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Spring Semester 2025

Date / Time Speaker Title Location
24 February 2025
15:15-16:30 		Erman Çineli
ETH
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Symplectic Geometry Seminar

Title Closed orbits of dynamically convex Reeb flows
Speaker, Affiliation Erman Çineli, ETH
Date, Time 24 February 2025, 15:15-16:30
Location HG G 43
Abstract In this talk we will discuss two results on the multiplicity problem for prime closed orbits of dynamically convex Reeb flows on the boundary of a star-shaped domain in R2n. The first result asserts that such a flow has at least n prime closed Reeb orbits, improving the previously known lower bound by a factor of two. The second main theorem is that when, in addition, the domain is centrally symmetric and the Reeb flow is non-degenerate, the flow has either exactly n or infinitely many prime closed orbits. This is a joint work with Basak Gurel and Viktor Ginzburg.
Closed orbits of dynamically convex Reeb flowsread_more
HG G 43
3 March 2025
15:15-16:30 		Felix Schlenk
Neuchâtel University
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Symplectic Geometry Seminar

Title Singular polarizations of open symplectic 4-manifolds, with applications
Speaker, Affiliation Felix Schlenk, Neuchâtel University
Date, Time 3 March 2025, 15:15-16:30
Location HG G 43
Abstract Twenty five years ago, Paul Biran introduced polarizations of closed symplectic manifolds and showed that their Lagrangian skeleta exhibit remarkable rigidity properties. He in particular found that their complements contain only small balls. I will introduce similar polarizations of certain open 4-dimensional symplectic manifolds. This leads to several symplectic embedding results, that in turn lead to new Lagrangian non-removable intersections and a novel phenomenon of Legendrian barriers. For instance, given any connected symplectic 4-manifold $(M,\omega)$ and a 4-ball of smaller volume, their exists an explicit finite union of Lagrangian discs in the 4-ball such that their complement symplectically embeds into~$(M,\omega)$, extending a result by Sackel--Song--Varolgunes--Zhu and Brendel. Other applications are new Lagrangian intersection results and relative versions of the Arnold chord conjecture. The talk will be non-technical and focus on the geometric constructions. This is joint work with Emmanuel Opshtein.
Singular polarizations of open symplectic 4-manifolds, with applicationsread_more
HG G 43
10 March 2025
15:15-16:15 		Rohil Prasad
UC Berkeley
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Symplectic Geometry Seminar

Title Invariant subsets in three-dimensional energy surfaces
Speaker, Affiliation Rohil Prasad, UC Berkeley
Date, Time 10 March 2025, 15:15-16:15
Location HG G 43
Abstract The goal of this series of talks is to present a proof, at a higher level of detail than usual, of the following theorem. Let H be any smooth function on R^4 and let Y be any compact and regular level set. Then Y admits an infinite family of proper compact subsets that are invariant under the Hamiltonian flow, which in addition have dense union in Y. This improves on a 2018 result by Fish-Hofer, which showed the existence of one proper invariant subset. Related results were proved jointly with Dan Cristofaro-Gardiner for area-preserving surface diffeomorphisms and 3D Reeb flows. I will mention them if there is time.
Invariant subsets in three-dimensional energy surfaces read_more
HG G 43
17 March 2025
15:15-16:15 		Rohil Prasad
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Symplectic Geometry Seminar

Title Invariant subsets in three-dimensional energy surfaces II
Speaker, Affiliation Rohil Prasad,
Date, Time 17 March 2025, 15:15-16:15
Location HG G 43
Abstract The goal of this series of talks is to present a proof, at a higher level of detail than usual, of the following theorem. Let H be any smooth function on R^4 and let Y be any compact and regular level set. Then Y admits an infinite family of proper compact subsets that are invariant under the Hamiltonian flow, which in addition have dense union in Y. This improves on a 2018 result by Fish-Hofer, which showed the existence of one proper invariant subset. Related results were proved jointly with Dan Cristofaro-Gardiner for area-preserving surface diffeomorphisms and 3D Reeb flows. I will mention them if there is time.
Invariant subsets in three-dimensional energy surfaces II read_more
HG G 43
* 18 March 2025
15:15-17:00 		Rohil Prasad
Details

Symplectic Geometry Seminar

Title Invariant subsets in three-dimensional energy surfaces III
Speaker, Affiliation Rohil Prasad,
Date, Time 18 March 2025, 15:15-17:00
Location HG G 19.2
Abstract The goal of this series of talks is to present a proof, at a higher level of detail than usual, of the following theorem. Let H be any smooth function on R^4 and let Y be any compact and regular level set. Then Y admits an infinite family of proper compact subsets that are invariant under the Hamiltonian flow, which in addition have dense union in Y. This improves on a 2018 result by Fish-Hofer, which showed the existence of one proper invariant subset. Related results were proved jointly with Dan Cristofaro-Gardiner for area-preserving surface diffeomorphisms and 3D Reeb flows. I will mention them if there is time.
Invariant subsets in three-dimensional energy surfaces IIIread_more
HG G 19.2
24 March 2025
15:15-16:30 		Laurent Côté
University of Bonn
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Symplectic Geometry Seminar

Title Fukaya categories of conical symplectic resolutions
Speaker, Affiliation Laurent Côté, University of Bonn
Date, Time 24 March 2025, 15:15-16:30
Location HG G 43
Abstract Conical symplectic resolutions are a rather loosely defined class of hyperkähler varieties arising from canonical constructions in representation theory. Important examples include hypertoric varieties, Nakajima quiver varieties and Hitchin spaces. I will talk about Fukaya categories of conical symplectic resolutions. These are very rich objects, and they also turn out to be related to geometric representation theory. I will try to give an overview of this circle of ideas (much of which is not new in the symplectic literature). Any new content discussed in this talk is joint work with (subsets of) Benjamin Gammage, Justin Hilburn, Christopher Kuo, David Nadler and Vivek Shende.
Fukaya categories of conical symplectic resolutionsread_more
HG G 43
31 March 2025
15:15-16:15 		Umut Varolgunes
Koç University
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Symplectic Geometry Seminar

Title Contact big fiber theorems
Speaker, Affiliation Umut Varolgunes, Koç University
Date, Time 31 March 2025, 15:15-16:15
Location HG G 43
Abstract Entov-Polterovich's celebrated symplectic big fiber theorem says that any smooth map from a closed symplectic manifold to an Euclidean space with Poisson commuting components has at least one Hamiltonian non-displaceable fiber. I will discuss contact analogues of this theorem that we proved with Yuhan Sun and Igor Uljarevic using symplectic cohomology with support. Unlike the symplectic case, the validity of the statements require conditions on the closed contact manifold. One such condition is to admit a Liouville filling with non-zero symplectic cohomology. In the case of Boothby-Wang (pre-quantization) contact manifolds, we prove the result under the condition that the Euler class of the circle bundle is not an invertible element in the quantum cohomology of the base symplectic manifold. I will also explain how to obtain Givental's Legendrian rigidity result in the standard contact real projective spaces as an application.
Contact big fiber theoremsread_more
HG G 43
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15:15-16:15 		Maksim Stokic
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Symplectic Geometry Seminar

Title C⁰-Contact Geometry of Smooth Submanifolds
Speaker, Affiliation Maksim Stokic,
Date, Time NaN undefined NaN, 15:15-16:15
Location HG G 43
Abstract A contact homeomorphism is defined as a C⁰-limit of a sequence of contact diffeomorphisms. In this talk, we will discuss C⁰-flexibility and C⁰-rigidity properties of various classes of submanifolds in the contact setting. Our primary focus will be on Legendrian submanifolds, which exhibit C⁰-rigidity in the closed case and C⁰-flexibility in the open case. More precisely, we will focus on the following question: if a contact homeomorphism maps a Legendrian submanifold to a smooth submanifold, must the image necessarily be Legendrian?
C⁰-Contact Geometry of Smooth Submanifoldsread_more
HG G 43
14 April 2025
15:15-16:30 		Marcelo Alves
University of Antwerp
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Symplectic Geometry Seminar

Title From curve shortening to Birkhoff sections of geodesic flows
Speaker, Affiliation Marcelo Alves, University of Antwerp
Date, Time 14 April 2025, 15:15-16:30
Location HG G 43
Abstract In this talk, based on joint work with Marco Mazzucchelli, I will present some new results on the dynamics of geodesic flows of closed Riemannian surfaces, proved using the curve shortening flow. The first result is a forced existence theorem for orientable closed Riemannian surfaces of positive genus, asserting that the existence of a contractible simple closed geodesic γ forces the existence of infinitely many closed geodesics in every primitive free homotopy class of loops and intersecting γ. I will then explain how this type of result can be used to show the existence of Birkhoff sections for the geodesic flow of any closed orientable Riemannian surface.
From curve shortening to Birkhoff sections of geodesic flowsread_more
HG G 43
5 May 2025
15:15-16:15 		Noah Porcelli
Imperial College London, United Kingdom
Details

Symplectic Geometry Seminar

Title Title T.B.A.
Speaker, Affiliation Noah Porcelli, Imperial College London, United Kingdom
Date, Time 5 May 2025, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43
12 May 2025
15:15-16:15 		Filip Broćić
Universität Augsburg, Germany
Details

Symplectic Geometry Seminar

Title Title T.B.A.
Speaker, Affiliation Filip Broćić, Universität Augsburg, Germany
Date, Time 12 May 2025, 15:15-16:15
Location HG G 43
Title T.B.A.
HG G 43
19 May 2025
15:15-16:30 		Joel Schmitz
Université de Neuchâtel
Details

Symplectic Geometry Seminar

Title Title T.B.A.
Speaker, Affiliation Joel Schmitz, Université de Neuchâtel
Date, Time 19 May 2025, 15:15-16:30
Location HG G 43
Title T.B.A.
HG G 43
26 May 2025
15:15-16:30 		Fabian Ziltener
Details

Symplectic Geometry Seminar

Title Title T.B.A.
Speaker, Affiliation Fabian Ziltener,
Date, Time 26 May 2025, 15:15-16:30
Location HG G 43
Title T.B.A.
HG G 43

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