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−  == Spring 2019 ==
 
−  { cellpadding="8"
 
−  !align="left"  date
 
−  !align="left"  speaker
 
−  !align="left"  title
 
−  !align="left"  host(s)
 
−  
 
−  April 5
 
−  Mark Pengitore (Ohio)
 
−  Translationlike actions on nilpotent groups
 
− 
 
−  (Dymarz)
 
−  
 
−  April 18
 
−  José Ignacio Cogolludo Agustín (Universidad de Zaragoza)
 
−  Even Artin Groups, cohomological computations and other geometrical properties.
 
− 
 
−  (Maxim)
 
−  '''Unusual date and time: B309 Van Vleck, 2:153:15'''
 
−  
 
− 
 
−  April 19
 
−  Yan Xu (University of Missouri  St. Louis)
 
−  Structure of minimal twospheres of constant curvature in hyperquadrics
 
−  (Huang)
 
   
−  }
 
   
−  == Fall 2018 ==  +  == Fall 2019 == 
   
 { cellpadding="8"   { cellpadding="8" 
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 !align="left"  host(s)   !align="left"  host(s) 
     
−  Sept. 14
 +  Oct. 25 
−  Teddy Einstein (UIC)
 +  Emily Stark (Utah) 
−  Quasiconvex Hierarchies for Relatively Hyperbolic NonPositively Curved Cube Complexes
 +   TBA 
−  (Dymarz)
 
−  
 
−  Oct. 12
 
−  Marissa Loving
 
−  Least dilatation of pure surface braids
 
−  (Kent)
 
−  
 
−  Oct. 19  
−  Sara Maloni
 
−  On typepreserving representations of thrice punctured projective plane group
 
−  (Kent)  
−    
−  Oct. 26
 
−  Dingxin Zhang (HarvardCMSA)
 
−  Relative cohomology and Ahypergeometric equations
 
−  (Huang)
 
−  
 
−  Nov. 9
 
−  Zhongshan An (Stony Brook)
 
−  Ellipticity of the Bartnik Boundary Conditions
 
−  (Huang)
 
−  
 
−  Nov. 16
 
−  Xiangdong Xie
 
−  Quasiisometric rigidity of a class of right angled Coxeter groups
 
 (Dymarz)   (Dymarz) 
     
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−  ==Spring Abstracts==
 +  ==Fall Abstracts== 
−   
−  ===Mark Pengitore===
 
−   
−  "Translationlike actions on nilpotent groups"
 
−   
−  Translationlike actions were introduced Whyte to generalize subgroup containment. Using this notion, he proved that a group is nonamenable if and only if it admits a translationlike action by a nonabelian free group. This result motivates us to ask what groups admit translationlike actions on various interesting classes of groups. As a consequence of Gromov's polynomial growth theorem, we have that only nilpotent groups may act translationlike on a nilpotent group which is the main focus of this talk. Thus, one may ask to characterize what nilpotent groups act translationlike on a fixed nilpotent group. We offer partial answer to this question by demonstrating that if two nilpotent groups have the same growth but distinct asymptotic cones, then there exist no translationlike action of these two groups on each other.
 
−   
−  ===José Ignacio Cogolludo Agustín===
 
−   
−  "Even Artin Groups, cohomological computations and other geometrical
 
−  properties."
 
−   
−  The purpose of this talk is to introduce even Artin groups and consider
 
−  their quasiprojectivity properties, as well as study the cohomological
 
−  properties of their kernels, that is, the kernels of their characters.
 
−   
−  ===Yan Xu===
 
−  "Structure of minimal twospheres of constant curvature in hyperquadrics"
 
−   
−  Veronese twosphere (also called rational normal curve) is an interesting projective variety in geometry. It is of constant curvature and unique up to action of unitary group. Based on this rigidity result and SVD (singular value decomposition) in linear algebra, we give a classification of a special class minimal, especially holomorphic, twospheres of constant curvature in hyperquadric, up to action of real orthogonal group and reparameterization of the twosphere. For degree less than or equal to three, we give an algorithm and explicit examples. As an application of this results, by computing the norm squared of second fundamental form, we show the generic twospheres constructed here are not homogeneous. This is a joint work with Professor QuoShin Chi and Zhenxiao Xie.
 
−   
−  == Fall Abstracts ==  
−   
−  ===Teddy Einstein===
 
−   
−  "Quasiconvex Hierarchies for Relatively Hyperbolic NonPositively Curved Cube Complexes"
 
−   
−  Nonpositively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.
 
−   
−  ===Marissa Loving===
 
−   
−  "Least dilatation of pure surface braids"
 
−   
−  The nstranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with npunctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudoAnosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.
 
−   
−  ===Sara Maloni===
 
−   
−  "On typepreserving representations of thrice punctured projective plane group"
 
−   
−  In this talk, after a brief overview on famous topological and dynamical open questions on character varieties, we will consider typepreserving representations of the fundamental group of the threeholed projective plane N into PGL(2, R). First, we prove Kashaev’s conjecture on the number of connected components with nonmaximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a nonhyperbolic element, while in euler class 1 or 1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to nonhyperbolic elements. This answers a generalisation of a question asked by Bowditch for orientable surfaces. In addition, we show, in most cases, that the action of the pure mapping class group Mod(N) on these nonmaximal components is ergodic, proving Goldman conjecture in those cases. Time permitting we will discuss a work in progress with Palesi where we expend these results to all five surfaces (orientable and nonorientable) of characteristic 2. (This is joint work with F. Palesi and T. Yang.)
 
−   
−  ===Dingxin Zhang===
 
−  "Relative cohomology and Ahypergeometric equations"
 
−   
−  The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of WaltherSchulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of HuangLianYauZhu. This is a joint work with TsungJu Lee.
 
−   
−   
−  ===Zhongshan An===
 
−  "Ellipticity of the Bartnik Boundary Conditions"
 
−   
−  The Bartnik quasilocal mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the socalled Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasilocal mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question.
 
−   
−  ===Xiangdong Xie===
 
−  "Quasiisometric rigidity of a class of right angled Coxeter groups"
 
   
−  Given any finite simplicial graph G with vertex set V and edge set E, the associated right angled Coxeter group (RACG) W(G) is defined
 +  ===Emily Stark=== 
−  as the group with generating set V whose generators all have order 2 and where uv=vu for each edge (u,v).
 
−  The classical examples are the reflection groups generated by the reflections about edges of right angled polygons (in the Euclidean plane or the hyperbolic plane). We classify a class of RACGs up to quasiisometry. This is joint work with Jordan Bounds.
 
   
−  == Spring Abstracts ==
 +  "TBA" 
   
 == Archive of past Geometry seminars ==   == Archive of past Geometry seminars == 
 +  20182019 [[Geometry_and_Topology_Seminar_20182019]] 
 +  <br><br> 
 20172018 [[Geometry_and_Topology_Seminar_20172018]]   20172018 [[Geometry_and_Topology_Seminar_20172018]] 
 <br><br>   <br><br> 