Current contacts: Dave Futer, Matthew Stover, or Sam Taylor.
The Seminar usually takes place on Wednesdays at 2:30 PM in Room 617 of Wachman Hall.
Wednesday January 31, 2024 at 14:30, Wachman 617
Transverse surfaces to pseudo-Anosov flows
Samuel Taylor (Temple University)
Our goal will be to describe some work-in-progress (joint with Landry and Minsky) that classifies transverse surfaces to pseudo-Anosov flows on 3—manifolds. This is an introductory talk and there’ll be lots of background and examples.
Wednesday February 21, 2024 at 14:30, Wachman 617
Quotients of free products
Thomas Ng, Brandeis University
Abstract: Quotients of free products are natural combinations of groups that have been exploited to study embedding problems. These groups have seen a resurgence of attention from a more geometric point of view following celebrated work of Haglund--Wise and Agol. I will discuss a geometric model for studying quotients of free products. We will use this model to adapt ideas from Gromov's density model to this new class of quotients, their actions on CAT(0) cube complexes, and combination theorems for residual finiteness. Results discussed will be based on ongoing work with Einstein, Krishna MS, Montee, and Steenbock.
Friday February 23, 2024 at 15:00, Swarthmore College, Science Center room 104
An eye towards understanding of smooth mapping class groups of 4-manifolds
Anubhav Mukherjee, Princeton University
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: The groundbreaking research by Freedman, Kreck, Perron, and Quinn provided valuable insights into the topological mapping class group of closed simply connected 4-manifolds. However, the development of gauge theory revealed the exotic nature of the smooth mapping class group of 4-manifolds in general. While gauge theory can at times obstruct smooth isotopy between two diffeomorphisms, it falls short of offering a comprehensive understanding of the existence of diffeomorphisms that are topologically isotopic but not smoothly so. In this talk, I will elucidate some fundamental principles and delve into the origins of such exotic diffeomorphisms. This is my upcoming work joint with Slava Krushkal, Mark Powell, and Terrin Warren.
In the morning background talk (at 10am), I will give an overview of mapping class groups of 4-manifolds.Friday February 23, 2024 at 16:30, Swarthmore College Science Center room 104
Canonical hierarchical decompositions of free-by-cyclic groups
Jean-Pierre Mutanguha, Princeton University and IAS
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: Free-by-cyclic groups can be defined as mapping tori of free group automorphisms. I will discuss various dynamical properties of automorphisms that turn out to be group invariants of the corresponding free-by-cyclic groups (e.g. growth type). In particular, certain dynamical hierarchical decompositions of an automorphism determine canonical hierarchical decompositions of its mapping torus. In the intro talk, I will discuss how Bass-Serre theory (actions on simplicial trees) gives us a grip on these groups.
In the morning background talk, at 11:30am, I will introduce free-by-cyclic groups from a tree's point of view.Wednesday February 28, 2024 at 14:30, Wachman 617
Dilatations of pseudo-Anosov maps and standardly embedded train tracks
Chi Cheuk Tsang (UQAM)
The minimum dilatation problem asks for the minimum value of the dilatation among all pseudo-Anosov maps defined on a fixed surface. This value can be thought of as the smallest amount of mixing one can perform on the surface while still doing something topologically interesting. In this talk, we will present some recent progress on the fully-punctured version of this problem. The strategy for proving these results involves something called standardly embedded train tracks. We will explain what these are and formulate some future directions that may be tackled using this technology. This is joint work with Eriko Hironaka, and with Erwan Lanneau and Livio Liechti.
Wednesday March 13, 2024 at 14:30, Wachman 617
Conformal dimension for Bowditch boundaries of Coxeter groups
Rylee Lyman
Rutgers University, Newark
Abstract: Coxeter groups, defined by a labeled simplicial graph, are a beautiful family of groups which are in a certain precise sense generated by reflections. With Elizabeth Field, Radhika Gupta and Emily Stark, we study the family of Coxeter groups whose defining graph is complete with all edges labels at least three. We show that they fall into infinitely many quasi-isometry classes. These groups were previously studied by Haulmark, Hruska and Sathaye, who showed that generically they all have visual boundary the Menger curve and posed the question of quasi-isometric classification. Along the way to our proof, we show that these groups have a geometrically finite action on a CAT(-1) space, whose geometry can be studied by reasoning about hyperbolic 3-space. I think this space and the geometric reasoning about it are really pretty — I'd like to spend most of the talk focusing on it.Wednesday March 20, 2024 at 14:30, Wachman 617
Satellite actions on knot concordance
Allison Miller, Swarthmore College
Abstract: The collection of knots in the 3-sphere modulo a 4-dimensionally defined equivalence relation called "concordance", is not just a set but a group and a metric space as well. Via the satellite construction, every knot in a solid torus induces a self-map of the concordance set/ group/ metric space. In this talk, we'll survey what is known about these functions: When are they injective/ surjective/ bijective? When are they group homomorphisms? How do they interact with the metric space structure? We will end by discussing recent joint work of mine with two Swarthmore students, Randall Johanningsmeier and Hillary Kim, that unexpectedly provided significant progress towards answering one of these questions.
Friday March 22, 2024 at 14:30, DRL room A4, University of Pennsylvania
Measuring fundamental groups using cochains and Hopf invariants
Nir Gadish, University of Michigan
PATCH Seminar, join with Bryn Mawr, Haverford, Penn, and Swarthmore
Abstract: The classical Hopf invariant uses the linking of two generic fibers to detect elements in higher-homotopy groups of spheres. Sinha-Walter generalized this idea and used "higher linking" to completely characterize elements in the (rational) homotopy groups of any simply connected space. By extending this setup to measure fundamental groups, we arrive at a new invariant theory for groups, which we have termed letter braiding. This is effectively a 0-dimensional linking theory for letters in words, and it realizes every finite-type invariant of any group. We will discuss the topological origins of this theory, its connection to loop spaces, and will explore an application to mapping class groups of surfaces.
In the background talk (10am in room A8), I will discuss studying topological spaces using invariants of words and groups.Friday March 22, 2024 at 16:00, DRL room A4, University of Pennsylvania
Interpolation method in mean curvature flow
Ao Sun, Lehigh University
PATCH Seminar, joint with Bryn Mawr, Haverford, Penn, and Swarthmore
Abstract: The interpolation method is a very powerful tool to construct special solutions in geometric analysis. I will present two applications in mean curvature flow: one is constructing a new genus one self-shrinking mean curvature flow, and another one is constructing immortal mean curvature flow with higher multiplicity convergence. The talk is based on joint work with Adrian Chu (UChicago) and joint work with Jingwen Chen (UPenn).
In the morning background talk (11:30-12:30 in room A8) I will discuss singularities and solitons of mean curvature flow.
Wednesday March 27, 2024 at 14:30, Wachman 617
Convergence of unitary representations and spectral gaps
Michael Magee, Durham University
Abstract: Let $G$ be an infinite discrete group e.g. hyperbolic 3-manifold group. Finite dimensional unitary representations of $G$ in fixed dimension are usually quite hard to understand. However, there are interesting notions of convergence of such representations as the dimension tends to infinity. One notion — strong convergence — is of interest both from the point of view of $G$ alone but also through recently realized applications to spectral gaps of locally symmetric spaces. For example, this notion bypasses (unconditionally) the use of Selberg's Eigenvalue Conjecture in obtaining existence of large area hyperbolic surfaces with near-optimal spectral gaps.
The talk is a discussion on these themes, based on joint works with W. Hide, L. Louder, D. Puder, J. Thomas.
Tuesday April 2, 2024 at 11:00, Wachman 527
Two-generator subgroups of free-by-cyclic groups
Edgar Bering, San Jose State University
Abstract: In general, the classification of finitely generated subgroups of a given group is intractable. Restricting to two-generator subgroups in a geometric setting is an exception. For example, a two-generator subgroup of a right-angled Artin group is either free or free abelian. Jaco and Shalen proved that a two-generator subgroup of the fundamental group of an orientable atoroidal irreducible 3-manifold is either free, free-abelian, or finite-index. In this talk I will present recent work proving a similar classification theorem for two generator mapping-torus groups of free group endomorphisms: every two generator subgroup is either free or conjugate to a sub-mapping-torus group. As an application we obtain an analog of the Jaco-Shalen result for free-by-cyclic groups with fully irreducible atoroidal monodromy. This is joint work with Naomi Andrew and Ilya Kapovich.
Friday April 12, 2024 at 10:00, Wachman 617
PATCH: An introduction to algebraic K-theory
Anna Marie Bohmann (Vanderbilt)
Algebraic K-theory is an important invariant of rings (and other related mathematical things). In this talk, we'll give a little bit of background on the classical story of algebraic K-theory and then talk about some of the many ways it's developed in recent years.
Friday April 12, 2024 at 11:30, Wachman 617
PATCH: The coarse geometry of Teichm\"uller space and a new notion of complexity length
Spencer Dowdall (Vanderbilt)
I will review the key features of Teichmuller space that are relevant to counting lattice points for the action of the mapping class group. Specifically, after introducing Teichmuller space I will discuss the thin regions and their inherent product structure. This will lead us to subsurface projections and Rafi's distance formula and associated combinatorial description of how Teichmuller geodesics pass through thin regions of subsurfaces. I will then introduce a new notion of "complexity length" in Teichmuller space that aims to carefully account for this motion of geodesics through product regions in a way that gives better control on the multiplicative errors and lends itself to counting problems.
Friday April 12, 2024 at 14:30, Wachman 617
PATCH: Scissors congruence and the K-theory of covers
Anna Marie Bohmann (Vanderbilt)
Scissors congruence, the subject of Hilbert's Third Problem, asks for invariants of polytopes under cutting and pasting operations. One such invariant is obvious: two polytopes that are scissors congruent must have the same volume, but Dehn showed in 1901 that volume is not a complete invariant. Trying to understand these invariants leads to the notion of the scissors congruence group of polytopes, first defined the 1970s. Elegant recent work of Zakharevich allows us to view this as the zeroth level of a series of higher scissors congruence groups.
In this talk, I'll discuss some of the classical story of scissors congruence and then describe a way to build the higher scissors congruence groups via K-theory of covers, a new framework for such constructions. We'll also see how to relate coinvariants and K-theory to produce concrete nontrivial elements in the higher scissors congruence groups. This work is joint with Gerhardt, Malkiewich, Merling and Zakharevich.
Friday April 12, 2024 at 16:00, Wachman 617
PATCH: Counting mapping classes by Nielsen-Thurston type
Spencer Dowdall (Vanderbilt)
I will discuss the growth rate of the number of elements of the mapping class group of each Nielsen-Thurston type, that is, either finite-order, reducible, or pseudo-Anosov, measured via the number of lattice points in a ball of radius $R$ in Teichm\"uller space. For the whole mapping class group of the closed genus $g$ surface, Athreya, Bufetov, Eskin, and Mirzakhani have shown this quantity is asymptotic to $e^{(6g-6)R}$ as $R$ tends to infinity. Maher has obtained the same asymptotics for those orbit points that are translates by pseudo-Anosov elements. Obtaining a count for the finite-order or reducible elements is significantly more challenging due to the fact these non-generic subsets are not perceptible to the standard dynamical techniques. I will explain a naive heuristic for why the finite-order elements should grow at the rate of $e^{(3g-3)R}$, that is, with half the exponent. While this approach presents several obstacles, our new notion of complexity length provides the tools needed to make the argument work. Time permitting, I will also explain why the reducible elements grow coarsely at the rate of $e^{(6g-7)R}$. Joint work with Howard Masur.
Wednesday April 17, 2024 at 14:30, Wachman 617
NonLERFness of arithmetic hyperbolic manifold groups
Hongbin Sun, Rutgers University
Abstract: We show that any arithmetric lattice $\Gamma<\text{Isom}_+(\mathbb{H}^n)$ with $n\geq 4$ is not LERF (locally extended residually finite), including type III lattices in dimension 7. One key ingredient in the proof is the existence of totally geodesic 3-dim submanifolds, which follows from the definition if $\Gamma$ is in type I or II, but is much harder to prove if $\Gamma$ is in type III. This is a joint work with Bogachev and Slavich.
Wednesday September 4, 2024 at 14:30, Wachman 617
Solving the word problem in the mapping class group in quasi-linear time
Saul Schleimer, University of Warwick
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, D.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.
We give an algorithm requiring only \(O(n log^3(n))\) time. We do this by combining Dynnikov's approach to curves on surfaces, M\"oller's version of the half-GCD algorithm, and a delicate error analysis in interval arithmetic.
This is joint work with Mark Bell.
Wednesday September 11, 2024 at 14:30, Wachman 617
A metric boundary theory for Carnot groups
Nate Fisher, Swarthmore College
Abstract: In this talk, I will try to motivate the use of horofunction boundaries to study nilpotent groups. In particular, for Carnot groups, i.e., stratified nilpotent Lie groups equipped with certain left-invariant homogeneous metrics, all horofunctions are piecewise-defined using Pansu derivatives. For higher Heisenberg groups and filiform Lie groups, two families which generalize the standard 3-dimensional real Heisenberg group, we will discuss the dimensions and topologies of their horofunction boundaries. In doing so, we find that filiform Lie groups of dimension greater than or equal to 8 provide the first-known examples of Carnot groups whose horofunction boundaries are not full-dimension, i.e., of codimension 1.
Wednesday September 25, 2024 at 14:30, Wachman 617
The admissible curve graph is not hyperbolic
Jacob Russell, Swarthmore College
Abstract: The mapping class group and its subgroups are often illuminated by actions on graphs built from curves on the surface. These actions allow for a variety of questions about the group to be translated into either combinatorial or geometric information about these graphs. We will examine this approach in the case of a stabilizer of a vector field on the surface. These are subgroups that Calderon and Salter have shown are important on the algebraic geometry of Moduli space. This work also suggests that the appropriate graph for these subgroups to act on is the graph of curves with winding number zero. We show the geometry of this graph can be well understood using Masur and Minsky's subsurface projections. As a consequence, we learn that, unlike the traditional curve graph, this admissible curve graph is not hyperbolic.
Friday October 4, 2024 at 14:30, Wachman 617
Surface bundles and their coarse geometry
Chris Leininger, Rice University
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: I’ll discuss surface bundles over various spaces with a focus on their monodromy representations and how this influences properties of the fundamental group. In the first talk (9:30am), I will explain Farb and Mosher’s notion of convex cocompactness in the mapping class group, its various incarnations, and its connections to the coarse hyperbolicity of surface bundles. Then I’ll describe more recent work generalizing convex cocompactness to notions of geometric finiteness, examples that illustrate hyperbolicity features, and mention several open problems. In the second talk, I’ll present a new construction of surface bundles over surfaces, providing the first examples of such bundles that are atoroidal.
The surface bundle construction in the second talk represents recent joint work with Autumn Kent. The work on convex cocompactness is also joint with Kent, as well as with Bestvina, Bromberg, Dowdall, Russell, and Schleimer in various combinations. The work on geometric finiteness is joint with Dowdall, Durham, and Sisto.
Friday October 4, 2024 at 16:00, Wachman 617
Cosmetic surgeries, knot complements, and Chern-Simons invariants
Tye Lidman, NC State
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: Dehn surgery is an important construction in low-dimensional topology which turns a knot into a new three-manifold. This is deeply tied to the study of knots through their complements. The Cosmetic Surgery Conjecture predicts two different Dehn surgeries on the same knot in the three-sphere always gives different three-manifolds. We show how tools from gauge theory can help to approach this problem, settling the conjecture for almost all knots in the three-sphere. If there is time, we will also discuss how these techniques can prove some generalizations of the knot complement theorem, which says that knots are determined by their complements. This is joint work with Ali Daemi and Mike Miller Eismeier.
In the morning background talk (at 11:30am), we will learn about instanton Floer homology, an invariant associated to three-manifolds coming from gauge theory which has had a reawakening as a trendy subject over the past 15 years. We will discuss the formal structure and see how it can be applied to topological problems without getting into any of the technical gauge theory.
Wednesday October 9, 2024 at 14:30, Wachman 617
Arithmeticity and commensurability of links in thickened surfaces
Rose Kaplan-Kelly, George Mason University
Abstract: In this talk, we will consider a generalization of alternating links and their complements in thickened surfaces. In particular, a family of generalized alternating links which each correspond to a Euclidean or hyperbolic tiling and admit a right-angled complete hyperbolic structure on their complement. We will give a complete characterization of which right-angled tiling links are arithmetic, and which are pairwise commensurable. This is joint work with David Futer.
Wednesday October 16, 2024 at 14:30, Wachman 617
Profinite properties of clean graphs of groups
Kasia Jankiewicz, UC Santa Cruz and IAS
Abstract: A graph of groups is algebraically clean if the edge groups embedding in vertex groups are inclusions of free factors. I will discuss some profinite properties of such groups, and applications to Artin groups. This will include joint work with Kevin Schreve.
Wednesday October 23, 2024 at 14:30, Wachman 617
Non-recognizing spaces for stable subgroups
Sahana Balasubramanya (Lafayette College)
We say an action of a group on a space recognizes all stable subgroups if every stable subgroup of G is quasi-isometrically embedded in the action on . The problem of constructing or identifying such spaces has been extensively studied for many groups, including mapping class groups and right angled Artin groups- these are well known examples of acylindrically hyperbolic groups. In these cases, the recognizing spaces are the largest acylindrical actions for the group. One can therefore ask the question if a largest acylindrical action of an acylindrically hyperbolic group (if it exists) is a recognizing space for stable subgroups in general. We answer this question in the negative by producing an example of a relatively hyperbolic group whose largest acylindrical action fails to recognize all stable subgroups. This is joint work with Marissa Chesser, Alice Kerr, Johanna Mangahas and Marie Trin.
Friday November 1, 2024 at 14:00, Room DRL 2C6, 209 S 33rd St, Philadelphia, PA 19104, USA
Geometric finiteness in the mapping class group
Jacob Russell, Swarthmore College
PATCH seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: Mosher proposed that the analogy between convex cocompactness in the isometries of hyperbolic space and the mapping class group should extend to the geometrically finite groups of isometries of the hyperbolic space. While no consensus definition of geometric finiteness in the mapping class group has emerged, there are several classes of subgroups that ought to be geometrically finite from several different points of view. We will survey these subgroups with a focus on the stabilizers of multicurves on the surface.
In the morning background talk, at 10am in room DRL A2, I will introduce the idea of convex cocompactness, in contexts ranging from Kleinian groups to surface bundles.
Friday November 1, 2024 at 15:45, David Rittenhouse Laboratory, 209 S 33rd St, Philadelphia, PA 19104, USA
Symplectic annular Khovanov homology and knot symmetry
Kristen Hendricks, Rutgers University
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Temple)
Abstract: Khovanov homology is a combinatorially-defined invariant which has proved to contain a wealth of geometric information. In 2006 Seidel and Smith introduced a candidate analog of the theory in Lagrangian Floer analog cohomology, which has been shown by Abouzaid and Smith to be isomorphic to the original theory over fields of characteristic zero. The relationship between the theories is still unknown over other fields. In 2010 Seidel and Smith showed there is a spectral sequence relating the symplectic Khovanov homology of a two-periodic knot to the homology of its quotient; in contrast, in 2018 Stoffregen and Zhang used the homotopy type to show that there is a spectral sequence from the combinatorial homology of a two-periodic knot to the annular Khovanov homology of its quotient. (An alternate proof of this result was subsequently given by Borodzik, Politarczyk, and Silvero.) These results necessarily use coefficients in the field of two elements. This inspired investigations of Mak and Seidel into an annular version of symplectic Khovanov homology, which they defined over characteristic zero. In this talk we introduce a new, conceptually straightforward, formulation of symplectic annular Khovanov homology, defined over any field. Using this theory, we show how to recover the Stoffregen-Zhang spectral sequence on the symplectic side. This is joint work with Cheuk Yu Mak and Sriram Raghunath.
In the morning background talk, at 11am in DRL A2, I will introduce equivariant cohomology and Lagrangian Floer cohomology.
Wednesday November 6, 2024 at 14:30, Wachman 617
Periodic points of endperiodic maps
Ellis Buckminster (Penn)
Endperiodic maps are a class of homeomorphisms of infinite-type surfaces whose compactified mapping tori have a natural depth-one foliation. By work of Landry-Minsky-Taylor, every atoroidal endperiodic map is homotopic to a type of map called a spun pseudo-Anosov. Spun pseudo-Anosovs share certain dynamical features with the more familiar pseudo-Anosov maps on finite-type surfaces. A theorem of Thurston states that pseudo-Anosovs minimize the number of periodic points of any given period among all maps in their homotopy class. We prove a similar result for spun pseudo-Anosovs, strengthening a result of Landry-Minsky-Taylor.
Wednesday November 20, 2024 at 14:30, Wachman 617
Uniform waist inequalities
Uri Bader, University of Maryland and Weizmann Institute
Abstract: Gromov’s waist inequality for the $n$-dimensional sphere $S^n$ is a fundamental result in geometry. It says that the maximal volume of a fiber of a (generic) map from $S^n$ to the $d$-dimensional Euclidean space is at least the $(n-d)$-dimensional volume of an equator sphere $S^{n−d}$, which is a constant times the volume of $S^n$. This constant is the "waist constant".
A question arises: is there an infinite family of $n$-dimensional compact manifolds satisfying a uniform waist inequality, that is a similar inequality with a uniform waist constant, for a given dimension $d$?
It is natural to consider the family of all finite covers of a given compact manifold $M$. A positive answer to this question in the case $d=1$ is provided by the Cheeger-Buser inequality, relating the waist constant with the spectrum of the Laplacian of $M$. In my talk I will survey gently all of the above and explain a recent solution to the case $d=2$, using a fixed point property for groups acting on $L^1$-spaces. Based on a joint work with Roman Sauer.
Friday December 6, 2024 at 14:00, Stokes 014, Haverford College
Local equivalence of Khovanov homology
Robert Lipshitz, University of Oregon and IAS
PATCH Seminar, joint with Bryn Mawr, Haverford, Penn, and Swarthmore
Abstract: The notion of local equivalence has been a key tool in recent work on concordance and homology cobordism groups. In this talk, I will describe a variant of this idea that uses a combination of even and odd Khovanov homology. The result is a group whose elements correspond to equivalence classes of certain simple algebraic structure, and which receives a homomorphism from the smooth concordance group. I will sketch some structures on this group and concrete invariants it defines, and perhaps speculate wildly about other places this strategy might be useful. This is joint work with Nathan Dunfield and Dirk Schütz.
In the morning background talk (9:15 in room KINSC L205), I will construct (Khovanov’s) even Khovanov homology and (Ozsváth-Rasmussen-Szabó’s) odd Khovanov homology and talk about some of their similarities and differences. Most of the talk will assume just an understanding of tensor products of abelian groups / vector spaces.
Friday December 6, 2024 at 15:30, Stokes 014, Haverford College
Spinal open books and symplectic fillings with exotic fibers
Luya Wang, Institute for Advanced Study
PATCH Seminar, joint with Bryn Mawr, Haverford, Penn, and Swarthmore
Abstract: Pseudoholomorphic curves are pivotal in establishing uniqueness and finiteness results in the classification of symplectic manifolds. In a series of works, Wendl used punctured pseudoholomorphic foliations to classify symplectic fillings of contact three-manifolds supported by planar open books, turning it into a problem about monodromy factorizations. In a joint work with Hyunki Min and Agniva Roy, we build on the works of Lisi--Van Horn-Morris--Wendl in using spinal open books to further delve into the classification problem of symplectic fillings of higher genus open books. In particular, we provide the local model of the mysterious "exotic fibers" in a generalized version of Lefschetz fibrations, which captures a natural type of singularity at infinity. We will give some applications to classifying symplectic fillings via this new phenomenon.
In the morning background talk (10:30am in room KINSC L205), I will survey some previous results on using planar open books to classify symplectic fillings. I will give some background on open books, contact structures and bordered Lefschetz fibrations. Then I will give an overview of Wendl's proof of his influential theorem: any symplectic filling of a contact 3-manifold supported by a planar open book is deformation equivalent to a bordered Lefschetz fibration.