As noted by Haydys, thinking of this holomorphic function as a superpotential on an infinite-dimensional symplectic manifold gives rise to a quaternionic analog of Floer's equation for holomorphic strips: the Fueter equation. This occurs in part because, in this setting, the symplectic action functional, the gradient flow of which computes Lagrangian Floer homology, is the real part of a holomorphic function.
They were given a symplectic interpretation by Dyckerhoff-Jasso-Lekili, who proved the equivalence (as $A_\).ġ5 March Semon Rezchikov Title: Holomorphic Floer Theory and the Fueter Equation Abstract: The Lagrangian Floer homology of a pair of holomorphic Lagrangian submanifolds of a hyperkahler manifold is expected to simplify, by work of Solomon-Verbitsky and others.
This family of non-commutative algebras arises very naturally as endomorphism algebras of indecomposable modules of quivers of finite type. Our objects of interest on the representation theoretical side are Auslander algebras of type A. Perutzġ0 May Ilaria Di Dedda Title: Realising perfect derived categories of Auslander algebras of type A as Fukaya-Seidel categories Abstract: The theme of this talk will be to build a bridge between two areas of mathematics: representation theory and symplectic geometry. Time permitting, we will sketch an application of our techniques in the context of ongoing joint work with T.
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We will start by studying the rather restricting yet convenient "strongly - monotone" case and then show how to generalise it to more general settings using an energy filtration argument due to K. The main step will be to use a neck-stretching argument to establish some energy lower bounds on certain trajectories realising differentials. Seidel (1996) for twists on surfaces, we gave an explicit description of the Floer cohomology of a Dehn twist in terms of Morse cohomology of some "sub-quotients" of M. Nowadays there are several methods to compute it, for example by using the Seidel exact triangle.
This is based on joint work with Roger Casals and John Etnyre.ġ7 May Riccardo Pedrotti Title: Fixed point Floer cohomology of a Dehn twist in a monotone setting and in more general contexts Abstract: In this talk we will talk about the fixed point Floer cohomology of a Dehn twist. In this talk we will investigate whether a 4-dimensional tracker (with the necessary mathematical education) can determine the 3-dimensional creature that left the trace. We will discuss how the existence of destabilising exact triangles obstructs special Lagrangians, under some additional assumptions, using the technique of integration over moduli spaces.Ģ4 May Marc Kegel Title: Stein traces Abstract: Every Legendrian knot leaves a traces in the 4-dimensional symplectic world. I will focus on the exact case (Stein Calabi-Yau manifolds), and deal only with almost calibrated Lagrangians. 14 June Yang Li Title: The Thomas-Yau conjecture Abstract: The Thomas-Yau conjecture is an open-ended program to relate special Lagrangians to stability conditions in Floer theory, but the precise notion of stability is subject to many interpretations. An online geometry seminar hosted via BBB on Tuesdays at (usually) 3 pm UTC.Ī link is sent to the e-mail list before each seminar.
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