Sean Gasiorek
Education
B.S., California Polytechnic State University, 2009
M.S., California Polytechnic State University, 2011
Ph.D., University of California, Santa Cruz, 2019
Research Interests
Mathematical billiards, dynamical systems, dynamics of charged particles in magnetic fields, integrable systems, celestial mechanics, differential geometry.
My research lies at the intersection of geometry and dynamical systems. An emphasis of my research is in the dynamical properties of mathematical billiards in various physical and geometric settings, particularly its interplay with integrable systems and classical mechanics. I use classical and modern techniques from algebra and geometry to prove the integrability of billiards in Minkowski space, prove algebrogeometric conditions for the existence of periodic orbits, and connect billiards to other areas of mathematics such as celestial mechanics.
I welcome the opportunity to include undergraduate and graduate students in my research, whether through senior projects, independent study, summer research, or master’s theses. Please contact me via email if you are interested in learning more about these opportunities.
Publications
- S. Gasiorek, Counting Collisions in an N-Billiard System Using Angles Between Collision Sub- spaces, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Volume 16 (2020), No. 119, 13 pages. DOI: 10.3842/SIGMA.2020.119.
- S. Gasiorek and M. Radnović, Pseudo-Euclidean Billiards within Confocal Curves on the Hyper- boloid of One Sheet, Journal of Geometry and Physics, (2020) DOI: 10.1016/j.geomphys.2020.104032.
- S. Gasiorek, On the Dynamics of Inverse Magnetic Billiards, Nonlinearity, Vol 34, no. 3, pp. 1503-1524 (2021). DOI: 10.1088/1361-6544/abe2f1.
- V. Dragović, S. Gasiorek, and M. Radnović, Billiard Ordered Games and Books. Regular and Chaotic Dynamics, Vol 27, no. 2, pp. 132-150 (2022). DOI: 10.1134/S1560354722020022.
- V. Dragović, S. Gasiorek, and M. Radnović, Billiard Ordered Games and Books. Regular and Chaotic Dynamics, Vol 27, no. 2, pp. 132-150 (2022). DOI: 10.1134/S1560354722020022.
