High-Dimensional Convexity: Covering, Illumination, and Borsuk's Question
Andrii Arman (University of Manitoba) , Andriy Prymak (University of Manitoba)Jan 5, 2027 — Apr 27, 2027
About the course
How do our classical geometric intuitions change as dimension of the ambient space grows? This course investigates high-dimensional convexity and discrete geometry through the lens of geometric covering and illumination problems.
Highlighting the intersection of asymptotic bounds and discrete structures, the course extensively covers different variations of Borsuk’s partition question and recent surprising counterexamples. We will discuss constructions of special bodies of constant width, discretization techniques, and probabilistic models.
These tools will be applied to explore asymptotic estimates of various covering methods in convex and discrete geometry, volume bounds for bodies of constant width, and recent advances in Lebesgue’s universal covering problem. Ultimately, students will master a versatile research toolkit at the active intersection of combinatorics, geometry, and probability, preparing them to tackle modern open problems in asymptotic geometric analysis and related areas.
Registration
This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.
Enrollment Details
- Course Name
- Mathematical foundations of stratified and anisotropic fluid flows
- Date
- Jan 5, 2027 — Apr 27, 2027
- Course Number
- MATH8810
- Section Number
- Section Code
Instructor(s)
For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website
Other Course Details
Availability
This course will be available to students at universities inside and beyond the PIMS network.
Remote Access
Lectures will be delivered live via Zoom using a 2-in-1 laptop and an on-screen writing application to ensure high-quality, real-time transmission of mathematical notation. To foster a collaborative learning environment at other PIMS network sites with multiple enrolled students, we will coordinate with those host institutions to request that dedicated seminar rooms equipped with projectors and videoconferencing hardware be booked for group participation.