Fotini Markopoulou-Kalamara is a theoretical physicist interested in foundational mathematics and quantum mechanics. She has apparently been influenced by those (for example Christopher Isham) who has been calling attention to the unstated assumption in most modern physics that physical properties are most naturally calibrated by a real-number continuum.
She, and others, attempt to make explicit some of the implicit mathematical assumptions underpinning modern theoretical physics and cosmology. Her foundational work in quantum physics has been compared to Cantor's foundational work on the theory of the continuum (this may be considered ironic).
In her interdisciplinary paper "The Internal Description of a Causal Set: What the Universe Looks Like from the Inside" Fotini Markopoulou-Kalamara instantiates some abstract terms from mathematical category theory to develop straightforward models of space-time. It proposes simple quantum models of space-time based on category-theoretic notions of a topos and its subobject classifier (which has a Heyting algebra structure, but not necessarily a Boolean algebra structure).
For example, hard-to-picture category-theoretic "presheaves" from topos theory become easy-to-picture "evolving (or varying) sets" in her discussions of quantum space-time. The diagrams in Markopoulou's papers (including hand-drawn diagrams in one of the earlier versions of "The Internal Description of a Causal Set") are straightforward presentations of possible models of space-time. They are intended as meaningful and provocative, not just for specialists but also for newcomers.
See books by Barr and Wells, Saunders MacLane, and by William Lawvere and Stephen Schanuel, "Conceptual Mathematics : A First Introduction to Categories"), for accessible accounts of the category theory.
From her page at the Perimeter Institute for Theoretical Physics at the University of Waterloo (Canada), where she is an Adjunct Professor:
"Fotini received her Ph.D. from Imperial College (1998). Dr. Markopoulou-Kalamara is a broadly talented researcher who recently shared First Prize in the Young Researchers competition at the Ultimate Reality Symposium in Princeton, New Jersey. Previous postdoctoral positions were held at the Albert Einstein Institute, Imperial College London, and Penn State University."
The Internal Description of a Causal Set: What the Universe Looks Like from the Inside:
Full text (Adobe Acrobat PDF file, PS and other formats) can be downloaded from:
http://xxx.lanl.gov/abs/gr-qc/9811053
Another version with color hand-drawn slides and audio is available at:
http://cgpg.gravity.psu.edu/online/Html/Seminars/Fall1998/Markopoulou/
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