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 The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm  2:10pm'''.   The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm  2:10pm'''. 
 <br>   <br> 
−  For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/luwang/ Lu Wang] .  +  For more information, contact Shaosai Huang. 
   
 [[Image:Hawk.jpgthumb300px]]   [[Image:Hawk.jpgthumb300px]] 
   
   
−   +  == Fall 2018 == 
−  == Fall 2017 ==  +  
   
 { cellpadding="8"   { cellpadding="8" 
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 !align="left"  host(s)   !align="left"  host(s) 
     
−  September 8
 
 TBA   TBA 
−  TBA
 
−  TBA
 
−  
 
−  September 15
 
−  Jiyuan Han (University of WisconsinMadison)
 
−  [[#Jiyuan Han "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"]]
 
−  Local
 
−  
 
−  September 22
 
−  Sigurd Angenent (UWMadison)
 
−  [[#Sigurd Angenent "Topology of closed geodesics on surfaces and curve shortening"]]
 
−  Local
 
−  
 
−  September 29
 
−  Ke Zhu (Minnesota State University)
 
−  [[#Ke Zhu "Isometric Embedding via Heat Kernel"]]
 
−  Bing Wang
 
−  
 
−  October 6
 
−  Shaosai Huang (Stony Brook)
 
−  [[#Shaosai Huang "\epsilonRegularity for 4dimensional shrinking Ricci solitons"]]
 
−  Bing Wang
 
−  
 
−  October 13
 
−  Sebastian Baader (Bern)
 
−  [[#Sebastian Baader "A filtration of the Gordian complex via symmetric groups"]]
 
−  Kjuchukova
 
−  
 
−  October 20
 
−  Shengwen Wang (Johns Hopkins)
 
−  [[#Shengwen Wang "Hausdorff stability of round spheres under smallentropy perturbation"]]
 
−  Lu Wang
 
−  
 
−  October 27
 
−  Marco MendezGuaraco (Chicago)
 
−  [[#Marco MendezGuaraco "Some geometric aspects of the AllenCahn equation"]]
 
−  Lu Wang
 
−  
 
−  November 3
 
 TBA   TBA 
 TBA   TBA 
 TBA   TBA 
     
−  November 10  +   
−  TBA
 +  
−  TBA
 +  
−  TBA
 +  
−  
 +  
−  November 17
 +  
−  Ovidiu Munteanu (University of Connecticut)
 +  
−  [[#Ovidiu Munteanu "The geometry of four dimensional shrinking Ricci solitons"]]
 +  
−  Bing Wang
 +  
−  
 +  
−  <b>Thanksgiving Recess</b>
 +  
−  
 +  
−  
 +  
−  
 +  
−  
 +  
−  December 1
 +  
−  TBA
 +  
−  TBA
 +  
−  TBA
 +  
−  
 +  
−  December 8
 +  
−  Brian Hepler (Northeastern University)
 +  
−  [[#Brian Hepler "Deformation Formulas for Parameterizable Hypersurfaces"]]
 +  
−  Max
 +  
−  
 +  
 }   } 
   
 == Fall Abstracts ==   == Fall Abstracts == 
   
−  === Jiyuan Han ===  +  === TBA === 
−  "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"
 +  
−   +  
−  Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK
 +  
−  metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with
 +  
−  Jeff Viaclovsky.
 +  
−   +  
−  === Sigurd Angenent ===
 +  
−  "Topology of closed geodesics on surfaces and curve shortening"
 +  
−   +  
−  A closed geodesic on a surface with a Riemannian metric defines a knot in the unit tangent bundle of that surface. Which knots can occur? Given a particular knot type, what is the lowest number of closed geodesics a surface must have if you are allowed to pick the metric on the surface? Curve shortening allows you to define an invariant for each knot type (called the Conley index) which gives some answers to these questions.
 +  
−   +  
−  === Ke Zhu===
 +  
−  "Isometric Embedding via Heat Kernel"
 +  
−   +  
−  The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.
 +  
−   +  
−  === Shaosai Huang ===
 +  
−  "\epsilonRegularity for 4dimensional shrinking Ricci solitons"
 +  
−   +  
−  A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound are expected when the local energy is sufficiently small. Such estimates, referred to as \epsilonregularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilonregularity result for 4dimensional shrinking Ricci solitons without a priori control of the Sobolev constant.
 +  
−   +  
−  === Sebastian Baader ===
 +  
−  "A filtration of the Gordian complex via symmetric groups"
 +  
−   +  
−  The Gordian complex is a countable graph whose vertices correspond to knot types and whose edges correspond to pairs of knots that are related by a crossing change in a suitable diagram. For every natural number n, we consider the subgraph of the Gordian complex defined by restricting to the knot types whose fundamental group surjects onto S_n. We will prove that the various inclusion maps from these subgraphs into the Gordian complex are isometric embeddings. From this, we obtain a simple metric filtration of the Gordian complex.
 +  
−   +  
−  === Shengwen Wang ===
 +  
−  "Hausdorff stability of round spheres under smallentropy perturbation"
 +  
−   +  
−  ColdingMinicozzi introduced the entropy functional on the space of all hypersurfaces in the Euclidean space when studying generic singularities of mean curvature flow. It is a measure of complexity of hypersurfaces. BernsteinWang proved that round nspheres minimize entropy among all closed hypersurfaces for n less than or equal to 6, and the result is generalized to all dimensions by Zhu. BernsteinWang later also proved that the round 2sphere is actually Hausdorff stable under smallentropy perturbations. I will present in this talk the generalization of the Hausdorff stability to round hyperspheres in all dimensions.
 +  
−   +  
−  === Marco MendezGuaraco ===
 +  
−  "Some geometric aspects of the AllenCahn equation"
 +  
−   +  
−  In this talk I will discuss both local and global properties of the stationary AllenCahn equation in closed manifolds. This equation from the theory of phase transitions has a strong connection with the theory of minimal hypersurfaces. I will summarize recent results regarding this analogy including a new minmax proof of the celebrated AlmgrenPitts theorem.
 +  
−   +  
−  === Ovidiu Munteanu ===
 +  
−  "The geometry of four dimensional shrinking Ricci solitons"
 +  
−   +  
−  I will present several results, joint with Jiaping Wang, about the asymptotic structure of four dimensional gradient shrinking Ricci solitons.
 +  
−   +  
−  === Brian Hepler ===
 +  
−  "Deformation Formulas for Parameterizable Hypersurfaces"
 +  
   
−  We investigate oneparameter deformations of functions on affine space which define parameterizable hypersurfaces. With the assumption of isolated polar activity at the origin, we are able to completely express the Lê numbers of the special fiber in terms of the Lê numbers of the generic fiber and the characteristic polar multiplicities of the multiplepoint complex, a perverse sheaf naturally associated to any parameterized hypersurface.
 
   
 == Archive of past Geometry seminars ==   == Archive of past Geometry seminars == 
 +  20172018 [[Geometry_and_Topology_Seminar_20172018]] 
 +  <br><br> 
 20162017 [[Geometry_and_Topology_Seminar_20162017]]   20162017 [[Geometry_and_Topology_Seminar_20162017]] 
 <br><br>   <br><br> 