Colloquium: October 20, Rafael De La Llave, Georgia Tech
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- Category: 2017-2018
Title: A posteriori versions of KAM theory: Rigorous results, computations and conjectures
Abstract: KAM theory deals with the existence of quasi-periodic solutions. The original formulation was for systems close to integrable.
In recent times, there have appeared versions of KAM theory without any reference to quasi- integrable systems. One can start from approximate solutions of an invariance equation and then validate them.
This leads easily to some rigorous results such as monogenicity properties and Whitney regularity. Moroever, it allows to validate numerical computations. The proof is based on an iterative method which also leads to very efficient and reliable computations. These computations lead to conjectures on what happens at breakdown and reveal scaling relations. Moreover, there is a very surprising order among scaling relations corresponding to different frequencies.
This is a report on work of many people.
News 2017
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- Category: News
- The following have been awarded Scholarships for 2017-2018:
- Simon Harris won the Bond Memorial Scholarship.
- Kevin Campbell won the Kauffman Scholarship.
- Alyssa Wilke won the Severin Scholarship.
- Ahmed Ghatasheh won the Ward Memorial Scholarship.
- Jonathan Kelleher won the Warner Scholarship.
- Kaitlyn Lee won the Travis Wood Memorial Scholarship.
- Kenneth Davis, Garrett Higginbotham, Harrison Mansour, Sakar Prasain, and Norman Schmitz won Department of Mathematics Scholarships. Congratulations to all.
- Fast-track student Garrett Higginbotham won an Alabama Space Grant Scholarship Award for FY2017-18. Congratulations!
- Fast-track student Kenneth Davis won a Benjamin A. Gilman International Scholarship sponsored by the US State Department and a Freeman-ASIA Scholarship sponsored by the Freeman Foundation. Kenneth will use these to study in Japan. Congratulations!
- On March 24 Ivan Mann successfully defended his Ph.D. thesis A Metrically Defined Uniformization Map of Planar Domains. His studies were directed by Dr. L. Oversteegen.
- Former Fast-track student Rachel Ejem (now Anthonia Carter) has been selected for a Fulbright award to the United Kingdom. She will study Multidisciplinary Innovation in Newcastle upon Tyne. Congratulations.
- Elizabeth Scribner won one of three College of Arts and Sciences’ 2017 Dean's Awards on the Graduate level. Congratulations.
