Departement Mathematik

Symplectic geometry seminar

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Herbstsemester 2023

Datum / Zeit Referent:in Titel Ort
9. Oktober 2023
15:15-16:10 		Fabian Ziltener
ETH
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Symplectic Geometry Seminar

Titel Capacities as a complete symplectic invariant
Referent:in, Affiliation Fabian Ziltener, ETH
Datum, Zeit 9. Oktober 2023, 15:15-16:10
Ort HG G 43
Abstract This talk is about joint work with Yann Guggisberg. The main result is that the set of generalized symplectic capacities is a complete invariant for every symplectic category whose objects are of the form $(M,\omega)$, such that $M$ is compact and 1-connected, $\omega$ is exact, and there exists a boundary component of $M$ with negative helicity. This answers a question of Cieliebak, Hofer, Latschev, and Schlenk. It appears to be the first result concerning this question, except for results for manifolds of dimension 2, ellipsoids, and polydiscs in $\mathbb{R}^4$. If time permits, then I will also present some answers to the following question and problem of Cieliebak, Hofer, Latschev, and Schlenk: Question: Which symplectic capacities are connectedly target-representable? Problem: Find a minimal generating set of symplectic capacities.
Capacities as a complete symplectic invariantread_more
HG G 43
9. Oktober 2023
16:25-17:20 		Valentin Bosshard
ETH
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Symplectic Geometry Seminar

Titel The Lagrangian cobordism group of Weinstein manifolds
Referent:in, Affiliation Valentin Bosshard, ETH
Datum, Zeit 9. Oktober 2023, 16:25-17:20
Ort HG G 43
Abstract Lagrangian cobordisms induce exact triangles in the Fukaya category. But how many exact triangles can be recovered by Lagrangian cobordisms? One way to measure this is by comparing the Lagrangian cobordism group to the Grothendieck group of the Fukaya category. In this talk, we discuss the setting of exact conical Lagrangian submanifolds in Liouville manifolds and compute Lagrangian cobordism groups of Weinstein manifolds. As an application, we get a geometric interpretation for Viterbo restriction for Lagrangian cobordism groups.
The Lagrangian cobordism group of Weinstein manifoldsread_more
HG G 43
23. Oktober 2023
15:15-16:10 		Pazit Haim Kislev
Tel-Aviv University
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Symplectic Geometry Seminar

Titel Symplectic Barriers
Referent:in, Affiliation Pazit Haim Kislev, Tel-Aviv University
Datum, Zeit 23. Oktober 2023, 15:15-16:10
Ort HG G 43
Abstract In his seminal 2001 paper, Biran introduced the concept of *Lagrangian Barriers*, a symplectic rigidity phenomenon coming from obligatory intersections with Lagrangian submanifolds which don't come from mere topology. In this joint work with Richard Hind and Yaron Ostrover, we present what appears to be the first illustration of *Symplectic Barriers, *a form of symplectic rigidity stemming from necessary intersections of symplectic embeddings with symplectic submanifolds (and in particular not Lagrangian). In our work, we also tackle a question by Sackel–Song–Varolgunes–Zhu and provide bounds on the capacity of the ball after removing a codimension 2 hyperplane with a prescribed Kähler angle.
Symplectic Barriersread_more
HG G 43
13. November 2023
15:15-16:10 		Ipsita Datta
ETH
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Symplectic Geometry Seminar

Titel Lagrangian cobordisms, enriched knot diagrams, and algebraic invariants
Referent:in, Affiliation Ipsita Datta, ETH
Datum, Zeit 13. November 2023, 15:15-16:10
Ort HG G 43
Abstract We introduce new invariants to the existence of Lagrangian cobordisms in R^4. These are obtained by studying holomorphic disks with corners on Lagrangian tangles, which are Lagrangian cobordisms with flat, immersed boundaries. We develop appropriate sign conventions and results to characterize boundary points of 1-dimensional moduli spaces with boundaries on Lagrangian tangles.  We use these to define algebraic structures on a related "linear" case  of Lagrangian cobordisms in surface times complex plane. This talk is based on my thesis work under the supervision of Y. Eliashberg and on work in progress joint with J. Sabloff.
Lagrangian cobordisms, enriched knot diagrams, and algebraic invariantsread_more
HG G 43
13. November 2023
16:25-17:20 		Yusuke Kawamoto
ETH
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Symplectic Geometry Seminar

Titel Spectral invariants over the integers
Referent:in, Affiliation Yusuke Kawamoto, ETH
Datum, Zeit 13. November 2023, 16:25-17:20
Ort HG G 43
Abstract Spectral invariants are quantitative measurements in symplectic topology coming from Floer homology theory. We study their dependence on the choice of coefficients in the context of Hamiltonian Floer homology. We discover phenomena in this setting which hold for $\Z$-coefficients and fail for all field coefficients. We apply this to answer a symplectic version of a question of Hingston.
Spectral invariants over the integersread_more
HG G 43
* 24. November 2023
14:15-15:30 		Jeff Hicks
University of Edinburgh
Details

Symplectic Geometry Seminar

Titel Complexity of topological spaces and complexity of triangulated categories
Referent:in, Affiliation Jeff Hicks, University of Edinburgh
Datum, Zeit 24. November 2023, 14:15-15:30
Ort NO E 39
Sonneggstrasse 5, 8092 Zürich
Abstract There are several different notions of "complexity" for a topological space M. For instance, when M is a manifold one can study: the Lebesgue covering dimension; sum of Betti numbers; minimal number of Morse critical values; or the Lusternik–Schnirelmann category. Similarly, given a triangulated category C, one can measure its complexity using invariants such as the Rouquier dimension; diagonal dimension; or minimal length of presentation as a homotopy colimit. In this talk, I will discuss some of the relations between these categorical invariants and topological invariants when the category C is the Fukaya category of the cotangent bundle of M (equivalently, the category of modules over chains on the based loop space on M). I will mostly focus on - introducing the above invariants of topological spaces and categories and - discussing how Lagrangian cobordisms play a role in bounding the diagonal dimension of C in terms of the minimal number of critical values of a Morse function on M.
Complexity of topological spaces and complexity of triangulated categoriesread_more
NO E 39
Sonneggstrasse 5, 8092 Zürich

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