Geometry and Topology Seminar 2019-2020: Difference between revisions

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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/~rkent Richard Kent].
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .


[[Image:Hawk.jpg|thumb|300px]]
[[Image:Hawk.jpg|thumb|300px]]


== Spring 2013 ==


== Spring 2018 ==


{| cellpadding="8"
{| cellpadding="8"
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!align="left" | host(s)
!align="left" | host(s)
|-
|-
|January 25
|January 26
| [http://www.maths.usyd.edu.au/u/athomas/ Anne Thomas] (Sydney)
|TBA
| [[#Anne Thomas (Sydney)| ''Divergence in right-angled Coxeter groups'']]
|TBA
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
|TBA
|-
|-
|February 1
|February 2
|
|TBA
|
|TBA
|
|TBA
|-
|February 8
|
|
|
|-
|-
|February 15
|February 9
| [http://www3.nd.edu/~lnicolae/ Liviu Nicolaescu] (Notre Dame)
|TBA
| [[#Liviu Nicolaescu (Notre Dame)| ''Random Morse functions and spectral geometry'']]
|TBA
|[http://www.math.wisc.edu/~oh/ Oh]
|TBA
|-
|-
|February 22
|February 16
|
|TBA
|
|TBA
|
|TBA
|-
|-
|March 1
|February 23
| [https://pantherfile.uwm.edu/chruska/www/ Chris Hruska] (UW Milwaukee)
|TBA
| [[#Chris Hruska (UW Milwaukee)| ''Local topology of boundaries and isolated flats'']]
|TBA
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
|TBA
|-
|-
|March 8
|March 2
|
|TBA
|
|TBA
|
|TBA
|-
|-
|March 11, <b>MONDAY in B113!</b>
|March 9
| [http://www.math.fsu.edu/~hironaka/ Eriko Hironaka] (FSU)
|TBA
| [[#Eriko Hironaka (FSU)| ''Small dilatation pseudo-Anosov mapping classes'']]
|TBA
|[http://www.math.wisc.edu/~rkent/ Kent]
|TBA
|-
|-
|March 15
|March 16
| Yu-Shen Lin (Harvard)
|TBA
| [[#Yu-Shen Lin (Harvard)| ''Open Gromov-Witten Invariants on K3 surfaces and Wall-Crossing'']]
|TBA
| [http://www.math.wisc.edu/~oh/ Oh]
|TBA
|-
|-
|March 20 <b>WEDNESDAY in 901!</b>
|March 23
|[http://www.math.nyu.edu/faculty/cappell/index.html Sylvain Cappell] (NYU)
|TBA
|[[#Sylvain Cappell (NYU)| ''Topological actions of compact, connected Lie Groups on Manifolds'']]
|TBA
| [http://www.math.wisc.edu/~maxim/ Maxim]
|TBA
|-
|-
|Spring Break
|<b> Spring Break </b>
|
|
|
|
|
|-
|-
|April 5
|April 6
|
|TBA
|
|TBA
|
|TBA
|-
|-
|April 12
|April 13
|Manuel Gonzalez Villa (Heidelberg)
|TBA
|''The monodromy conjecture for plane meromorphic germs''
|TBA
|Laurentiu
|TBA
|-
|-
|April 19
|April 20
|
|TBA
|
|TBA
|
|TBA
|-
|-
|April 26
|April 27
| Emmy Murphy (MIT)
|TBA
| [[#Emmy Murphy| ''Exact Lagrangian immersions with few transverse self intersections'']]
|TBA
| [http://www.math.wisc.edu/~oh/ Oh]
|TBA
|-
|-
|May 3
|May 4
| Yuan-qi Wang (UCSB)
|TBA
| [[#Yuan-qi Wang (UCSB)| ''TBA'']]
|TBA
| [http://www.math.wisc.edu/~bwang/ Wang]
|TBA
|-
|-
|
|
|
|-
|May 10
| [http://www.math.wisc.edu/~oh/ Yong-Geun Oh] (Wisconsin)
| [[#Yong-Geun Oh| ''TBA'']]
| Local
|-
|}
|}
== Spring Abstracts ==
== Spring Abstracts ==


===Anne Thomas (Sydney)===
=== TBA ===
''Divergence in right-angled Coxeter groups''


Abstract:
TBA
The divergence of a pair of geodesic rays emanating from a point is a
measure of how quickly they are moving away from each other. In
Euclidean space divergence is linear, while in hyperbolic space
divergence is exponential. Gersten used this idea to define a
quasi-isometry invariant for groups, also called divergence, which has
been investigated for classes of groups including fundamental groups
of 3-manifolds, mapping class groups and right-angled Artin groups. I
will discuss joint work with Pallavi Dani on divergence in
right-angled Coxeter groups (RACGs).  We characterise 2-dimensional
RACGs with quadratic divergence, and prove that for every positive
integer d, there is a RACG with divergence polynomial of degree d.
 
===Liviu Nicolaescu (Notre Dame)===
''Random Morse functions and spectral geometry''
 
Abstract:
I will discuss the distribution of critical values of a  smooth random function on a compact m-dimensional Riemann manifold (M,g)  described as a random  superposition  of eigenfunctions of the Laplacian.  The  notion of randomness that we use    has a naturally  built in  small parameter $\varepsilon$, and we show that    as $\varepsilon\to 0$ the distribution of critical  values closely resemble the distribution  of eigenvalues  of  certain  random symmetric  $(m+1)\times (m+1)$-matrices  of the type introduced by E. Wigner  in quantum mechanics. Additionally, I will  explain how to recover the metric  $g$ from  statistical  properties of the Hessians of the above random function.
 
===Chris Hruska (UW Milwaukee)===
''Local topology of boundaries and isolated flats''
 
Abstract:  Swarup proved that every one-ended word hyperbolic group has a
locally connected Gromov boundary.  However for CAT(0) groups,
non-locally connected boundaries are easy to construct.  For instance
the boundary of F_2 x Z is the suspension of a Cantor set.
 
In joint work with Kim Ruane, we have studied boundaries of CAT(0)
spaces with isolated flats.  If G acts properly, cocompactly on such a
space X, we give a necessary and sufficient condition on G such that
the boundary of X is locally connected.  As a corollary, we deduce
that such a group G is semistable at infinity.
 
===Eriko Hironaka (FSU)===
''Small dilatation pseudo-Anosov mapping classes''
 
The theory of fibered faces implies that  pseudo-Anosov
mapping classes with bounded normalized dilatation can be partitioned
into a finite number of families with related dynamics.  In this talk we
discuss the problem of finding concrete description
of the members of these families.  One conjectural way generalizes a
well-known sequence
defined by Penner in '91.  However, so far no known examples  of
this type come close to
the smallest known accumulation point of normalized dilatations.
In this talk we describe a different construction that uses mixed-sign
Coxeter systems.  A deformation of the simplest pseudo-Anosov braid monodromy
can be obtained in this way, and hence this model does realize the
smallest known accumulation point.
 
===Yu-Shen Lin (Harvard)===
''Open Gromov-Witten Invariants on K3 surfaces and Wall-Crossing''
 
Strominger-Yau-Zaslow conjecture suggests that the Ricci-flat metric on Calabi-Yau manifolds might be related to holomorphic discs. In this talk, I will define a new open Gromov-Witten invariants on elliptic K3 surfaces trying to explain this conjecture. The new invariant satisfies certain wall-crossing formula and multiple cover formula. I will also establish a tropical-holomorphic correspondence. Moreover, this invariant is expected to be equivalent to the generalized Donaldson-Thomas invariants in the hyperK\"ahler metric constructed by Gaiotto-Moore-Neitzke. If time allowed, I will talk about the connection with disks counting on Calabi-Yau 3-folds.
 
===Sylvain Cappell (NYU)===
''TBA''
 
===Manuel Gonzalez Villa (Heidelberg)===
''The monodromy conjecture for plane meromorphic germs''
 
Joint work with  Ann Lemahieu (Lille). A notion of Milnor fibration  for meromorphic functions and the corresponding concepts of  monodromy and monodromy zeta function, introduced by Gussein-Zade, Luengo and Melle, invite to consider the notion of  topological zeta function for meromorphic germs and the corresponding monodromy conjecture. We try to motive these notions and discuss the plane case. We show that the poles do not behave as in the holomorphic case but still do satisfy a generalization of the monodromy conjecture.
 
===Yong-Geun Oh (Wisconsin)===
''TBA''
 
===Emmy Murphy (MIT)===
''Exact Lagrangian immersions with few transverse self intersections''
 
This talk will focus on the following question: supposing a
smooth manifold immerses into C^n as an exact Lagrangian, what is the
minimal number of transverse self-intersections necessary? Finding lower
bounds on the number of intersections of two embedded Lagrangians is a
central problem in symplectic topology which has seen much success; in
contrast bounding the number of self-intersections of an exact Lagrangian
immersion requires more advanced tools and the known results are far less
general. We show that no Arnold-type lower bound exists for exact
Lagrangian immersions by constructing examples with surprisingly few
self-intersections. For example, we show that any three-manifold immerses
as an exact Lagrangian in C^3 with a single transverse self-intersection.
We also apply Lagrangian surgery to these immersions to give some
interesting new examples of Lagrangian embeddings. (This is joint work of
the speaker with T. Ekholm, Y. Eliashberg, and I. Smith.)
 
===Yuan-qi Wang (UCSB)===
''TBA''
 
== Fall 2012==




== Fall 2017 ==


{| cellpadding="8"
{| cellpadding="8"
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!align="left" | host(s)
|-
|-
|September 21
|September 8
| [http://www.math.wisc.edu/~josizemore/ Owen Sizemore] (Wisconsin)
|TBA
| [[#Owen Sizemore (Wisconsin) |
|TBA
''Operator Algebra Techniques in Measureable Group Theory'']]
|TBA
| local
|-
|-
|September 28
|September 15
|[https://engineering.purdue.edu/~mboutin/ Mireille Boutin] (Purdue)
|Jiyuan Han (University of Wisconsin-Madison)
|[[#Mireille Boutin (Purdue) |
|[[#Jiyuan Han| "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"]]
''The Pascal Triangle of a discrete Image: <br>
|Local
definition, properties, and application to object segmentation'']]
|[http://www.math.wisc.edu/~maribeff/ Mari Beffa]
|-
|-
|October 5
|September 22
| [http://www.math.msu.edu/~schmidt/ Ben Schmidt] (Michigan State)
|Sigurd Angenent (UW-Madison)
| [[#Ben Schmidt (Michigan State)|
|[[#Sigurd Angenent| "Topology of closed geodesics on surfaces and curve shortening"]]
''Three manifolds of constant vector curvature'']]
|Local
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
|-
|-
|October 12
|September 29
| [https://www2.bc.edu/ian-p-biringer/ Ian Biringer] (Boston College)
|Ke Zhu (Minnesota State University)
| [[#Ian Biringer (Boston College)|
|[[#Ke Zhu| "Isometric Embedding via Heat Kernel"]]
''Growth of Betti numbers and a probabilistic take on Gromov Hausdorff convergence'']]
|Bing Wang
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
|-
|-
|October 19
|October 6
| Peng Gao (Simons Center for Geometry and Physics)
|Shaosai Huang (Stony Brook)
| [[#Peng Gao (Simons Center for Geometry and Physics)|
|[[#Shaosai Huang| "\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"]]
''string theory partition functions and geodesic spectrum'']]
|Bing Wang
|[http://www.math.wisc.edu/~bwang/ Wang]
|-
|-
|October 26
|October 13
| [http://www.math.wisc.edu/~nelson/ Jo Nelson] (Wisconsin)
|Sebastian Baader (Bern)
| [[#Jo Nelson (Wisconsin) |
|[[#Sebastian Baader| "A filtration of the Gordian complex via symmetric groups"]]
''Cylindrical contact homology as a well-defined homology theory? Part I'']]
|Kjuchukova
| local
|-
|-
|November 2
|October 20
| [http://www.bowdoin.edu/~jtaback/ Jennifer Taback] (Bowdoin)
|Shengwen Wang (Johns Hopkins)
| [[#Jennifer Taback (Bowdoin)|
|[[#Shengwen Wang| "Hausdorff stability of round spheres under small-entropy perturbation"]]
''The geometry of twisted conjugacy classes in Diestel-Leader groups'']]
|Lu Wang
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
|-
|-
|November 9
|October 27
| [http://math.uchicago.edu/~wilsonj/ Jenny Wilson] (Chicago)
|Marco Mendez-Guaraco (Chicago)
| [[#Jenny Wilson (Chicago)|
|[[#Marco Mendez-Guaraco| "Some geometric aspects of the Allen-Cahn equation"]]
''FI-modules for Weyl groups'']]
|Lu Wang
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]
|-
|-
|November 16
|November 3
|[http://www.math.uic.edu/people/profile?id=GasJ574 Jonah Gaster] (UIC)
|TBA
|[[#Jonah Gaster (UIC)|
|TBA
''A Non-Injective Skinning Map with a Critical Point'']]
|TBA
|[http://www.math.wisc.edu/~rkent/ Kent]
|-
|-
| Thanksgiving Recess
|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>
|  
|  
|  
|-
|-
|November 30
|December 1
| [http://www.its.caltech.edu/~shinpei/ Shinpei Baba] (Caltech)
|TBA
|[[#Shinpei Baba (Caltech)|
|TBA
''Grafting and complex projective structures'']]
|TBA
|[http://www.math.wisc.edu/~rkent/ Kent]
|-
|-
|December 7
|December 8
| [http://math.uchicago.edu/~mann/ Kathryn Mann] (Chicago)
|Brian Hepler (Northeastern University)
|[[#Kathryn Mann (Chicago)|
|[[#Brian Hepler| "Deformation Formulas for Parameterizable Hypersurfaces"]]
''The group structure of diffeomorphism groups'']]
|Max
|[http://www.math.wisc.edu/~rkent/ Kent]
|-
|-
|
|}
|}


== Fall Abstracts ==
== Fall Abstracts ==


===Owen Sizemore (Wisconsin)===
=== Jiyuan Han ===
''Operator Algebra Techniques in Measureable Group Theory''
"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"


Measurable group theory is the study of groups via their actions on measure spaces. While the classification for amenable groups was essentially complete by the early 1980's, progress for nonamenable groups has been slow to emerge. The last 15 years has seen a surge in the classification of ergodic actions of nonamenable groups, with methods coming from diverse areas. We will survey these new results, as well as, give an introduction to the operator algebra techniques that have been used.
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.


===Mireille Boutin (Purdue)===
=== Sigurd Angenent ===
''The Pascal Triangle of a discrete Image: definition, properties, and application to object segmentation''
"Topology of closed geodesics on surfaces and curve shortening"


We define the Pascal Triangle of a discrete (gray scale) image as a pyramidal ar-
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.
rangement of complex-valued moments and we explore its geometric significance. In
particular, we show that the entries of row k of this triangle correspond to the Fourier
series coefficients of the moment of order k of the Radon transform of the image. Group
actions on the plane can be naturally prolonged onto the entries of the Pascal Triangle. We study the induced action of some common group actions, such as translation,
rotations, and reflections, and we propose simple tests for equivalence and self-
equivalence for these group actions. The motivating application of this work is the
problem of recognizing ”shapes” on images, for example characters, digits or simple
graphics. Application to the MERGE project, in which we developed a fast method for segmenting hazardous material signs on a cellular phone, will be also discussed.  


This is joint work with my graduate students Shanshan Huang and Andrew Haddad.
=== Ke Zhu===
"Isometric Embedding via Heat Kernel"


===Ben Schmidt (Michigan State)===
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.
''Three manifolds of constant vector curvature.''


A Riemannian manifold M is said to have extremal curvature K if all sectional curvatures are bounded above by K or if all sectional curvatures are bounded below by K.  A manifold with extremal curvature K has constant vector curvature K if every tangent vector to M belongs to a tangent plane of curvature K.  For surfaces, having constant vector curvature is equivalent to having constant curvature.  In dimension three, the eight Thurston geometries all have constant vector curvature.  In this talk, I will discuss the classification of closed three manifolds with constant vector curvature.  Based on joint work with Jon Wolfson.
=== Shaosai Huang ===
"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"


===Ian Biringer (Boston College)===
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 \epsilon-regularity, 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 \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant.
''Growth of Betti numbers and a probabilistic take on Gromov Hausdorff convergence''


We will describe an asymptotic relationship between the volume and the Betti numbers of certain locally symmetric spaces. The proof uses an exciting new tool: a synthesis of Gromov-Hausdorff convergence of Riemannian manifolds and Benjamini-Schramm convergence from graph theory.
=== Sebastian Baader ===
"A filtration of the Gordian complex via symmetric groups"


===Peng Gao (Simons Center for Geometry and Physics)===
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.
''string theory partition functions and geodesic spectrum''


String theory partition functions often have nice modular properties, which is well understood within the context of representation theory of (supersymmetric extensions) of Virasoro algebra.
=== Shengwen Wang ===
However, many questions of physical importance are preferrably addressed when string theory is formulated in terms of non-linear sigma model on a Riemann surface with a Riemannian manifold as target space. Traditionally, physicists have studied such sigma models within the realm of perturbation theory, overlooking a large class of very natural critical points of the path integral, namely, closed geodesics on the target space Riemannian manifold. We propose how to take into account the effect of these critical points on the path integral, and initiate its study on Ricci flat targe spaces, such as the K3 surface.
"Hausdorff stability of round spheres under small-entropy perturbation"


===Jo Nelson (Wisconsin)===
Colding-Minicozzi 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. Bernstein-Wang proved that round n-spheres minimize entropy among all closed hypersurfaces for n less than or equal to 6, and the result is generalized to all dimensions by Zhu. Bernstein-Wang later also proved that the round 2-sphere is actually Hausdorff stable under small-entropy perturbations. I will present in this talk the generalization of the Hausdorff stability to round hyper-spheres in all dimensions.
''Cylindrical contact homology as a well-defined homology theory? Part I''


In this talk I will define all the concepts in the title, starting with what a contact manifold is.  I will also  explain how the heuristic arguments sketched in the literature since 1999 fail to define a homology theory and provide a foundation for a well-defined cylindrical contact homology, while still providing an invariant of the contact structure.  A later talk will provide us with a large class of examples under which one can compute a well-defined version of cylindrical contact homology via a new approach the speaker developed for her thesis that is distinct and completely independent of previous specialized attempts.
=== Marco Mendez-Guaraco ===
"Some geometric aspects of the Allen-Cahn equation"


===Jennifer Taback (Bowdoin)===
In this talk I will discuss both local and global properties of the stationary Allen-Cahn 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 min-max proof of the celebrated Almgren-Pitts theorem.
''The geometry of twisted conjugacy classes in Diestel-Leader groups''


The problem of computing the Reidemsieter number R(f)  of a group automorphism f, that is, the number of f-twisted conjugacy classes, is related to questions in Lefschetz-Nielsen fixed point theory.  We say a group has property R-infinity if every group automorphism has infinitely many twisted conjugacy classes.  This property has been studied by Fel’shtyn, Gonzalves, Wong, Lustig, Levitt and others, and has applications outside of topology.
=== Ovidiu Munteanu ===
"The geometry of four dimensional shrinking Ricci solitons"
Twisted conjugacy classes in lamplighter groups are well understood both geometrically and algebraically.  In particular the lamplighter group L_n does not have property R-infinity iff (n,6)=1. In this talk I will extend these results to Diestel-Leader groups with a surprisingly different conclusion.  The family of Diestel-Leader groups provides a natural geometric generalization of the lamplighter groups.  I will define these groups, as well as Diestel-Leader graphs and describe how these results include a computation of the automorphism group of this family.
This is joint work with Melanie Stein and Peter Wong.


===Jenny Wilson (Chicago)===
I will present several results, joint with Jiaping Wang, about the asymptotic structure of four dimensional gradient shrinking Ricci solitons.  
''FI-modules for Weyl groups''
 
Earlier this year, Church, Ellenberg, and Farb developed a new framework for studying sequences of representations of the symmetric groups, using a concept they call an FI--module. I will give an overview of this theory, and describe how it generalizes to sequences of representations of the classical Weyl groups in Type B/C and D. The theory of FI--modules has provided a wealth of new results by numerous authors working in algebra, geometry, and topology. I will outline some of these results, including applications to configurations spaces and groups related to the braid group.
 
===Jonah Gaster (UIC)===
''A Non-Injective Skinning Map with a Critical Point''
 
Following Thurston, certain classes of 3-manifolds yield holomorphic maps on the Teichmuller spaces of their boundary components. Inspired by numerical evidence of Kent and Dumas, we present a negative result about the regularity of such maps. Namely, we construct a path of deformations of the hyperbolic structure on a genus-2 handlebody, with two rank-1 cusps. The presence of some extra symmetry yields information about the convex core, which is used to conclude some inequalities involving the extremal length of a certain symmetric curve family. The existence of a critical point for the associated skinning map follows.
 
===Shinpei Baba (Caltech)===
''Grafting and complex projective structures''
 
A complex projective structure is a certain geometric structure on a (real) surface, and it corresponds a representation from the fundamental group of the base surface into PSL(2,C).  We discuss about a certain surgery operation, called a 2&pi;&ndash;grafting, which produces a different projective structure, preserving its holonomy representation.
This surgery is closely related to three-dimensional hyperbolic geometry.
 
===Kathryn Mann (Chicago)===
''The group structure of diffeomorphism groups''
 
Abstract:
What is the relationship between manifolds and the structure of their
diffeomorphism groups?
On the positive side, a remarkable theorem of Filipkiewicz says that the
group structure determines the manifold: if Diff(M) and Diff(N) are
isomorphic, then M and N are diffeomorphic.
On the negative side, we know little else.  Could the group Diff(M) act by
diffeomorphisms on M in nonstandard ways?  Does the "size" of Diff(M) say
anything about the complexity of M?  Ghys asked if M and N are manifolds,
and the group of compactly supported diffeomorphisms of N injects into the
group of compactly supported diffeomorphisms of M, can the dimension of M
be less than dim(N)?  We'll discuss these and other questions, and answer
these in the (already quite rich) case of dim(M)=1.


=== Brian Hepler ===
"Deformation Formulas for Parameterizable Hypersurfaces"


We investigate one-parameter 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 multiple-point complex, a perverse sheaf naturally associated to any parameterized hypersurface.


== Archive of past Geometry seminars ==
== Archive of past Geometry seminars ==
 
2016-2017  [[Geometry_and_Topology_Seminar_2016-2017]]
<br><br>
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]
<br><br>
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]
<br><br>
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]
<br><br>
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]
<br><br>
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]
<br><br>
<br><br>
2010: [[Fall-2010-Geometry-Topology]]
2010: [[Fall-2010-Geometry-Topology]]

Revision as of 02:58, 12 January 2018

The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Alexandra Kjuchukova or Lu Wang .

Hawk.jpg


Spring 2018

date speaker title host(s)
January 26 TBA TBA TBA
February 2 TBA TBA TBA
February 9 TBA TBA TBA
February 16 TBA TBA TBA
February 23 TBA TBA TBA
March 2 TBA TBA TBA
March 9 TBA TBA TBA
March 16 TBA TBA TBA
March 23 TBA TBA TBA
Spring Break
April 6 TBA TBA TBA
April 13 TBA TBA TBA
April 20 TBA TBA TBA
April 27 TBA TBA TBA
May 4 TBA TBA TBA

Spring Abstracts

TBA

TBA


Fall 2017

date speaker title host(s)
September 8 TBA TBA TBA
September 15 Jiyuan Han (University of Wisconsin-Madison) "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces" Local
September 22 Sigurd Angenent (UW-Madison) "Topology of closed geodesics on surfaces and curve shortening" Local
September 29 Ke Zhu (Minnesota State University) "Isometric Embedding via Heat Kernel" Bing Wang
October 6 Shaosai Huang (Stony Brook) "\epsilon-Regularity for 4-dimensional shrinking Ricci solitons" Bing Wang
October 13 Sebastian Baader (Bern) "A filtration of the Gordian complex via symmetric groups" Kjuchukova
October 20 Shengwen Wang (Johns Hopkins) "Hausdorff stability of round spheres under small-entropy perturbation" Lu Wang
October 27 Marco Mendez-Guaraco (Chicago) "Some geometric aspects of the Allen-Cahn equation" Lu Wang
November 3 TBA TBA TBA
November 10 TBA TBA TBA
November 17 Ovidiu Munteanu (University of Connecticut) "The geometry of four dimensional shrinking Ricci solitons" Bing Wang
Thanksgiving Recess
December 1 TBA TBA TBA
December 8 Brian Hepler (Northeastern University) "Deformation Formulas for Parameterizable Hypersurfaces" Max

Fall Abstracts

Jiyuan Han

"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

"\epsilon-Regularity for 4-dimensional 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 \epsilon-regularity, 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 \epsilon-regularity result for 4-dimensional 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 small-entropy perturbation"

Colding-Minicozzi 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. Bernstein-Wang proved that round n-spheres minimize entropy among all closed hypersurfaces for n less than or equal to 6, and the result is generalized to all dimensions by Zhu. Bernstein-Wang later also proved that the round 2-sphere is actually Hausdorff stable under small-entropy perturbations. I will present in this talk the generalization of the Hausdorff stability to round hyper-spheres in all dimensions.

Marco Mendez-Guaraco

"Some geometric aspects of the Allen-Cahn equation"

In this talk I will discuss both local and global properties of the stationary Allen-Cahn 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 min-max proof of the celebrated Almgren-Pitts 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 one-parameter 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 multiple-point complex, a perverse sheaf naturally associated to any parameterized hypersurface.

Archive of past Geometry seminars

2016-2017 Geometry_and_Topology_Seminar_2016-2017

2015-2016: Geometry_and_Topology_Seminar_2015-2016

2014-2015: Geometry_and_Topology_Seminar_2014-2015

2013-2014: Geometry_and_Topology_Seminar_2013-2014

2012-2013: Geometry_and_Topology_Seminar_2012-2013

2011-2012: Geometry_and_Topology_Seminar_2011-2012

2010: Fall-2010-Geometry-Topology