Geometry and Topology seminar series
The seminars are usually held on Thursdays at 13:15 in room Å64119 and on Zoom.
For more info contact the organiser: Alex Takeda
Upcoming seminars
Previous talks
2026
April 23: Tobias Ekholm (UU)
Title: U(1)-invariant associatives and skein valued curve counts
Abstract: Consider an orientable 3-manifold and a Lagrangian in its cotangent bundle that projects to the zero-section as an n-fold cover branched over a link. We equip the 7-manifold that fibers over the cotangent bundle with circle fibers degenerating over the Lagrangian as a Hopf bundle over the linking sphere with a closed positive 3-form invariant under the circle action. We then relate invariant associative submanifolds in the 7-manifold to holomorphic curves in the cotangent bundle with boundary on the Lagrangian, and discuss the resulting deformation invariant skein valued counts. The talk reports on joint work in progress with Esfahani, Shende, and Wang.
April 23: Paolo Ghiggini (University of Grenoble)
Title: Floer homology for singular Lagrangians; a theory looking for applications
April 16: Mark Lawrence
Title: Polynomial hulls of fibered tori in S^1 x C
Abstract: For a compact set in K ⊆ C^n, very little can be said about its polynomial hull, K^. The best case is when the polynomial hull is a union of analytic varieties, but even for a smooth manifold, this may not be true. The case of a totally real torus in S^1 x C is more promising, and there are some results in this case. Results depend on the knot class of the core of the torus. For a torus whose core is isotopic to wn = z, I can how that the polynomial hull is a union of n-sheeted discs. This is an improvement of a result of Duval and Lawrence for the case n = 2. The proof contains an analysis of a family index 2 discs which must pass through a singular totally real manifold. Open questions regarding more general knot types will be discussed.
April 9: Coline Emprin (Stockholm University)
Title: Obstruction theory to formality and homotopy equivalences
Abstract: Here are seemingly unrelated problems: Koszul duality for the category of a reductive group in representation theory, the existence of a K-contact non-Sasakian manifold in differential geometry, splitting Drinfeld space’s de Rham complex in the p-adic Langlands program, deformation quantization of Poisson manifolds in mathematical physics. And yet, all of them boil down to the same question: formality. A differential graded algebraic structure A (e.g. an associative algebra, a Lie algebra, a pre-Calabi-Yau algebra, etc.) is formal if it is related to its homology H(A) by a zig-zag of quasi-isomorphisms preserving the algebraic structure.
Kaledin classes were introduced as an obstruction theory fully characterizing the formality of associative algebras over a characteristic zero field. In this talk, I will present a generalization of Kaledin classes to any coefficients ring, to other algebraic structures (encoded by operads, possibly colored, or by properads), and to address a more general problem: the existence of homotopy equivalences between algebraic structures. On the one hand, it incorporates aforementioned results into a single theory. On the other hand, it provides tools to study these questions in cases little studied hitherto: over any coefficient ring and for algebraic structures with several outputs, algebras encoded by properads.
March 19: Thomas Kragh (UU)
Title: Why twisted algebraic K-theory of spaces should enhance family Floer invariants
Abstract: In this talk, I will discuss how twisted algebraic K-theory of spaces should lift the usual notion of family Floer homology. That is, I want to present a heuristic that should generalize the invariants we obtained from twisted generating functions in cotangent bundles (arising from joint work with Abouzaid, Courte and Guillermou). These invariants, which are related to algebraic K-theory of spaces, were seen to be much stronger than the usual family Floer homology given by the family of fibers in the cotangent bundle (at least as treated so far). I will rely heavily on very specific examples for motivation. This heuristic generalization, motivates the need for a twisted version of Waldhausen's theorem, which would relate a twisted assembly map to a space of twisted h-cobordisms. If time permits, I will discuss ongoing joint work with Oldervoll trying to prove such a twisted Waldhausen theorem – relying on a category closely related to the category of flow categories.
March 19: Ipsita Datta (ETH Zurich)
Title: Geometry of Lagrangian Tangles
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 gradient field tangent to the boundary. We show existence of a LES of persistence modules giving quantitative obstructions to the existence of Lagrangian tangle links.
This is joint work with Josh Sabloff (Haverford College).
March 5: Matthias Scharitzer (UU)
Title: A Reconstruction Lemma for Enhanced Bypass Sequences
Abstract: An often used folklore theorem in 3D contact topology asserts that one can classify contact structures on Σ × I using bypasses. In joint work with Licata and Vértesi, we use foliation-theory to assign a combinatorial invariant to such contact structures. We term this invariant an Enhanced Bypass Sequence. In ongoing work, I prove that this invariant admits a Reconstruction Lemma, i.e. one can reconstruct a unique contact structure from its data, and that it implies the folklore theorem about classification using bypasses.
January 29: Jian Qiu (UU)
Title: Tangle invariants valued in derived category of sheaves
Abstract: In this talk, I report on the joint project with Alex Takeda. In their work, Cautis and Kamnitzer constructed a family of varieties Y_n, and associate to a tangle of m incoming and n outgoing strands a functor between derived category of categories of sheaves on Y_m and Y_n. More specifically, this functor is a Fourier Mukai transform, so the invariant assigned to the tangle is the FM kernel. This gives an alternative construction of categorification of the Jones polynomial. Our main result is to introduce the tilting complex into the computation, so that the construction is lifted up to the homotopy category, and the invariant assigned to a tangle is an explicit complex of projectives in the homotopy category of modules of the quiver algebra associated to Y_n.
January 22: Michael Sullivan (UMass Amherst)
Title: Higher torsion of Legendrians in one-jet space
Abstract: I'll introduce higher torsion from algebraic topology using the language of generating families for Legendrian submanifolds in standard contact one-jet spaces. I'll also propose a possible higher-dimensional generalization of rulings for such Legendrians. If the Legendrian is the lift of a nearby Lagrangian with such a ruling, then the torsion is trivial. (Although the torsion is non-trivial in general, any Legendrian which is the lift of a nearby Lagrangian and with non-trivial torsion would disprove the Nearby Lagrangian Conjecture.) This is joint work in progress with Dani Alvarez-Gavela and Kiyoshi Igusa.
January 22: Filip Broćić (University of Augsburg)
Title: Arnol'd's chord conjecture for conormal Legendrian lifts
Abstract: The chord conjecture, due initially to Arnol'd in the case of the standard contact three-sphere, asserts the existence of a Reeb chord with boundary on every closed Legendrian submanifold of a closed contact manifold for every contact form. This conjecture was established in various settings by Cieliebak, Mohnke, Hutchings and Taubes, and others. In this talk, I will sketch a proof of the chord conjecture for conormal bundles of closed submanifolds of any closed manifold seen as Legendrians in the co-sphere bundle. This generalizes a result of Grove in Riemannian geometry regarding the existence of geodesics normal to the submanifold. The method of proof involves wrapped Floer cohomology with local coefficients. This talk is based on joint work with Dylan Cant and Egor Shelukhin.
2025
December 4: Victor Carmona (MPI-MiS Leipzig)
Title: Not too little discs and TQFTs
Abstract: The celebrated approach to perturbative QFTs proposed by K.Costello and O.Gwilliam uses factorization algebras as the main algebraic device to encode algebras of observables. An important point about this formulation is that the RG flow on field theories over the n-dimensional euclidean space becomes a simple action on factorization algebras. In this talk, we will motivate a closely related "RG flow" and the whole idea of renormalization using prefactorization algebras defined at fixed scales. We will discuss how this approach allows us to show that "topological field theories" over euclidean spaces are always renormalizable. As an application, we will explain how this can be used to construct the canonical deformation quantization of constant Poisson structures via discrete models. Time permitting, we will address what happens when the theory has defects. This talk is based on arXiv:2407.18192, joint with D.Calaque.
November 20: Daniil Mamaev (UU)
Title: On Banach’s isometric subspaces problem
Abstract: In 1932 Banach asked if there exists a non-Euclidean normed vector space V and an integer 2 <= n < dim V such that all n-dimensional subspaces of V are isometric. The answer is negative for some pairs (n, dim V) and unknown for others. I will explain a novel differential geometric approach to the problem that settles the case n = 3. This is joint work with S. Ivanov and A. Nordskova.
November 13: Santiago Achig (UU)
Title: Singular Lagrangian Fibrations and Applications to Symplectic Embeddings
Abstract: We construct explicit singular Lagrangian fibrations on disk cotangent bundles and show how simple manipulations of their base diagrams produce toric domains that encode sharp symplectic embeddings. The method recovers and streamlines known computations, offering a geometric, picture-driven route to embedding results. (Joint with R. Vianna and A. Vicente).
November 3: Thomas Wasserman (Aalto University)
Title: A unitary three-functor formalism for commutative Von Neumann algebras
Abstract: Six-functor formalisms are ubiquitous in mathematics, and I will start this talk by giving a quick introduction to them. A three-functor formalism is, as the name suggests, (the better) half of a six-functor formalism. I will discuss what it means for such a three-functor formalism to be unitary, and why commutative von Neumann algebras (and hence, by the Gelfand-Naimark theorem, measure spaces) admit a unitary three-functor formalism that can be viewed as mixing sheaf theory with functional analysis. Based on joint work with André Henriques.
October 23: Noah Porcelli (MPIM Bonn)
Title: Bordism from quasi-isomorphism
Abstract: The Fukaya category detects lots of topological infomation, both intrinsic and extrinsic, about (closed, exact) Lagrangians: such as their cohomology ring (intrinsic) and their fundamental class in the ambient symplectic manifold (extrinsic). I'll explain why it also detects bordism-theoretic infomation, with applications to studying nearby Lagrangians. This involves using a spectral Fukaya category, and using obstruction theory to "lift'' an equivalence from the ordinary to the spectral world. Based on joint work with Ivan Smith.
October 23: Simo S. Mthethwa (University of KwaZulu-Natal), Smegnsh Demelash (Kotebe University of Education)
Titles: "A closer look at Michael's J-spaces and the like" (Simo) and "Rational Homotopy Type and Nilpotency of Mapping Spaces Between Projective Spaces" (Smegnsh)
Abstrcts: see webpage
October 16: Oscar Harr (Stockholm University)
Title: Stokes theorem and characteristic classes of manifold bundles
Abstract: The family Stokes theorem is an equation relating fiber integration along a bundle of manifolds (with boundary) and its associated boundary bundle. We lift this equation to a commutative diagram in the derived category of sheaves on the base space of the family, with coefficients in an arbitrary presentably symmetric monoidal stable ∞-category. Using this diagram, we deduce new relations among characteristic classes of bundles of manifolds with boundary.
October 2: Maksim Stokic (UU)
Title: C⁰-Contact Geometry of Surfaces in 3-Manifolds
Abstract: We study the behavior of surfaces in contact 3-manifolds under C⁰-limits of contactomorphisms. We prove that contact homeomorphisms preserve characteristic foliations on surfaces: singular points are mapped to singular points, and the image of every 1-dimensional leaf is again a 1-dimensional leaf in the image surface. As a consequence, regular coisotropic surfaces are C⁰-rigid. In contrast, convex surfaces exhibit C⁰-flexibility: we construct a contact homeomorphism sending a convex 2-torus to a non-convex one. This is joint work with Baptiste Serraille.
September 11: Tobias Ekholm (UU)
Title: Skein trace formulas and applications
Abstract: We show that flow tree degenerations of holomorphic curves give rise to skein lifts for multiple covers of a 3-manifold branched along a link. This leads to wall-crossing formulas and a new formula for the HOMFLYPT polynomial from a braid presentation of a knot. The talk reports on joint work with Longhi, Park, and Shende.
September 4: Yin Li (UU)
Title: The symplectic topology of contractible affine surfaces of log Kodaira dimension one
Abstract: Eliashberg's regular Lagrangian conjecture, if ture, would imply the homological essentiality of closed exact Lagrangian submanifolds in Weinstein manifolds. However, the progress towards this conjecture is very little. One instance of such an embrassment is that C^2 is the only known contractible affine surface which does not contain an exact Lagrangian surface at this point. In this talk, I will sketch a proof of the nonexistence of closed exact Lagrangian surfaces in contractible affine surfaces of log Kodaira dimension 1. The proof is based on three ingredients: Seidel representation of the fundamental group of Liouville automorphisms, McLean's technique for the symplectic cohomology of Kaliman modifications and Ganatra-Pomerleano's logarithmic PSS map.