Intersections in Projective Spaces (23frg006)


Justyna Szpond (Pedagogical University of Cracow)

(University of Nebraska-Lincoln)


The Banff International Research Station will host the "Intersections in Projective Spaces" workshop at the UBC Okanagan campus in Kelowna, B.C., from July 23 to August 6, 2023.

Understanding 3-dimensional structure from 2-dimensional photos is the essential issue behind CT scans and is a significant hurdle in computer vision. A version of this problem has arisen in recent research in algebraic geometry:
if the photographic image of a finite set of points have a nice structure (known technically as being a complete intersection) no matter what angle the photo is taken from, what can we say about the arrangement of the original set of points?

There are significant obstructions to extending what is known in dimension 3 to higher dimensions. The research to be undertaken under this proposal has the goal of exploring how to relax the condition of being a complete intersection in an interesting way that is fruitful for higher dimensions.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. BIRS is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).