
AMS: American Mathematical Society SIAM: Society of Industrial and Applied Mathematics SIAG Control and Systems Theory MAA: Mathematical Association of America