This is the website of the symplectic cut seminar, which meets online weekly and served on open source software. There is also a Matrix chat room where you can find annoucements and have discusssions related to the seminar. You can access it by creating an account at Freemath (make sure to choose Other so that your account is created in freemath.xyz) and joining the room called Symplectic Cut.
  • Seminar time in Autumn 2020 : Wednesday 3 - 5 pm UTC+01:00.
  • Seminar location : BBB server (the link for each talk is e-mailed to the participants before the seminar) The theme for this term is Homological Mirror Symmetry for cluster varieties. We are collecting some references here (please send me more references). Toric varieties https://pages.uoregon.edu/njp/tv.pdf - Nicholas Proudfoot lecture notes https://arxiv.org/abs/math/0511644 - Abouzaid HMS for toric varieties https://arxiv.org/abs/1105.0640 - Abreu-Macarini Remarks on Lagrangian intersections in toric manifolds (friendly non-technical introduction to toric manifolds, symplectic reduction, and Floer theory) https://arxiv.org/abs/0904.1686 - McDuff Displacing Lagrangian toric fibres via probes (nice companion paper to Abreu-Macarini) https://arxiv.org/abs/math/0503102 - Kawamata Complete exceptional collections for toric varieties Books: Audin - The topology of torus actions on symlectic manifolds Fulton - Intro to toric varieties Cluster varieties https://arxiv.org/abs/1109.3255 - Pascaleff C^2-conic computation of wrapped category https://arxiv.org/abs/1309.2573 This is the geometer's way of understanding what a cluster variety is. https://arxiv.org/abs/2008.03265 Recent paper by Mandy Cheung and Renato Vianna https://arxiv.org/pdf/1407.6241.pdf - Classification of rank2 cluster varieteis by Mandel Theta functions https://arxiv.org/abs/1411.1394 - GHKK https://arxiv.org/abs/1309.5922 - Goncharov Shen https://arxiv.org/abs/1310.8609 - a symplectic approach to theta functions Grassmannians https://arxiv.org/abs/1711.04456 - Nohara-Ueda Potential functions on Grassmannians of planes and cluster transformations https://arxiv.org/abs/1805.11738 - Hong-Kim-Lau Immersed two-spheres and SYZ with application to Grassmannians https://arxiv.org/abs/1808.02955 and https://arxiv.org/abs/1910.10888 - Castronovo Fukaya categories of, and exotic tori in, Grassmannians https://arxiv.org/abs/math/0511124 - (Rietsch) A mirror symmetric construction of qH*_T(G/P)_(q) https://arxiv.org/abs/1307.1085 - (Marsh-Rietsch) The B-model connection and mirror symmetry for Grassmannians https://arxiv.org/abs/1712.00447 - (Rietsch-Williams) Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians Tropical https://arxiv.org/abs/2004.14314 - Venugopalan-Woodward Tropical Fukaya algebras https://jeffhicks.net/ - Jeff has several preprints on tropical Lagrangians and we should try to get him to talk about them https://arxiv.org/abs/math/0312530 - Mikhalkin's tropical curve counting in the plane
  • Schedule of talks: 23 Sep - Yankı Lekili - An overview of HMS for toric and cluster varieties 30 Sep - Matt Habermann - AKO mirror symmetry for weighted projective planes 7 Oct - Marco Castronovo - Close encounters of the cluster kind 14 Oct - Tim Magee - Cluster varieties 21 Oct - Cheuk Yu Mak - Symplectic analogue of Tim's talk 28 Oct - Jeff Hicks - Almost toric base diagrams 4 Nov - Jie Min - Localized mirror functor using immersed Lagrangians 11 Nov - Daping Weng - Augmentations, Fillings, and Clusters 18 Nov - Cancelled. 25 Nov - Tim Magee 2 Dec - Ian Le 9 Dec - Tom Sutherland