# Welcome to Freemath!

An online geometry seminar hosted at BBB on Tuesdays at (usually) 3 pm UTC+01:00.

A link is sent to the e-mail list before each seminar.

**9 June** Yuhan Sun (Stony Brook)

**Title:** Displacement energy of Lagrangian 3-spheres

**Abstract:** We study local and global Hamiltonian dynamical behaviours of some Lagrangian submanifolds near a Lagrangian sphere S in a symplectic manifold X. When dim S = 2, we show that there is a one-parameter family of Lagrangian tori near S, which are nondisplaceable in X. When dim S = 3, we obtain a new estimate of the displacement energy of S, by estimating the displacement energy of a one-parameter family of Lagrangian tori near S.

**2 June** Octav Cornea (Univ. of Montreal)

**Title:** Lagrangians, surgery and rigidity

**Abstract:** I will discuss a framework for analyzing classes of Lagrangian submanifolds that aims to endow them with a metric structure. The tools involve certain Floer type machinery for immersed Lagrangians. Part of the picture is a correspondence between certain cobordism categories endowed with surgery models and derived Fukaya categories. The talk is based on joint work with Paul Biran.

**26 May (at 10 am UTC+01:00) **Kazushi Ueda (Univ. of Tokyo, Japan)

**Title:** Noncommutative del Pezzo surfaces

**Abstract:** It is known after the works of Artin-Tate-Van den Bergh and Bondal-Polishchuk that noncommutative deformations of the projective plane are classified by triples consisting of a cubic curve and two line bundles. Similarly, Van den Bergh gave a classification of noncommutative quadric surfaces in terms of quadruples consisting of (a degeneration of) an elliptic curve and three line bundles. In the talk, I will discuss a joint work in progress with Tarig Abdelgadir and Shinnosuke Okawa on classifications of noncommutative del Pezzo surfaces.

**19 May** Gleb Smirnov (ETH, Zürich)

**Title:** Isotopy problem for symplectic forms in the presence of an anti-holomorphic involution

**Abstract:** Suppose we are given an algebraic surface equipped with an anti-holomorphic involution. From the symplectic viewpoint, a natural question to ask is: are there cohomologous anti-invariant symplectic forms on this manifold which are not isotopic within anti-invariant forms? And, if so, how many? During the talk, we will look at a particularly simple case of complex quadrics and do some explicit computations.

**12 May** Jenny August (MPIM, Bonn)

**Title:** Stability for Contraction Algebras

**Abstract:** For a finite dimensional algebra, Bridgeland stability conditions can be viewed as a continuous generalisation of tilting theory, providing a geometric way to study the derived category. Describing this stability manifold is often very challenging but in this talk, I'll look at a special class of symmetric algebras whose tilting theory is very well behaved, allowing us to describe the entire stability manifold of such an algebra. This is joint work with Michael Wemyss.

**5 May** Alexandru Oancea (Sorbonne, Paris)

**Title:** Duality for Rabinowitz-Floer homology

**Abstract:** I will explain a duality theorem with products in Rabinowitz-Floer homology. This has a bearing on string topology and explains a number of dualities that have been observed in that setting. Joint work in progress with Kai Cieliebak and Nancy Hingston.

**28 Apr.** Pierrick Bousseau (ETH, Zürich)

**Title:** Holomorphic curves, Lagrangians, and coherent sheaves

**Abstract:** I will describe a new correspondence between coherent sheaves on the projective plane and holomorphic curves in the projective plane with tangency condition along a smooth cubic curve. This correspondence is motivated by a combined application of hyperkaehler rotation and mirror symmetry. The actual proof uses tropical geometry as a connecting bridge.

Organised by Jonny Evans and Yankı Lekili