For the 2025-26 winter semester, the seminar meets on Mondays, 13:30-15:00 in the BMS Seminar Room (1.023) at the HU math department (Rudower Chaussee 25). See below for a precise schedule.
If you plan to participate in the seminar, please join the moodle (the enrollment key is "cookies"). The moodle will be used for occasional time-sensitive announcements. Users affiliated with the HU can access moodle using their HU username and password. Non-HU users can access it by following this link and then clicking on "Create new account".
The seminar will begin in the second week of the semester.
| Monday October 13, 2025 | No seminar due to dies academicus |
|---|---|
| Monday October 20, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: Gerard Bargalló i Gómez Topic: Markov numbers, singularities and symplectic geometry Abstract: Markov numbers are solutions to a certain diophantine equation that surprisingly pop up in unexpected places: quadratic forms, rational approximation, combinatorics, hyperbolic geometry, algebraic geometry and, indeed, symplectic geometry. After a short introduction to this equation and the century old uniqueness conjecture, I will explain some basics of singularity theory and how symplectic geometry helps in their study. The goal of the talk is to explore the following question: what are the possible degenerations of the complex projective plane? We will hopefully explain the elements and intuition behind an answer to this question (Evans-Smith), which involve the Markov numbers. If time permits, I will also talk about Vianna's tori, Fibonacci and Markov staircases for embeddings of balls and pinballs, and a problem I am working on with N. Adaloglou and J. Hauber: a nearby Lagrangian conjecture for the mysterious main characters of the talk. |
| Monday October 27, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: Chun-Sheng Hsueh Topic: An invitation to fibered links Abstract: We introduce the notion of fibered links and briefly explain their role in major conjectures in the field of low-dimensional topology. We then discuss some results related to fibered links, obtained in collaboration with B. Bode, which will form part of the speakerâÃÂÃÂs PhD thesis. |
| Monday November 3, 2025 | No seminar |
| Monday November 10, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: Partha Ghosh Topic: Seiberg-Witten equations in all dimensions Abstract: In this talk, I present a generalised form of the Seiberg-Witten equations in higher dimensions, originally introduced by Joel Fine and myself. Starting with an oriented n-dimensional Riemannian manifold equipped with a spinc-structure, I describe an elliptic system of equations that recovers the classical Seiberg-Witten equations in dimensions 3 and 4. I also adrress the construction of explicit solutions to the equations in dimensions 5, 6, and 8, where harmonic perturbation terms are sometimes necessary to ensure the existence of solutions. A key challenge in higher dimensions is the potential noncompactness of the solution space, in contrast to the compact moduli spaces in lower dimensions. In our constructions, this noncompactness is linked to the presence of certain odd-dimensional harmonic forms, with an explicit example provided in dimension 6. Finally, we discuss potential applications of these equations in symplectic geometry. |
| Monday November 17, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: Jean-Baptiste Bellynck Topic: Understanding mapping classes combinatorially Abstract: Mapping classes of surface homeomorphisms often appear in geometric group theory, geometric topology and many other fields. Especially classes of pseudo-Anosov maps are interesting as they express chaotic-like behaviour while still possessing an elaborate structure. This structure can easily be made visible by repeadedly applying a map to a curve. The curve will then converge to a foliation called the unstable foliation. Thurston homotoped the foliation into a weighted graph resembling a railway, aptly coined a measured train track by his students. Even though this construction does not yield a unique measured train track, it still contains a lot of information on the original homeomorphism class. Agol showed that it is possible to apply splits -- naturally, yielding a splitting sequence. Doing this often enough will, surprisingly, recreate the action of the original pseudo-Anosov homeomorphism on the train track. This makes it possible to study mapping classes by analysing their splitting sequences. Or in short, studying mapping classes combinatorially. |
| Monday November 24, 2025 13:30-15:00 RUD 25, Room 1.023 |
No seminar; Weinstein manifold seminar meeting instead at same time and place |
| Monday December 1, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: Medha Yelimeli Topic: Symplectic 4-manifolds with symplectic spheres Abstract: The existence of certain symplectically embedded spheres in a closed symplectic 4-manifold can impose strong restrictions on the manifold's topology and symplectic structure. Results of this kind were proved by McDuff in 1990-92 using the theory of J-holomorphic curves, which is especially powerful in dimension four. They also yield characterizations of symplectic rational surfaces and blown-up ruled surfaces precisely as those closed symplectic 4-manifolds possessing non-vanishing Gromov–Witten invariants. The aim of this talk is to explain these results along with the key techniques that underlie them. |
| Monday December 8, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: Gerard Bargalló i Gómez Topic: The index toolbox Abstract: In this talk I will introduce the Conley-Zehnder index and explain its crucial role in Floer theory and SFT. I hope to describe its key role in dynamical questions, such as showing that all simply connected Riemannian manifolds (under some topological conditions) have infinitely many different closed geodesics; or that Hamiltonian diffeomorphisms of symplectic Calabi-Yau's must have infinitely many periodic points. I also hope to touch on a striking application in algebraic geometry: a normal 3-fold singularity is smooth if and only if its link is the standard contact 5-sphere. |
| Monday December 15, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: David Suchodoll Topic: Knot Floer immersed curves - Part II Abstract: We recall the connection between knot Floer homology and the Hanselman-Rasmussen-Watson construction of immersed curves and their cables. Building on a result of Hom, Lidman, and Park, we establish a deeper relationship governing the knot Floer order under cabling. If time permits, we will also discuss how HFK concordance invariants can be extracted from these immersed curves. |
| Monday January 5, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: TBA Topic: TBA |
| Monday January 12, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: TBA Topic: TBA |
| Monday January 19, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: TBA Topic: TBA |
| Monday January 26, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: TBA Topic: TBA |
| Monday February 2, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: TBA Topic: TBA |
| Monday February 9, 2025 13:30-15:00 RUD 25, Room 1.023 |
Speaker: TBA Topic: TBA |