Many claim that math is the language of the universe; string the words with careful deliberation and you might end up with an almost poetic reconstruction of reality. To the contrary of most of our school level pedagogy, mathematics can be perplexingly enriched with visuals, a form of visual poetry. In a universe that binds us in three spatial dimensions, mathematics is the ultimate liberator that lets us imagine, quite tangibly, the possibilities of dimensions higher (and lower) than what we inhabit. Be it a daedal tesseract, or a complex reconstruction of the Mandelbrot set, mathematics has an innate power to inform our wildest imagination.
Fukaya category is one startling example of the many ways in which complex mathematics can be expressed through the study of surfaces and topology.
Dr. Haniya Azam is an Assistant Professor at the department of mathematics who is the first author of a paper which has been published in the Journal of Pure and Applied Algebra, one of the most well reputed journals of mathematics. Dr. Haniya’s paper tackles the complex topic of mathematical surfaces called Fukaya category, a mathematical concept whose applications spill over to other disciplines, such as in the famous string theory, by providing vital support for the mirror symmetry conjecture.
This research constructs the topological Fukaya category of a surface with genus greater than one, making this model intrinsic to the topology of the surface.
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)
Pictured above: non-separating curves on a surface of genus two.
In their paper, Dr. Haniya and her team review the definition of Floer homology for unobstructed curves. Floer chain complex will be generated by intersection points, which requires the usual transversality condition on the pair of curves giving these intersection points. Defined in this naive manner, their chain complexes are not invariant under isotopy. For a given choice of disjoint representatives of two curves the intersection could be empty, whereas a little perturbation may give rise to intersection points.
Instead of using the area form of the surface, the researchers use an admissibility condition borrowed from Heegaard-Floer theory which ensures invariance under isotopy. The paper shows finiteness of the moduli space using purely topological means and compute the Grothendieck group of the topological Fukaya category.
You can read the complete paper below for a much deeper dive into Dr. Haniya’s work.
Reference
Haniya Azam, Christian Blanchet, Topological Fukaya categories of surfaces, Journal of Pure and Applied Algebra, Volume 226, Issue 6, 2022, 106941, ISSN 0022-4049.