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Autumn Semester 2025

Date / Time Speaker Title Location
22 September 2025
15:15-16:30 		Richard Hind
University of Notre Dame
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Symplectic Geometry Seminar

Title Lagrangian intersections and symplectic embeddings
Speaker, Affiliation Richard Hind, University of Notre Dame
Date, Time 22 September 2025, 15:15-16:30
Location HG G 43
Abstract We prove an intersection result between Lagrangian tori inside the 4 dimensional cylinder and certain codimension 1 hypersurfaces with Lagrangian torus boundary. Intersections between polydisks and the hypersurfaces are also obtained, under weaker conditions. Consequences are computations of various shape type invariants, which result in symplectic embedding obstructions. There is a lot of rigidity, provided the domain is not 'thin' relative to the target. This is joint work with Ely Kerman.
Lagrangian intersections and symplectic embeddingsread_more
HG G 43
29 September 2025
15:15-16:15 		Kyler Siegel
University of Southern California
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Symplectic Geometry Seminar

Title Symplectic ellipsoid embeddings, singular plane curves, and scattering diagrams
Speaker, Affiliation Kyler Siegel, University of Southern California
Date, Time 29 September 2025, 15:15-16:15
Location HG G 43
Abstract A fundamental problem in quantitative symplectic geometry is to understand in which ways a Hamtilonian flow can "squeeze" phase space. The special case of ellipsoids has been a great source of motivation for the last several decades, in many ways mirroring various important developments in the field (e.g. Gromov-Witten theory, Floer homology, symplectic field theory, embedded contact homology, and more). In this talk, I will survey some new developments in the study of high dimensional symplectic embeddings, and in particular the recent resolution of the so-called stabilized ellipsoid conjecture. Our framework sets up a bridge between quantitative symplectic geometry and the classical study of singular algebraic curves, studying the latter using tools from log Calabi-Yau mirror symmetry. I will not assume familiarity with any of this background.
Symplectic ellipsoid embeddings, singular plane curves, and scattering diagramsread_more
HG G 43
* 29 September 2025
16:30-17:30 		Leonid Polterovich
Tel-Aviv University
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Symplectic Geometry Seminar

Title Contact topology meets thermodynamics
Speaker, Affiliation Leonid Polterovich, Tel-Aviv University
Date, Time 29 September 2025, 16:30-17:30
Location HG G 43
Abstract I discuss the appearance of certain notions and results from contact topology in both equilibrium and non-equilibrium thermodynamics. These include non-smooth Legendrian submanifolds, Reeb chords, and the partial order on the space of Legendrians. Based on joint work with Michael Entov and Lenya Ryzhik.
Contact topology meets thermodynamicsread_more
HG G 43
6 October 2025
15:15-16:15 		Eva Miranda
UPC and CRM-Barcelona
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Symplectic Geometry Seminar

Title Contact and Cosymplectic Geometry in the Flow
Speaker, Affiliation Eva Miranda, UPC and CRM-Barcelona
Date, Time 6 October 2025, 15:15-16:15
Location HG G 43
Abstract In this talk I will explore the correspondence, established by Etnyre and Ghrist, between Reeb vector fields and Beltrami vector fields, which are stationary solutions of the Euler equations. This bridge allows us to apply techniques from contact geometry to fluid dynamics. As an example, I will show how universality of Beltrami fields can be deduced via an h-principle in contact geometry, and how Reeb embeddings can be used to construct Turing-complete solutions of the Euler equations, i.e. stationary flows capable of emulating the computation of a universal Turing machine. Extending these ideas, I will discuss how Reeb vector fields on cosymplectic manifolds provide a framework to build Turing-complete stationary solutions of the Navier–Stokes equations, thus giving a positive answer to a question raised by Terence Tao. These results illustrate a striking connection between contact and symplectic geometry, fluid dynamics, and theoretical computer science — all in the flow.
Contact and Cosymplectic Geometry in the Flow read_more
HG G 43
13 October 2025
15:15-16:15 		Ángel González-Prieto
Universidad Complutense de Madrid
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Symplectic Geometry Seminar

Title Computability in dynamical systems
Speaker, Affiliation Ángel González-Prieto, Universidad Complutense de Madrid
Date, Time 13 October 2025, 15:15-16:15
Location HG G 43
Abstract The relationship between computational models and dynamical systems has fascinated mathematicians and computer scientists since the earliest formulations of computation. In recent years, this connection has attracted renewed interest, driven by groundbreaking results showing that Turing machines can be simulated by the flow lines of solutions to the Euler and Navier–Stokes equations. In this talk, we propose a novel viewpoint on computability within dynamical systems, inspired by ideas from Topological Quantum Field Theory. We prove that any computable function can be realized as the flow of a volume-preserving vector field on a smooth bordism. Beyond providing a new computational model, this perspective reveals deep connections between the topological features of the flow, the existence of compatible contact-type geometric structures on the bordism, and the computational complexity of the function. Joint work with E. Miranda and D. Peralta-Salas
Computability in dynamical systemsread_more
HG G 43
20 October 2025
15:15-16:15 		Ipsita Datta
ETH
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Symplectic Geometry Seminar

Title Geometry of Lagrangian Tangles
Speaker, Affiliation Ipsita Datta, ETH
Date, Time 20 October 2025, 15:15-16:15
Location HG G 43
Abstract Lagrangian tangles are cobordisms between smooth links that generalize the classical Arnol'd theory of Lagrangian cobordism and the theory of Lagrangian cobordisms between Legendrian links. In this talk, we will explore the symplectic geometry of Lagrangian tangle links in the product of a surface with the complex numbers. The main tool is a novel Floer theory for Lagrangian tangles inspired by Morse theory for manifolds with a gradient field tangent to the boundary. We show the existence of an LES of persistence modules giving quantitative obstructions to the existence of Lagrangian tangle links. This is joint work with Josh Sabloff (Haverford College).
Geometry of Lagrangian Tanglesread_more
HG G 43
27 October 2025
15:15-16:15 		Nikolas Adaloglou
Leiden University
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Symplectic Geometry Seminar

Title Which symplectic forms on S2xS2 have Lagrangian Klein Bottles?
Speaker, Affiliation Nikolas Adaloglou, Leiden University
Date, Time 27 October 2025, 15:15-16:15
Location HG G 43
Abstract Using (almost) toric fibrations and their visible Lagrangians, we can construct many novel and interesting examples of Lagrangian submanifolds of symplectic four-manifolds. Naturally, one can ask whether visible Lagrangians are all the Lagrangians that exist, or, in other words, how faithful the pictures coming from almost toric fibrations are. I will answer this question for Klein bottles in $(S^2 \times S^2,\omega_{\lambda})$, i.e. the product of two spheres where the first factor has area 1 and the other factor has area $\lambda$. In particular, I will first construct a visible Lagrangian Klein bottle when $\lambda < 2$. Then I will show that no Lagrangian Klein bottles exist otherwise. The key input for obstructing the existence of the Klein bottles is Luttinger surgery along with techniques of (compact) pseudoholomorphic curves and Seiberg--Witten theory. This is joint work with J. Evans.
Which symplectic forms on S2xS2 have Lagrangian Klein Bottles?read_more
HG G 43
10 November 2025
15:15-16:30 		Giovanni Ambrosioni
ETH
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Symplectic Geometry Seminar

Title Approximability for spaces of Lagrangian submanifolds
Speaker, Affiliation Giovanni Ambrosioni, ETH
Date, Time 10 November 2025, 15:15-16:30
Location HG G 43
Abstract In this talk I will introduce a new notion of approximability for metric spaces that can be seen as a categorification of a concept introduced by Turing for metric groups and as a generalization of total-boundedness. I will explain how recent technological advances in symplectic topology and persistence category theory allow us to talk about approximablity of spaces of Lagrangian submanifolds and discuss applications to rigidity and complexity of Lagrangians, as well as potential relations to open problems in Lagrangian topology. This talk is based on joint work with Paul Biran and Octav Cornea.
Approximability for spaces of Lagrangian submanifoldsread_more
HG G 43
* 17 November 2025
15:00-16:00 		Adrian Dawid
Cambridge University
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Symplectic Geometry Seminar

Title Probability measures on the Hamiltonian diffeomorphism group
Speaker, Affiliation Adrian Dawid, Cambridge University
Date, Time 17 November 2025, 15:00-16:00
Location HG G 19.2
Abstract What is a random Hamiltonian diffeomorphism? In this talk, we will try to answer this question by constructing a family probability measure on the group of Hamiltonian diffeomorphisms. We will see that classical invariants such as the Hofer norm and spectral invariants become well-behaved random variables in this setting. Furthermore, these measures have (for suitable choices of parameters) several desirable properties, such as full support on Ham(M), explicit estimates of the measure of Hofer-balls, and well-behaved extensions to the world of C^0-symplectic geometry. Additionally, these measures behave like Gaussian measures in certain ways. After a careful review of the construction, we will review these properties and some open problems. Note: the seminar begins at 15:00 rather than 15:15. The location is HG 19.2 and not the usual room.
Probability measures on the Hamiltonian diffeomorphism group read_more
HG G 19.2
* 24 November 2025
14:30-15:30 		Levin Maier
Universität Heidelberg
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Symplectic Geometry Seminar

Title Hopf–Rinow Type Theorems and Periodic Geodesics on Half Lie Groups
Speaker, Affiliation Levin Maier, Universität Heidelberg
Date, Time 24 November 2025, 14:30-15:30
Location HG G 19.2
Abstract The geometric formulation of hydrodynamics by Arnold motivated the study of infinite-dimensional manifolds, and more precisely, half Lie groups — topological groups in which right multiplication is smooth while left multiplication is continuous. The main examples are groups of ( H^s ) or ( C^k ) diffeomorphisms of compact manifolds. In this talk, we will prove several Hopf–Rinow type theorems for right-invariant magnetic systems and certain Lagrangian systems on half Lie groups, extending the recent work of Bauer–Harms–Michor from the case of geodesic flows to this more general setting. Towards the end, we will show that on a half Lie group which is non-aspherical and equipped with a strong Riemannian metric, there always exists a contractible periodic geodesic. This is based on joint work with M. Bauer and F. Ruscelli.
Hopf–Rinow Type Theorems and Periodic Geodesics on Half Lie Groupsread_more
HG G 19.2
1 December 2025
15:15-16:30 		Fabio Gironella
Université de Nantes
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Symplectic Geometry Seminar

Title Confoliations in high dimensions
Speaker, Affiliation Fabio Gironella, Université de Nantes
Date, Time 1 December 2025, 15:15-16:30
Location HG G 43
Abstract In a pioneering work of 1998, Eliashberg and Thurston proved that, in ambient dimension 3, C^2 foliations can always (besides one example) be C^0-approximated by contact structures in the space of plane fields. To do so, they introduce what they called ``confoliations'', that are geometric structures which are mid-way between foliations and contact structures. While these have been studied extensively in dimension 3 by many authors, the situation in higher dimensions is less clear, and there is not even a consensus on what their definition should be. In this talk, I will introduce a new notion of high-dimensional symplectic confoliation, and describe how on one hand it naturally leads to a notion of approximation by contact structures that encompasses all previously known ad-hoc examples, and on the other hand how it also constitute a good class of structures, generalizing contact ones, of which one can study symplectic fillability questions. This is based on work joint with Robert Cardona and on work in progress joint with Seungook Yu.
Confoliations in high dimensionsread_more
HG G 43
8 December 2025
15:15-16:30 		Skander Charfi
Laboratoire de Mathématiques d'Orsay
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Symplectic Geometry Seminar

Title A Multidimensional Birkhoff Theorem for Recurrent Lagrangian Submanifolds
Speaker, Affiliation Skander Charfi, Laboratoire de Mathématiques d'Orsay
Date, Time 8 December 2025, 15:15-16:30
Location HG G 43
Abstract A classical theorem of Birkhoff (1922) asserts that any essential invariant curve of a symplectic twist map on the cylinder is a Lipschitz graph over the circle. Since then, several extensions of this result to higher-dimensional settings have been obtained (Herman, Katznelson–Ornstein, Siburg, Bialy–Polterovich, among others). A generalization due to Arnaud (2010) in the contangent bundle of any closed manifold, states that an invariant exact Lagrangian, under the flow of a convex Hamiltonian, is a C1 graph over the base. We will try to show that this graph property is not a consequence of invariance itself but rather of recurrence. We will provide an optimal condition on the orbit of an exact Lagrangian submanifold under the Hamiltonian flow, requiring backward and forward convergence (up to subsequences) in a topology controlling the Liouville primitives, which ensures that the submanifold and all its iterates are C1 graphs over the base. We will see that this implies recurrence. The proof combines two complementary viewpoints on weak solutions of the Hamilton–Jacobi equation : the variational viewpoint via graph selectors of exact Lagrangian submanifolds, and the regularity properties of viscosity solutions provided by the weak-KAM approach.
A Multidimensional Birkhoff Theorem for Recurrent Lagrangian Submanifoldsread_more
HG G 43
15 December 2025
15:15-16:30 		Renato Vianna
University of São Paulo
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Symplectic Geometry Seminar

Title Open-string Quantum Lefschetz formula
Speaker, Affiliation Renato Vianna , University of São Paulo
Date, Time 15 December 2025, 15:15-16:30
Location HG G 43
Abstract Let Y be a symplectic divisor of X, \omega. In the Kahler setting, Givental's (closed-string) Quantum Lefschetz formula relates certain Gromov-Witten invariants (encoded by the G function) of X and Y. Given an Lagrangian L in (Y, \omega|Y), we can lift it to a Lagrangian L' in neighbourhood NY \subset X. We will introduce the notion of the potential of a Lagrangian, which encodes information of Maslov index 2 J-holomorphic disks with boundary on it. From the work of Biran-Khanevski, we can extract a formula for when (X,L',Y,L) forms a monotone tuple (we will define this notion), and the minimal Chern number of Y is 2. We generalise the formula in this setting when we allow the minimal Chern number to be 1. We can use this to show the existence of infinitely many Lagrangian tori in CP^n, Quadrics, Cubics, and other symplectic manifolds, among other results. Following the work of Tonkonog on gravitational descendants, we recover an explicit Quantum Lefschetz formula appearing in the work of Coates-Corti-Galkin-Kasprczyk. Interestingly, their formula applies in a different context--specifically when X is toric -- which neither contains nor is contained in the monotone tuple setting. Motivated by this, we introduce an alternative set of hypotheses, typically satisfied when X degenerates to a toric manifold, under which a broader open-string Quantum Lefschetz formula applies. The differences between these sets of hypotheses will be discussed. This is joint work with Luis Diogo, Dmitry Tonkonog and Weiwei Wu.
Open-string Quantum Lefschetz formularead_more
HG G 43

Notes: red marked events are important, events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location and if you want you can subscribe to the iCal/ics Calender.

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