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

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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 spaces
Abstract: 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 groups
Abstract: 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 F
Abstract: 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 Maps
Abstract: 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 links
Abstract: 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
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 reduction
Abstract: 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 angles
Abstract: 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 Roberts
Abstract: 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)
On word hyperbolic surface bundles.
Abstract: There is a characterization of hyperbolicity of the fundamental group of a surface bundle due to Farb-Mosher-Hamenstaedt, namely that the bundle has hyperbolic fundamental group if and only if the fundamental group is ``convex cocompact,'' a notion analogous to the synonymous notion in Kleinian groups. I will discuss joint work with Bestvina, Bromberg, and Leininger that gives a new characterization of convex cocompactness, namely that the group is purely pseudo-Anosov and undistorted in the mapping class group.

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)
To Be Announced

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)
To Be Announced

Thursday, April 20, 2017

Geometry, Groups and Dynamics/GEAR
12:00 pm   in 243 Altgeld Hall,  Thursday, April 20, 2017
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Submitted by cuyanik2.
Michelle Chu (UT Austin Math)
To Be Announced
Abstract: TBA

Tuesday, April 25, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, April 25, 2017
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Submitted by clein.
Funda Gultepe (Illinois Math)
To Be Announced