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Amgen Scholars: Announcements of Opportunity

Below are Announcements of Opportunity posted by Caltech faculty for the Amgen Scholars program.

Announcements of Opportunity are posted as they are received. Please check back regularly for new AO submissions! Remember: This is just one way that you can go about identifying a suitable project and/or mentor. For additional tips on identifying a mentor click here.

Please remember:

  • Students pursuing Amgen must be U.S. citizens, U.S. permanent residents, or students with DACA status.
  • Students pursuing Amgen must complete the 10-week program from June 21 - August 25, 2023. Students must commit to these dates. No exceptions will be made.
  • Accepted students must live in provided Caltech housing.

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Project:  Research in Computational Differential Geometry
Disciplines:  Mathematics, Computer Science, Physics
Mentor:  Yakov Berchenko-Kogan, Assistant Professor, (PMA), yberchenkokogan@fit.edu
Mentor URL:  https://www.fit.edu/faculty-profiles/b/berchenko-kogan-yakov/  (opens in new window)
Background:  NOTE: This project is being offered by a Caltech alum and is open only to Caltech students. The project will be conducted at Florida Institute of Technology in Melbourne, Florida. A limited amount of travel funding is also available for this project.

Computational differential geometry is a rapidly evolving field. A notable recent success is the breakthrough in numerical relativity in the early 2000s that was instrumental in LIGO's Nobel-winning detection of gravitational waves in 2015. Computational differential geometry has also found applications in robotics, as well as the processing of geometric data, both for the purposes of autonomous identification of objects in the environment and for the design of objects for fabrication.

An overarching research goal is to develop numerical methods for geometric problems that are both quantitatively and qualitatively accurate. Quantitative accuracy means that the numerical approximations converge to the true solutions quickly as we increase computational time. Qualitative accuracy means that the numerical method _exactly_ preserves any structure present in the original problem, such as for example conservation of angular momentum.

Description:  The problems above are beyond the scope of a summer project, but there are many simpler potential projects in computational geometry that are both doable in ten weeks and have potential for publication, focusing on geometric flows such as mean curvature flow, curve-shortening flow, and/or curve-straightening flow, depending on the student’s interests and background. During the ten weeks, the student will learn the necessary background to work with these flows, write and modify code to implement numerical algorithms related to these flows, and explore and/or prove properties about these numerical methods. The student will be expected to write up their work for publication, to present a talk about their work at the Florida Tech math department seminar, and to prepare a poster or talk for the SURF Seminar Day and the Joint Math Meetings.
References:  Feel free to get in touch with me via email for more information.
Student Requirements:  An A in CS1 or equivalent experience. (Advanced programming skills are not required, but the basic skills must be solid.) Ma109 will be very helpful, but not required, as some research questions are accessible with just Ma1 and some reading.
Programs:  This AO can be done under the following programs:

  Program    Available To
       SURF    Caltech students only 

Click on a program name for program info and application requirements.

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