Damghan University Press Journal of Holography Applications in Physics 2783-4778 5 3 2025 09 18 Advancements in Functorial Homological Mirror Symmetry 64 106 1896 10.22128/jhap.2025.3019.1130 EN Veronica Pasquarella Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS); Block A, International Innovation Plaza, No. 657 Songhu Road, 200433 Yangpu District, Shanghai, China 0000-0002-3276-0341 Journal Article 2025 08 16 Mostly inspired by recent work by Katzarkov, Kontsevich, and Sheshmani, combined with previous work by Aganagic, Ooguri, Saulina and Vafa with regard to BPS black hole microstate counting in terms of topological field theory calculations, we will show how these tools can be applied to concrete setups arising from String Theory, and why the formalism of functorial Homological Mirror Symmetry needs to be further developed. A crucial ingredient will turn out being cobordism techniques for evaluating invariants. cobordisms Gromov-Witten invariants smooth projective varieties black hole microstate counting https://jhap.du.ac.ir/article_1896_d993e13cce351fd7859f86c75829c1dd.pdf