Geometry and Topology Seminar: 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'''. For more information, contact Shaosai Huang.
The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1pm - 2:20pm'''. For more information, contact Alex Waldron.
 
In the fall of 2020, we will hold '''online meetings''' on
[https://uwmadison.zoom.us/j/94578957620 Zoom platform] 
(available every '''Friday 1:00pm - 2:30pm''').
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== Fall 2020 ==
== Fall 2021 ==


{| cellpadding="8"
{| cellpadding="8"
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!align="left" | speaker
!align="left" | speaker
!align="left" | title
!align="left" | title
!align="left" | host(s)
|-
|-
|Oct. 23
|Sep. 10
|Yu Li (Stony Brook)
|
| On the ancient solutions to the Ricci flow
|Organizational meeting
|(Huang)
|-
|Sep. 17
|Alex Waldron
|Harmonic map flow for almost-holomorphic maps
|-
|Sep. 24
|Sean Paul
|
|-
|Oct. 1
|Andrew Zimmer
|
|-
|Oct. 8
|Laurentiu Maxim
|
|-
|Oct. 15
|Gavin Ball
|
|-
|-
|Oct. 30
|Oct. 22
|Yi Lai (Berkeley)
|Botong Wang
| A family of 3d steady gradient solitons that are flying wings
|
|(Huang)
|-
|-
|Nov. 6
|Oct. 29
|Jiyuan Han (Purdue)
|Brian Hepler
| On the Yau-Tian-Donaldson conjecture for generalized Kähler-Ricci soliton equations
|
|(Chen)
|-
|-
|Nov. 13
|Nov. 5
|Ilyas Khan (Madison)
|Chenxi Wu
|Rigidity Properties of Mean Curvature Flow Translators with Curvature Conditions
|
|(Local)
|-
|-
|Nov. 20
|Nov. 12
|Max Hallgren (Cornell)
|Sigurd Angenent
|The Entropy of Ricci Flows with a Type-I Scalar Curvature Bound
|
|(Huang)
|-
|-
|Dec. 4
|Yang Li (IAS)
| TBA
|(Chen)
|}
|}


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


===Yu Li===
===Alex Waldron===
Ancient solutions model the singularity formation of the Ricci flow.  In two and three dimensions, we currently have complete classifications for κ-noncollapsed ancient solutions, while the higher dimensional problem remains open. This talk will survey some recent developments of κ-noncollapsed ancient solutions with nonnegative curvature in higher dimensions.


===Yi Lai===
I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.
We found a family of $\mathbb{Z}_2\times O(2)$-symmetric 3d steady gradient Ricci solitons. We show that these solitons are all flying wings. This confirms a conjecture of Hamilton.


===Jiyuan Han===
Let (X,D) be a log variety with an effective holomorphic torus action, and Θ be a closed positive (1,1)-current. For any smooth positive function g defined on the moment polytope of the torus action, we study the Monge-Ampere equations that correspond to generalized and twisted Kahler-Ricci g-solitons. We prove a version of Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing that the existence of solutions is always equivalent to an equivariantly uniform Θ-twisted g-Ding-stability. When Θ is a current associated to a torus invariant linear system, we further show
that equivariant special test configurations suffice for testing the stability. Our results allow arbitrary klt singularities and generalize most of previous results on (uniform) YTD conjecture for (twisted) Kahler-Ricci/Mabuchi solitons or Kahler-Einstein metrics. This is a joint work with Chi Li.


===Ilyas Khan===
In this talk we discuss some uniqueness results for mean curvature flow translators. Under certain curvature conditions, we classify the blow-down limits of translating solutions of the mean curvature flow and employ recent techniques from the theory of ancient MCF solutions to show the uniqueness of translators with these blow-down limits.
===Max Hallgren===
In this talk, we study the singularities of closed Ricci flow solutions which satisfy a Type-I scalar curvature assumption. Bamler's structure theory of Ricci flows with bounded scalar curvature shows that singularities are modeled on shrinking Ricci solitons with singularities of codimension 4. We extend the analysis by characterizing the singular set of the flow in terms of a Gaussian density functional, and also establish entropy uniqueness of dilation limits at a fixed point, generalizing results previously known assuming a Type-I bound on the full curvature tensor.  We also show that in dimension 4, the singular Ricci soliton is smooth away from finitely many points, which are conical smooth orbifold singularities.


== Archive of past Geometry seminars ==
== Archive of past Geometry seminars ==
2020-2021  [[Geometry_and_Topology_Seminar_2020-2021]]
<br><br>
2019-2020 [[Geometry_and_Topology_Seminar_2019-2020]]
2019-2020 [[Geometry_and_Topology_Seminar_2019-2020]]
<br><br>
<br><br>
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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]]<br>
[[Fall-2010-Geometry-Topology]]<br>
[[Dynamics_Seminar_2020-2021]]
[[Dynamics_Seminar_2020-2021]]

Revision as of 14:58, 17 September 2021

The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1pm - 2:20pm. For more information, contact Alex Waldron.


Hawk.jpg


Fall 2021

date speaker title
Sep. 10 Organizational meeting
Sep. 17 Alex Waldron Harmonic map flow for almost-holomorphic maps
Sep. 24 Sean Paul
Oct. 1 Andrew Zimmer
Oct. 8 Laurentiu Maxim
Oct. 15 Gavin Ball
Oct. 22 Botong Wang
Oct. 29 Brian Hepler
Nov. 5 Chenxi Wu
Nov. 12 Sigurd Angenent



Fall Abstracts

Alex Waldron

I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.


Archive of past Geometry seminars

2020-2021 Geometry_and_Topology_Seminar_2020-2021

2019-2020 Geometry_and_Topology_Seminar_2019-2020

2018-2019 Geometry_and_Topology_Seminar_2018-2019

2017-2018 Geometry_and_Topology_Seminar_2017-2018

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

Fall-2010-Geometry-Topology

Dynamics_Seminar_2020-2021