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
2025
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.
June 5: Severin Barmeier (University of Cologne)
Title: Fukaya categories of orbifold surfaces from deformation theory
Abstract: In work by Haiden, Katzarkov and Kontsevich, so-called gentle algebras, studied by representation theorists since the late '80s, naturally appear as endomorphism algebras of formal generators of Fukaya categories of surfaces. Lekili and Polishchuk showed that, conversely, any (graded) gentle algebra arises as such an endomorphism algebra. I will explain how deformation theory gives rise to a generalization of this correspondence. On the geometric side, one generalizes from smooth surfaces to surfaces with order 2 orbifold singularities. On the algebraic side, one naturally obtains A∞-deformations of gentle algebras. Restricting to formal generators of these Fukaya categories of orbifold surfaces, one naturally obtains a class of associative algebras strictly containing the class of so-called skew-gentle algebras, which have been studied in representation theory since the late '90s. In this way, A∞-deformations of graded gentle algebras give new insights into derived equivalences between strictly associative algebras. This talk is based on joint work with Sibylle Schroll and Zhengfang Wang and joint work in progress with Cheol-hyun Cho, Kyoungmo Kim, Kyungmin Rho, Sibylle Schroll and Zhengfang Wang.
May 8: Alice Merz (Université de Lille)
Title: The Alexander and Markov theorems for links with symmetries
Abstract: The Alexander theorem (1923) and the Markov theorem (1936) are two classical results in knot theory that show respectively that every link can be represented as the closure of a braid and that braids that have the same closure are related by a finite number of simple operations, namely conjugation and (de-)stabilization. In this talk we will construct an equivariant closure operator that takes in input two braids with a particular symmetry, called palindromic braids, and outputs a link that is preserved by an involution. Links with such symmetry are called strongly involutive, and when we restrict ourselves to knots they form a well-studied class of knots, called strongly invertible. We will hence give analogues of the Alexander and Markov theorems for the equivariant closure operator. In fact we will show that every strongly involutive link is the equivariant closure of two palindromic braids, drawing a parallel to the Alexander theorem. Moreover, we will see that any two pairs of palindromic braids yielding the same strongly involutive link are related by some operations akin to conjugation and (de-)stabilization.
April 9: Fadi Mezher (University of Copenhagen)
Title: On the arithmeticity of automorphism groups of high dimensional manifolds
Abstract: Given a smooth manifold of dimension at least 5, are the groups of isotopy classes of isomorphisms (both in the smooth and topological categories) arithmetic groups? Building on work of Sullivan, and combined with embedding calculus and profinite homotopy theory, we answer this question positively in the case of the topological mapping class group, and isolate the obstruction for arithmeticity in terms of
exotic spheres for the smooth mapping class group. Time permitting, I will discuss applications of the above result to the question of detectability of exotic spheres in embedding calculus, as part of ongoing joint work with M. Krannich and A. Kupers.
March 27: Dylan Cant (Université Paris-Saclay)
Title: Spectral diameter and Lagrangian capacity
Abstract: I will present some aspects of two papers (arXiv:2408.07214 and arXiv:2409.14142) concerning spectral invariants for compactly supported Hamiltonian systems in Cn. First, I will explain our discovery in arXiv:2408.07214 that the spectral diameter of a ball B(a) (of capacity a) is half of that of a cylinder Z(a). Thus the spectral diameter is not a normalized capacity. Then I will explain how this fact is used to prove certain cases of the conjecture that: any closed Lagrangian L in a ball B(1) in Cn, n>1, bounds holomorphic disks with area at most 1/2 (note that the Lagrangian lift of RPn-1 inside the boundary of B(1) bounds disks with area 1/2, so the conjecture cannot be improved). Our proof is based on a delicate version of the Lagrangian control property which incorporates spectral invariants, boundary depth, and the minimal area of holomorphic disks.
March 20: Adrien Currier (University of Nantes)
Title: Exact Lagrangians in cotangent bundles with locally conformally
symplectic structure
Abstract: First considered by Lee in the 40s, locally conformally
symplectic (LCS) geometry appears as a generalization of symplectic
geometry which allows for the study of Hamiltonian dynamics on a wider
range of manifolds while preserving the local properties of symplectic
geometry. After a long period of hibernation (especially as far as the
topological aspect is concerned), this topic has recently seen renewed
interest. However, to this day, the field of LCS topology remains vastly
unexplored.
In this talk, we will introduce the various objects of LCS geometry and
their behavior through both definitions and examples. We will then
explore some questions around an LCS version of the nearby Lagrangian
conjecture and some of the connections between LCS and contact
geometry.
March 13: Zuyi Zhang (Peking University)
Title: Immersed Lagrangian Floer theory, Lagrangian compositions, and bounding cochains on surfaces
Abstract: In this talk, I will first give the background of immersed Lagrangian Floer theory based on character varieties. Then I will focus on the relation between immersed quilted Lagrangian Floer theory and the usual immersed Lagrangian Floer theory when they are related by a Lagrangian correspondence, in the topological aspect. I will use many examples to explore this relation. If time permitted, I will give some examples about bounding cochains.
February 27: Tobias Ekholm (UU)
Title: The skein valued topological vertex
Abstract: We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Using 1-parameter families of curves at infinity, we derive three skein valued operator equations that determines the count uniquely. The solution count agrees with the topological vertex from topological string theory. The talk reports on joint work with P. Longhi and V. Shende.
February 20: Leon Menger (University of Notre Dame)
Title: The Fukaya–Morse Category: Enhancements and Field-Theoretic Approach
Abstract: The Fukaya–Morse category is an A-infinity-(pre-)category proposed by Fukaya in 93. It makes use of multiple Morse functions and their flow lines to represent higher Massey products and is intimately tied to the rational homotopy type of a manifold. In this talk we will go over its construction, highlight some of its issues and talk about a recent proposal by Chekeres, Losev, Mnev and Youmans to tackle them. We will then discuss further enhancements of this category to Morse–Bott functions and graphs with one loops. Time permitting I will sketch how the category arises as a particular effective field theory.
January 23: Russell Avdek (Sorbonne Université)
Title: Transverse stabilization in dim>3 contact topology
Abstract: We'll define stabilization for codim=2 contact manifolds of dim>3 contact manifolds so that a contact manifold is overtwisted iff its "standard contact unknot" is a stabilization. The talk will outline a proof that for n>1 there are two (smoothly unknotted) embedding of the standard contact 2n-1 sphere into the standard contact 2n+1 sphere which are formally contact isotopic, but which are not contact isotopic.