Abstracts

• ATHANASE PAPADOPOULOS:

 Title:  Rigidity for mapping class group actions.

Abstract: I will describe several rigidity theorems for actions of mapping class groups. I will mention in particular two results I obtained with Mustafa Kurkmaz, in 2010 and 2012, on actions of mapping class groups on graph complexes on surfaces, then three rigidity results I obtained with Ken’ichi Ohshika in 2018, 2019 and 2024 on actions of mapping class groups on spaces of laminations on surfaces, then finally recent rigidity results I obtained with Yi Huang and Ken’ichi Ohshika on the infinitesimal rigidity of  mapping class group actions on Teichm\"uller space equipped with the Thurston metric.

•  SAUL SCHLEIMER

Title: Solving the word problem in the mapping class group in quasi-linear time.

Abstract: Mapping class groups of surfaces are of fundamental importance in dynamics, geometric group theory, and low-dimensional topology.  The word problem for groups in general, the definition of the mapping class group, its finite generation by twists, and the solution to its word problem were all set out by Dehn [1911, 1922, 1938].  Some of this material was rediscovered by Lickorish [1960's] and then by Thurston [1970-80's] -- they gave important applications of the mapping class group to the topology and geometry of three-manifolds.  In the past fifty years, various mathematicians (including Penner, Mosher, Hamidi-Tehrani, Dylan Thurston, Dynnikov) have given solutions to the word problem in the mapping class group, using a variety of techniques.  All of these algorithms are quadratic-time. 

•  HARRY PETYT:

Title: Introduction to the hierarchical perspective on mapping class groups

     Abstract: The curve graph of a surface S is a hyperbolic space that holds a lot of information about the 

mapping class group MCG(S). The "hierarchy" approach to studying the geometry of mapping class groups consists in trying to reduce questions about MCG(S) to questions about the curve graphs of the subsurfaces of S and relations between them. In this talk I will give an introduction to some of these techniques and outline some of their successes.

• SINEM ONARAN:

     Title: Pure Braids, Contact Structures and Legendrian Knots

     Abstract: In this talk, I will discuss the pure braided plat presentation for knots and links in lens spaces. After a brief introduction on contact 3-manifolds and open book decompositions, we will focus on a class of knots in contact 3-manifolds called Legendrian knots. Using the pure braided plat presentation for knots, I will present an algorithm to put the Legendrian knots on a planar page of an open book decomposition whose monodromy is a product of positive Dehn twists. I will conclude with a discussion of its applications. 

• BURAK OZBAGCI:

     Title: Symplectic rational homology ball fillings of Seifert fibered spaces

     Abstract: (This is a joint work with J. Etnyre and B. Tosun)  We characterize when some small Seifert       fibered spaces can be the convex boundary of a symplectic rational homology ball and give strong restrictions for others to bound such manifolds. As part of this we show that the only spherical 3-manifolds that are the boundary of a symplectic rational homology ball are the lens spaces L(p^2,pq-1) found by Lisca. 

• INANC BAYKUR:

Title: Geometric simple connectivity in dimension four 

Abstract: Every simply connected closed smooth manifold of dimension other than four admits a handle decomposition without 1-handles; this follows from the celebrated work of Smale in higher dimensions and of Perelman in dimension three. Whether the same holds in dimension four remains a wide open question. I’ll survey the state of the art and explain our recent (partial) progress, which includes settling a 30-year-old problem from Kirby’s list. 

• JAVIER ARAMAYONA:

    Title: Lego surfaces and their asymptotically rigid mapping class group

    Abstract: A Lego surface is a non-compact surface obtained by gluing copies of a fixed compact surface in an  inductive manner. To every Lego surface one may associate its asymptotically rigid mapping class group, whose elements are isotopy classes of homeomorphisms of the Lego surface which are "eventually trivial" in a suitable sense. Through their action on the space of ends of the Lego surface, asymptotically rigid mapping class groups resemble some classical families of groups, namely Thompson groups and Houghton groups. 

After introducing all these concepts, I will talk about the finiteness properties enjoyed by these groups, which are determined by the end space of the corresponding Lego surface.

• NICK VLAMIS:

Title: Large-scale geometry of huge groups

Abstract: I will introduce and discuss SB-generated groups, which are the discrete CB-generated groups in the language of Rosendal. These groups generalize finitely generated groups by admitting generating sets for which the large-scale geometry of the associated word metric is an algebraic invariant. This framework enables the application of tools from geometric group theory to the study of large abstract groups. The main focus of the talk will be to establish a natural and rich family of examples, including homeomorphism groups of closed manifolds and a class of big mapping class groups.

• JING TAO:

Title: Homomorphisms between big mapping class groups

      Abstract: I will talk about some recent work on homomorphisms between big mapping class groups.

• CHRIS LEININGER:

Title: Atoroidal Surface Bundles

     Abstract: I will discuss joint work with Autumn Kent in which we establish the existence of purely pseudo-Anosov surface subgroups of mapping class groups. We do this by constructing a type-preserving representation of the figure eight knot group into the mapping class group of the thrice-punctured sphere. As a corollary we obtain the first examples of closed atoroidal surface bundles over surfaces.

• CAGLAR UYANIK:

     Title: Cannon-Thurston maps, boundaries, and rigidity

     Abstract:  Cannon and Thurston showed that a closed hyperbolic 3-    manifold that fibers over the circle gives rise to a sphere-filling curve. The universal cover of the fiber surface is quasi-isometric to the hyperbolic plane, whose boundary is a circle, and the universal cover of the 3-manifold is 3-dimensional hyperbolic space, whose boundary is the 2-sphere. Cannon and Thurston showed that the inclusion map between the universal covers extends to a continuous map between their boundaries, whose image is onto. In particular, any measure on the circle pushes forward to a measure on the 2-sphere using this map. We compare several natural measures coming from this construction.

•  VALENTINA DISARLO:

Title: The model theory of the curve graph 

• Abstract: The curve graph of a surface of finite type is a graph that encodes the combinatorics of isotopy classes of simple closed curves. It is a fundamental tool for the study of the geometric group theory of the mapping class group. In 1987 N.K. Ivanov proved that the automorphism group of the curve graph of a finite surface is the extended mapping class groups. In the following decades, many people proved analogue results for many "similar" graphs, such as the pants graph, the arc graph, etc. In response to the many results, N.V. Ivanov formulated a metaconjecture. which asserts that any "natural and sufficiently rich" object associated to a surface has automorphism group isomorphic to the extended mapping class group. In this talk, I will present a joint work with Thomas Koberda (Virginia) and Javier de la Nuez Gonzalez (KIAS) where we provide a model theoretical framework for Ivanov’s metaconjecture and we conduct a thorough study of curve graphs from the model theoretic point of view, with particular emphasis in the problem of interpretability between different "similar" geometric complexes. In particular, we will prove that the curve graph of a surface of finite type is w-stable. This talk does not assume any prior knowledge in model theory.

• HUGO PARLIER

     Title: Criss-crossing curves

    Abstract: The crossing lemma for simple graphs gives a lower bound on  the  necessary number of crossings of any drawing of a graph in the plane in terms of its number of edges and vertices. Viewed through the lens of topology, thisleads to other questions about arcs and curves on surfaces.  

In joint work with Alfredo Hubard, we provide estimates on the necessary number of intersections of any realization of $m$ distinct homotopy classes of curves on a (fixed) surface. These estimates allow us to answer questions raised by Pach, Tardos, and Toth concerning a version of the crossing lemma for graph drawings with non-homotopic edges. Our approach uses the geometry of hyperbolic surfaces in an essential way. 

• ELIF DALYAN

Title: Free groups and free products generated by Dehn twists

     Abstract: We discuss subgroups of the mapping class group generated by Dehn twists, focusing on the free ones. We begin with the classical result that Dehn twists about two curves with geometric intersection number at least two generate a free group of rank two. We provide a new proof of this theorem using Dynnikov coordinates, update rules, and the Ping-Pong Lemma. Then, we introduce our recent result concerning subgroups generated by more than two Dehn twists on the n-punctured disk. By identifying a class of curves called opposite curves and introducing the concept of complete partitions, we characterize when Dehn twists about such collection of curves generate either a free group or a free product of free Abelian groups. 

• KATE VOKES

Title: Thickness and relative hyperbolicity for graphs of multicurves

Abstract: Various graphs associated to surfaces have proved to be important tools for studying the large-scale geometry of mapping class groups of surfaces, among other applications. A seminal paper of Masur and Minsky proved that perhaps the most well-known example, the curve graph, has the property of Gromov hyperbolicity, a powerful notion of negative curvature. However, this is not the case for every naturally defined graph associated to a surface. We will present joint work with Jacob Russell classifying a wide family of graphs associated to surfaces according to whether the graph is Gromov hyperbolic, relatively hyperbolic or not relatively hyperbolic.

Lightning Talks

•  Ethan Dlugie

Title: Truncated braid groups 

• Ignat Soroko

Title: Artin groups via mapping class groups 

• Saliha Kıvanç 

Title: Legendrian Non-simple Whitehead Double of Trefoil 

• Megha Bhat 

Title: Homeomorphism groups of ordinals

• Joshua Perlmutter

Title: Graph Products of Morse Local-to-Global Groups 

• Filippo Bianchi

Title: Spin mapping class groups and 4-manifolds

• Kerem Inal

Title: Minimal generating set for spin mapping class group 

• Sandy Guadalupe Aguilar Rojas

Title: The Geometry of the Mapping Class Group of a Non-Oriented Surface 

• Sayantika Mondal: 

Title: Distinguishing filling curves via designer metrics