Seminar Calendar
for Geometry, Groups and Dynamics/GEAR events the next 12 months of Sunday, January 1, 2017.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, January 19, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Thursday, January 19, 2017
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Submitted by nmd.
 Xinghua Gao   [email] (University of Illinois)Orders from $\widetilde{PSL_2(\mathbb{R})}$ Representations and Non-examples.Abstract: Let $M$ be an integer homology 3-sphere. One way to study left-orderability of $\pi_1(M)$ is to construct a non-trivial representation from $\pi_1(M)$ to $\widetilde{PSL_2(\mathbb{R})}$. However this method does not always work. In this talk, I will give examples of non L-space irreducible integer homology 3-spheres whose fundamental groups do not have nontrivial $\widetilde{PSL_2(\mathbb{R})}$ representations.

Tuesday, January 24, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, January 24, 2017
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Submitted by clein.
 Sarah Mousley (Illinois Math)Boundary maps for some hierarchically hyperbolic spacesAbstract: There are natural embeddings of right-angled Artin groups $G$ into the mapping class group $Mod(S)$ of a surface $S$. The groups $G$ and $Mod(S)$ can each be equipped with a geometric structure called a hierarchically hyperbolic space (HHS) structure, and there is a notion of a boundary for such spaces. In this talk, we will explore the following question: does an embedding $\phi: G \rightarrow Mod(S)$ extend continuously to a boundary map $\partial G \rightarrow \partial Mod(S)$? That is, given two sequences $(g_n)$ and $(h_n)$ in $G$ that limit to the same point in $\partial G$, do $(\phi(g_n))$ and $(\phi(h_n))$ limit to the same point in $\partial Mod(S)$? No background in HHS structures is needed.

Thursday, February 2, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Thursday, February 2, 2017
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Submitted by clein.
 Nick Vlamis (U Michigan Math)Algebraic and topological properties of big mapping class groupsAbstract: There has been a recent surge in studying surfaces of infinite type, i.e. surfaces with infinitely-generated fundamental groups. In this talk, we will focus on their mapping class groups, often called big mapping class groups. In contrast to the finite-type case, there are many open questions regarding the basic algebraic and topological properties of big mapping class groups. I will discuss several such questions and provide some answers. In particular, I will focus on automorphisms of pure mapping class groups and topological generating sets. This work is joint with Priyam Patel.

Tuesday, February 7, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, February 7, 2017
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Submitted by clein.
 Gili Golan (Vanderbilt)The generation problem in Thompson group FAbstract: We show that the generation problem in Thompson group F is decidable, i.e., there is an algorithm which decides if a finite set of elements of F generates the whole F. The algorithm makes use of the Stallings 2-core of subgroups of F, which can be defined in an analogue way to the Stallings core of subgroups of a free group. An application of the algorithm shows that F is a cyclic extension of a group K which has a maximal elementary amenable subgroup B. The group B is a copy of a subgroup of F constructed by Brin and Navas.

Tuesday, February 21, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, February 21, 2017
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Submitted by clein.
 John P. D'Angelo (Illinois Math)Groups Associated with Rational Proper MapsAbstract: Given a rational proper map $f$ between balls of typically different dimensions, we define a subgroup $\Gamma_f$ of the source automorphism group. We prove that this group is noncompact if and only if $f$ is linear. We show how these groups behave under certain constructions such as juxtaposition and partial tensor products. We then sketch a proof of the following result. If $G$ is an arbitrary finite subgroup of the source automorphism group, then there is a rational map $f$ for which $\Gamma_f = G$. We provide many examples and, if time permits, discuss the degree estimate conjecture. This work is joint with Ming Xiao.

Thursday, March 2, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Thursday, March 2, 2017
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Submitted by nmd.
 Malik Obeidin   [email] (University of Illinois)Hyperbolic volumes of random linksAbstract: What does a random link look like? There have been a few different proposed models for sampling from the set of links -- in this talk, I will describe a model based on random link diagrams in the plane. Such diagrams can be sampled uniformly on a computer due to the work of Gilles Schaeffer, so one can experiment with various invariants of links with the topology software SnapPy. I will present data showing what happens with some of the different invariants SnapPy can compute, and I will outline a proof that the hyperbolic volume of the complement of a random alternating link diagram is asymptotically a linear function of the number of crossings. In contrast, for nonalternating links, I will show why the diagrams we get generically represent satellite (and hence nonhyperbolic) links.

Thursday, March 9, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Thursday, March 9, 2017
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Submitted by clein.
 Mark Bell (Illinois Math)Polynomial-time curve reductionAbstract: A pair of curves on a surface can appear extremely complicated and so it can be difficult to determine properties such as their intersection number. We will discuss a new argument that, when the curve is given by its intersections with the edges of an ideal triangulation, there is always a "reduction" to a simpler configuration in which such calculations are straightforward. This relies on finding an edge flip or a (power of a) Dehn twist that decreases the complexity of a curve by a definite fraction.

Tuesday, March 14, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, March 14, 2017
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Submitted by clein.
 Mark Sapir (Vanderbilt and Illinois Math)Flat submaps in CAT(0) $(p,q)$-maps and maps with anglesAbstract: This is a joint work with A. Olshanskii. Let $p, q$ be positive integers with $1/p+1/q=1/2$. We prove that if a $(p,q)$-map $M$ does not contain flat submaps of radius $\ge r$, then its area does not exceed $c(r+1)n$ where $n$ is the perimeter of $M$ and $c$ is an absolute constant. Earlier Ivanov and Schupp proved an exponential bound in terms of $r$. We prove an estimate similar to Ivanov and Schupp for much more general maps with angles" which include, for example, van Kampen diagrams over the presentation of the Baumslag-Solitar group $BS(1,2)$ and many groups corresponding to $S$-machines. We also show that a $(p,q)$ map $M$ tessellating a plane ${\mathbb R}^2$ has path metric quasi-isometric to the Euclidean metric on the plane if and only if $M$ has only finitely many non-flat vertices and faces.

Tuesday, March 28, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by clein.
 Charles Delman (EIU Math)Alternating knots and Montesinos knots satisfy the L-space knot conjecture. Joint work with Rachel RobertsAbstract: An L-space is a homology $$3$$-sphere whose Heegard-Floer homology has minimal rank; lens spaces are examples (hence the name). Results of Ozsváth - Szabó, Eliashberg -Thurston, and Kazez - Roberts show that a manifold admitting a taut, co-orientable foliation cannot be an L-space. Let us call such a manifold foliar. Ozsváth and Szabó have asked whether or not the converse is true for irreducible $$3$$-manifolds; Juhasz has conjectured that it is. Restricting attention to manifolds obtained by Dehn surgery on knots in $$S^3$$, we posit the following: L-space Knot Conjecture. Suppose $$\kappa \subset S^3$$ is a knot in the 3-sphere. Then a manifold obtained by Dehn filling along $$\kappa$$ is foliar if and only if it is irreducible and not an L-space. Using generalized surface decomposition techniques that build on earlier work of Gabai, Menasco, Oertel, and the authors, we prove that both alternating knots and Montesinos Knots satisfy the L-space Knot Conjecture. We believe these techniques will prove fruitful in the further study of taut foliations in $$3$$-manifolds.

Thursday, April 6, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Thursday, April 6, 2017
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Submitted by clein.
 Autumn Kent (Wisconsin Math)Crash course in convex cocompactness.Abstract: Farb and Mosher introduced the notion of convex cocompactness from Kleinian groups to the theory of mapping class groups, with the beautiful application of potentially producing atoroidal non-hyperbolic groups of finite type, which would provide counterexamples to Gromov's coarse-hyperbolization conjecture for infinite groups. I'll give an overview of the foundations of the theory and the current state of things.

Tuesday, April 11, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, April 11, 2017
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Submitted by clein.
 Mark Bell (Illinois Math)The conjugacy problem for Mod(S)Abstract: We will discuss a new approach for tackling the conjugacy problem for the mapping class group of a surface. This relies on recently developed tools for finding tight geodesics in the curve complex. This is joint work with Richard Webb.

Thursday, April 13, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Thursday, April 13, 2017
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Submitted by clein.
 Catherine Pfaff (UC Santa Barbara)Stable Strata of Geodesics in Outer SpaceAbstract: Outer automorphisms of free groups are understood via their action on Culler-Vogtmann Outer space. We study the behavior of geodesics in Outer Space by focusing on a class of geodesics that have strong stability properties. We further show that pathologies exist among these geodesics that don't occur, for example, in the Teichmuller space setting. This is joint work with Yael Algom-Kfir and Ilya Kapovich.

Tuesday, April 18, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, April 18, 2017
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Submitted by clein.
 Edgar Bering (UIC Math)Compatibility of length functions and the geometry of their deformation spaces Abstract: Given two length functions l, m of minimal irreducible G actions on R-trees A, B, when is l + m again the length function of a minimal irreducible G action on an R-tree? We will show that additivity is characterized by the geometry of the Guirardel core of A and B, and also by a combinatorial compatibility condition generalizing the condition given by Behrstock, Bestvina, and Clay for Fn actions on simplicial trees. This compatibility condition allows us to characterize the PL-geometry of common deformation spaces of R-trees, such as the closure of Culler-Vogtmann Outer Space or the space of small actions of a hyperbolic group G.

Thursday, April 20, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Thursday, April 20, 2017
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Submitted by cuyanik2.
 Michelle Chu (UT Austin Math)Special subgroups of Bianchi groupsAbstract: The study of (virtually) special cube complexes and groups played a key role in the resolution of the virtual Haken and virtual fibering conjectures. Recently there has been interest in determining the index of special subgroups of virtually special groups. In this talk, we answer this question in the case of the Bianchi groups. We find special congruence subgroups for each Bianchi group $PSL(2,O_d)$ with uniformly bounded index independent of d.

Thursday, May 4, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Thursday, May 4, 2017
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