Geometry and Topology Seminar 2019-2020: Difference between revisions

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== Fall 2010 ==
The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.
<br>
For more information, contact [http://www.math.wisc.edu/~kjuchukova Alexandra Kjuchukova] or [https://sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] .


The seminar will be held  in room B901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm
[[Image:Hawk.jpg|thumb|300px]]
 
 
== Spring 2018 ==
 
{| cellpadding="8"
!align="left" | date
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|January 26
|Jingrui Cheng
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence"]]
|Local
|-
|February 2
|Jingrui Cheng
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]
|Local
|-
|February 9
|Jingrui Cheng
|[[#Jingrui Cheng|"Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued)]]
|Local
|-
|February 16
|TBA
|TBA
|TBA
|-
|February 23
|TBA
|TBA
|TBA
|-
|March 2
|TBA
|TBA
|TBA
|-
|March 9
|TBA
|TBA
|TBA
|-
|March 16
|Yu Li
|[[#Yu Li|"The Rigidity of Ricci shrinkers of dimension four"]]
|Bing Wang
|-
|March 23
|TBA
|TBA
|TBA
|-
|<b> Spring Break </b>
|
|
|-
|April 6
|Wei Ho
|TBA
|Daniel Erman
|-
|April 13
|TBA
|TBA
|TBA
|-
|April 20
|Pei-Ken Hung (Columbia Univ.)
|TBA
|Lu Wang
|-
|April 27
|TBA
|TBA
|TBA
|-
|May 4
|TBA
|TBA
|TBA
|-
|
|}
 
== Spring Abstracts ==
 
=== Jingrui Cheng ===
 
"Estimates for constant scalar curvature Kahler metrics with applications to existence"
 
We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.
 
===Yu Li===
 
"The rigidity of Ricci shrinkers of dimension four"
 
In dimension 4, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov- Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curva- ture and potential functions on Ricci shrinkers satisfying some natural geometric properties.
This is a joint work with Bing Wang.
 
== Fall 2017 ==


{| cellpadding="8"
{| cellpadding="8"
Line 9: Line 114:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|September 10
|September 8
|[http://www.math.wisc.edu/~oh/ Yong-Geun Oh] (UW Madison)
|TBA
|[[#Yong-Geun Oh (UW Madison)|
|TBA
''Counting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants'']]
|TBA
|local
|-
|-
|September 17
|September 15
|Leva Buhovsky (U of Chicago)
|Jiyuan Han (University of Wisconsin-Madison)
|[[#Leva Buhovsky (U of Chicago)|
|[[#Jiyuan Han| "On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"]]
''On the uniqueness of Hofer's geometry'']]
|Local
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
|-
|-
|September 24
|September 22
|[http://sites.google.com/site/polterov/home/ Leonid Polterovich] (Tel Aviv U and U of Chicago)
|Sigurd Angenent (UW-Madison)
|[[#Leonid Polterovich (Tel Aviv U and U of Chicago)|
|[[#Sigurd Angenent| "Topology of closed geodesics on surfaces and curve shortening"]]
''Poisson brackets and symplectic invariants'']]
|Local
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
|-
|-
|October 8
|September 29
|[http://www.math.wisc.edu/~stpaul/ Sean Paul] (UW Madison)
|Ke Zhu (Minnesota State University)
|[[#Sean Paul (UW Madison)|
|[[#Ke Zhu| "Isometric Embedding via Heat Kernel"]]
''Canonical Kahler metrics and the stability of projective varieties'']]
|Bing Wang
|local
|-
|-
|October 15
|October 6
|Conan Leung (Chinese U. of Hong Kong)
|Shaosai Huang (Stony Brook)
|[[#Conan Leung (Chinese U. of Hong Kong)|
|[[#Shaosai Huang| "\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"]]
''SYZ mirror symmetry for toric manifolds'']]
|Bing Wang
|Honorary fellow, local
|-
|-
|October 22
|October 13
|[http://www.mathi.uni-heidelberg.de/~banagl/ Markus Banagl] (U. Heidelberg)
|Sebastian Baader (Bern)
|[[# Markus Banagl (U. Heidelberg)|
|[[#Sebastian Baader| "A filtration of the Gordian complex via symmetric groups"]]
''Intersection Space Methods and Their Application to Equivariant Cohomology, String Theory, and Mirror Symmetry'']]
|Kjuchukova
|[http://www.math.wisc.edu/~maxim/ Maxim]
|-
|-
|October 29
|October 20
|[http://www.math.umn.edu/~zhux0086/ Ke Zhu] (U of Minnesota)
|Shengwen Wang (Johns Hopkins)
|[[#Ke Zhu (U of Minnesota)|
|[[#Shengwen Wang| "Hausdorff stability of round spheres under small-entropy perturbation"]]
''Thick-thin decomposition of Floer trajectories and adiabatic gluing'']]
|Lu Wang
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
|-
|-
|November 5
|October 27
|[http://www.math.psu.edu/tabachni/ Sergei Tabachnikov]  (Penn State)
|Marco Mendez-Guaraco (Chicago)
|[[#Sergei Tabachnikov (Penn State)|
|[[#Marco Mendez-Guaraco| "Some geometric aspects of the Allen-Cahn equation"]]
''Algebra, geometry, and dynamics of the pentagram map'']]
|Lu Wang
|[http://www.math.wisc.edu/~maribeff/ Gloria]
|-
|-
|December 3
|November 3
|[http://www.math.northwestern.edu/~zaslow/ Eric Zaslow]  (Northwestern University)
|TBA
|[[#Eric Zaslow (Northwestern University)|
|TBA
''TBA'']]
|TBA
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
|-
|-
|December 10
|November 10
|Wenxuan Lu  (MIT)
|TBA
|[[#Wenxuan Lu (MIT)|
|TBA
''TBA'']]
|TBA
|[http://www.math.wisc.edu/~oh/ Young-Geun and Conan Leung]
|-
|-
|January 21
|November 17
|Mohammed Abouzaid (Clay Institute & MIT)
|Ovidiu Munteanu (University of Connecticut)
|[[#Mohammed Abouzaid (Clay Institute & MIT)|
|[[#Ovidiu Munteanu| "The geometry of four dimensional shrinking Ricci solitons"]]
''TBA'']]
|Bing Wang
|[http://www.math.wisc.edu/~oh/ Yong-Geun]
|-
|<b>Thanksgiving Recess</b>
|
|
|
|-
|December 1
|TBA
|TBA
|TBA
|-
|December 8
|Brian Hepler (Northeastern University)
|[[#Brian Hepler| "Deformation Formulas for Parameterizable Hypersurfaces"]]
|Max
|-
|-
|}
|}


== Abstracts ==
== Fall Abstracts ==
===Yong-Geun Oh (UW Madison)===
 
''Counting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants''
=== 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.


Gopakumar-Vafa BPS invariant is some integer counting invariant of the cohomology
=== Sigurd Angenent ===
of D-brane moduli spaces in string theory. In relation to the Gromov-Witten theory,
"Topology of closed geodesics on surfaces and curve shortening"
it is expected that the invariant would coincide with the `number' of embedded
(pseudo)holomorphic curves (Gopakumar-Vafa conjecture). In this talk, we will explain the speaker's recent
result that the latter integer invariants can be defined for a generic choice of
compatible almost complex structures. We will also discuss the corresponding
wall-crossing phenomena and some open questions towards a complete solution to
the Gopakumar-Vafa conjecture.


===Leva Buhovsky (U of Chicago)===
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.
''On the uniqueness of Hofer's geometry''


In this talk we address the question whether Hofer's metric is unique among the Finsler-type bi-invariant metrics on the group of Hamiltonian diffeomorphisms. The talk is based on a recent joint work with Yaron Ostrover.
=== Ke Zhu===
"Isometric Embedding via Heat Kernel"


===Leonid Polterovich (Tel Aviv U and U of Chicago)===
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.
''Poisson brackets and symplectic invariants''


We discuss new invariants associated to collections of closed subsets
=== Shaosai Huang ===
of a symplectic manifold. These invariants are defined
"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"
through an elementary variational problem involving Poisson brackets.
The proof of non-triviality of these invariants requires methods of modern
symplectic topology (Floer theory). We present applications
to approximation theory on symplectic manifolds and to Hamiltonian dynamics.
The talk is based on a work in progress with Lev Buhovsky and Michael Entov.


===Sean Paul (UW Madison)===
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.
''Canonical Kahler metrics and the stability of projective varieties"


I will give a survey of my own work on this problem, the basic reference is:
=== Sebastian Baader ===
http://arxiv.org/pdf/0811.2548v3
"A filtration of the Gordian complex via symmetric groups"


===Conan Leung (Chinese U. of Hong Kong)===
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.
''SYZ mirror symmetry for toric manifolds''


===Markus Banagl (U. Heidelberg)===
=== Shengwen Wang ===
''Intersection Space Methods and Their Application to Equivariant Cohomology, String Theory, and Mirror Symmetry.''
"Hausdorff stability of round spheres under small-entropy perturbation"


Using homotopy theoretic methods, we shall associate to certain classes of
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.
singular spaces generalized geometric Poincaré complexes called intersection
spaces. Their cohomology is generally not isomorphic to intersection
cohomology.
In this talk, we shall concentrate on the applications of the new
cohomology theory to the equivariant real cohomology of isometric actions of
torsionfree discrete groups, to type II string theory and D-branes, and to
the relation of the new theory to classical intersection cohomology under
mirror symmetry.


===Ke Zhu (U of Minnesota)===
=== Marco Mendez-Guaraco ===
''Thick-thin decomposition of Floer trajectories and adiabatic gluing''
"Some geometric aspects of the Allen-Cahn equation"


Let f be a generic Morse function on a symplectic manifold M.
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.
For Floer trajectories of Hamiltonian \e f, as \e goes to 0 Oh proved that
they converge to “pearl complex” consisiting of J-holomorphic spheres
and joining gradient segments of f. The J-holomorphic spheres come from the
“thick” part of Floer trajectories and the gradient segments come from
the “thin” part. Similar “thick-thin” compactification result has
also been obtained by Mundet-Tian in twisted holomorphic map setting. In
this talk, we prove the reverse gluing result in the simplest setting: we
glue from disk-flow-dsik configurations to nearby Floer trajectories of  
Hamitonians K_{\e} for sufficiently small \e and also show the  
surjectivity. (Most part of the Hamiltonian K_{\e} is \ef). We will discuss
the application to PSS isomorphism. This is a joint work with Yong-Geun Oh.


===Sergei Tabachnikov (Penn State)===
=== Ovidiu Munteanu ===
''Algebra, geometry, and dynamics of the pentagram map''
"The geometry of four dimensional shrinking Ricci solitons"


Introduced by R. Schwartz almost 20  years ago, the pentagram map acts on plane n-gons, considered up to projective equivalence, by drawing the diagonals that connect second-nearest vertices and taking the new n-gon formed by their intersections. I shall survey recent work on the pentagram map, in particular, I shall demonstrate  that the dynamics of the pentagram map  is completely integrable. I shall also explain that the pentagram map is a discretization of the Boussinesq equation, a well known completely integrable partial differential equation. A surprising relation between the spaces of polygons and combinatorial objects called the 2-frieze patterns (generalizing the frieze patterns of Coxeter) will be described. Eight new(?) configuration theorems of projective geometry will be demonstrated. The talk is illustrated by computer animation.
I will present several results, joint with Jiaping Wang, about the asymptotic structure of four dimensional gradient shrinking Ricci solitons.  


===Eric Zaslow (Northwestern University)===
=== Brian Hepler ===
''TBA''
"Deformation Formulas for Parameterizable Hypersurfaces"


===Wenxuan Lu (MIT)===
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.
''TBA''


===Mohammed Abouzaid (Clay Institute & MIT)===
== Archive of past Geometry seminars ==
''TBA''
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]]
<br><br>
2010: [[Fall-2010-Geometry-Topology]]

Revision as of 22:10, 9 March 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 Jingrui Cheng "Estimates for constant scalar curvature Kahler metrics with applications to existence" Local
February 2 Jingrui Cheng "Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued) Local
February 9 Jingrui Cheng "Estimates for constant scalar curvature Kahler metrics with applications to existence" (continued) Local
February 16 TBA TBA TBA
February 23 TBA TBA TBA
March 2 TBA TBA TBA
March 9 TBA TBA TBA
March 16 Yu Li "The Rigidity of Ricci shrinkers of dimension four" Bing Wang
March 23 TBA TBA TBA
Spring Break
April 6 Wei Ho TBA Daniel Erman
April 13 TBA TBA TBA
April 20 Pei-Ken Hung (Columbia Univ.) TBA Lu Wang
April 27 TBA TBA TBA
May 4 TBA TBA TBA

Spring Abstracts

Jingrui Cheng

"Estimates for constant scalar curvature Kahler metrics with applications to existence"

We develop new a priori estimates for scalar curvature type of equations on a compact Kahler manifold. As an application, we show that the properness of K-energy implies the existence of constant scalar curvature Kahler metrics. I will also talk about other applications if time permits. This is joint work with Xiuxiong Chen.

Yu Li

"The rigidity of Ricci shrinkers of dimension four"

In dimension 4, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov- Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curva- ture and potential functions on Ricci shrinkers satisfying some natural geometric properties. This is a joint work with Bing Wang.

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