Meeting dates: Tuesdays (Topology Seminar) 1:50-2:50 pm in JR0274 and
Thursdays (Geometric Group Theory Seminar) from 1:50 to 2:50 pm in SM1138
Organizers - Jingyin Huang, Annette Karrer, Jean Lafont, Beibei Liu, Alex Margolis, Francis Wagner
August 27 - Jean Lafont (OSU)
High dimensional hyperbolic Coxeter groups that virtually fiber
I'll describe a construction of right-angled Coxeter groups, which are hyperbolic, and virtually algebraically fiber. Our inductive construction produces examples of arbitrarily high virtual cohomological dimension. This is joint work with Minemyer, Sorcar, Stover, and Wells.
August 29- Italiano Giovanni (Oxford)
Hyperbolic manifolds, maps to the circle, and fibering
We provide a way to define maps from a hyperbolic manifold tessellated in right angled polytopes to the circle, in a combinatorial way. The critical points of such map can be studied using Bestvina-Brady Morse theory, and it is possible to describe them combinatorially.
We employ this method to build a fibration in dimension 5, and other "nice" maps in dimension 6, 7, 8.
Sep 3- Yifan Jing (OSU)
Measure Doubling for Small Sets in SO(3,R)
Confirming a conjecture by Breuillard and Green, we show that if A is an open subset of SO(3,R) with sufficiently small measure, then the measure of A^2 is strictly greater than 3.99 times the measure of A. This is joint work with Chieu-Minh Tran and Ruixiang Zhang.
Sep 5-
Sep 10-
Sep 12-
Sep 17- Jingyin Huang (OSU)
Non-positive curved subcomplexes of spherical Deligne complexes
The spherical Deligne complex is a simplicial complex introduced in Deligne's work when he studied the K(pi,1) problem for some complex hyperplane arrangement complements. The complex is homotopic to a wedge of spheres, and bear some similarities with the spherical buildings, though it is not a building. While the topology of this complex prevent a CAT(0) metric on it, we show that it contains large pieces supporting equivariant non-positive curvature metric, and deduce some new results on the K(pi,1) conjecture for several classes of Artin groups.
Sep 19- Srivatsav Kunnawalkam Elayavalli (UCSD)
Sofic actions on sets and graphs
I will describe recent joint work with David Gao and Greg Patchell which develops a new theory of soficity for group actions on sets (2401.04945) and graphs (upcoming work), with several applications, including proving soficity for vast families of generalized wreath products, among other results. Various interesting examples will be presented.
Sep 19- Nicholas Wawrykow (University of Chicago)
Graph Configuration Spaces
While configuration spaces of points in a surface have been studied for over a century, interest in graph configuration spaces only dates back to the turn of the millennium. As in the surface case, much is known about unordered configurations of points in a graph, whereas the topology of ordered configurations remains mysterious. In this talk we discuss one of the simplest ordered graph configuration spaces, that of points in a star graph. We determine generators for the homology of these spaces and see how adding leaves tames the behavior of these classes.
Sep 24- Ben Lowe (U Chicago)
Rigidity and Finiteness of Totally Geodesic Hypersurfaces in Negative Curvature
This talk will discuss progress towards answering the following question: if a closed negatively curved manifold M has infinitely many totally geodesic hypersurfaces, then must it have constant curvature (and thus, by work of Bader-Fisher-Stover-Miller and Margulis-Mohamaddi, be homothetic to an arithmetic hyperbolic manifold)? First, I will talk about work that gives a partial answer to this question under the assumption that M is hyperbolizable. This part uses Ratner’s theorems in an essential way. I will also talk about work that gives an affirmative answer to the question if the metric on M is analytic. In this case the analyticity condition together with properties of the geodesic flow in negative curvature allow us to conclude what in constant curvature would follow from Ratner’s theorems. This talk is based on joint work with Fernando Al Assal, and Simion Filip and David Fisher.
Sep 26- John Loftin (Rutgers)
The Geometry of Limits of Cubic Differentials
Consider a closed Riemann surface $\Sigma$ of genus at least 2 equipped with a holomorphic cubic differential $U$. Such a pair induces a rich set of geometric structures of a convex real projective structure on the surface and an equivariant minimal embedding of its universal cover into the symmetric space $X=SL(3,R)/SO(3)$. These results heavily depend on nonconstructive analytic techniques (from affine differential geometry and Higgs bundles). I will discuss recent joint work with Andrea Tamburelli and Mike Wolf, in which the limiting structure for $tU$ as $t$ increases to infinity induces a minimal embedding into the asymptotic cone of $X$ which is explicitly determined by the geometry of $U$.
Oct 1-
Oct 3-
Oct 8-Jesus Gonzalez (CINVESTAV)
Abrams' stabilization theorem for no-k-equal configurations on graphs
For a cell complex X, Abrams defined a discrete version of Conf(X,n), the configuration space of n non-colliding labelled particles on X. Then, for a graph X, Abrams showed that, under mild conditions, his model captures the homotopy type of Conf(X,n). In this talk I will describe an analogue within the context of no-k-equal configuration spaces of graphs. This is joint work with Omar Alvarado-Garduño.
Oct 10- Fall break
Oct 15-
Oct 17-Daniel Ruberman (Brandeis)
Homotopy properties of diffeomorphism groups and spaces of positive scalar curvature on 4-manifolds
We show that the higher homotopy groups of the diffeomorphism group of a smooth 4-manifold can have infinitely generated free abelian summands. The same applies to the homology of the Torelli subgroup and of its classifying space. We show that the homotopy groups of the space of positive scalar curvature metrics on a large connected sum of S^2 x S^2's can have infinitely generated free abelian subgroups. This is all joint work with Dave Auckly.
Oct 22-Ishan Banerjee (OSU)
Monodromy and vanishing cycles for curves in an algebraic surface I
This talk will be about the monodromy group associated to a family of algebraic curves in an algebraic surface as a subgroup of the mapping class group. I will start by surveying some older results in this area about the image of monodromy in the symplectic group. I will then discuss joint work with Nick Salter, where we describe the precise image of monodromy in the mapping class group in the special case of complete intersections.
This talk will be relatively self contained and should be accessible to graduate students in topology or algebraic geometry.
Oct 24- Ishan Banerjee (OSU)
Monodromy and vanishing cycles for curves in an algebraic surface II
Oct 29- Yu-chan Chang (Wesleyan University)
The RAAG Recognition Problem for Bestvina--Brady Groups
When a group is finitely presented by commutators, is it isomorphic to a right-angled Artin group (RAAG)?
Bridson recently showed that there is no algorithm to determine whether such a group is a
RAAG. However, this recognition problem remains interesting for certain classes of groups.
In this talk, I will discuss the RAAG recognition problem for Bestvina–Brady groups from a graph theory point of view.
This is joint work with Lorenzo Ruffoni.
Oct 31-
Nov 5-
Nov 7- Ian Zemke (University of Oregon)
Title: L-space satellite operators and knot Floer homology
Abstract: Satellite operators are an important subject in knot theory. Many authors have studied the effect of satellite operations on knot Floer homology, though there are still many open questions. Most authors have used the bordered theory of Lipshtiz, Ozsvath and Thurston. There are some very helpful reformulations of these algorithms in terms of immersed curve invariants of Hanselman, Rasmussen and Watson. In this talk we will give a different approach, using the link surgery theorem of Manolescu and Ozsvath. We will consider the family of satellite operators where the corresponding 2-component link is an L-space link. (This family includes all cabling patterns, the Whitehead pattern, as well as a family of generalized Mazur patterns). For such operators, we will describe how to compute the full knot Floer complex of the satellite knot in terms of the knot Floer complex of the original knot as well as the Alexander polynomials of the corresponding pattern link. A key algebraic result is a computation of the link Floer complex of 2-component L-space links in terms of their Alexander polynomials. This is joint work with Daren Chen and Hugo Zhou and the computation of 2-component L-space link complexes is related to earlier joint work with Maciej Borodzik and Beibei Liu.
Nov 12- Beibei Liu (OSU)
Title: Rigidity of convex cocompact diagonal actions
Abstract: Convex subsets in higher-rank symmetric spaces are pretty rigid compared to rank 1 symmetric spaces, as proved by Kleiner and Leeb. In this talk, I will talk about convex subsets in products of negatively curved Hadamard manifolds. In particular, we show the limit cone is 1-dimensional if the diagonal action is convex cocompact, which induces some rigidity result of the diagonal representation.
Nov 14-
Nov 19-
Nov 21- Jing Tao (University of Oklahoma)
Density of Penner-Thurston pseudo-Anosov mapping classes
By Nielsen-Thurston Classification, every mapping class of a surface of finite type is one of three types: periodic, reducible or pseudo-Anosov. Pseudo-Anosov maps are precisely those with a representative preserving a pair of transverse measured foliations and they are shown to be generic in the mapping class group due to the work of Maher and Rivin. One of the main ways to construct explicit pseudo-Anosov mapping classes is via the Penner-Thurston construction, and fairly recently, it was shown by Shin-Strenner that not all pseudo-Anosov mapping classes arise from this construction. In this talk, I will discuss how dense/generic the Penner-Thurston pseudo-Anosovs are. This is joint with Justin Malestein and Joshua Pankau.
Nov 26- Piotr Przytycki (McGill)
Trees, fixed points, and the Cremona group
An action of a group on a space is called decent if every finitely generated subgroup all of whose elements have fixed-points has a global fixed-point. An example is the automorphism group of a tree or a finite product of trees. I will give a sufficient condition for a group acting on a restricted infinite product of trees to be decent. This allows to prove that every finitely generated subgroup of the Cremona group of P2 all of whose elements are algebraic is bounded. Joint work with Anne Lonjou and Christian Urech.
Nov 28- Thanksgiving