https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Dwang&feedformat=atomUW-Math Wiki - User contributions [en]2020-04-07T08:20:39ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Fall_2012_Symplectic_Geometry_Seminar&diff=5006Fall 2012 Symplectic Geometry Seminar2013-02-04T18:39:11Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|12/05<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group(continued)<br />
|<br />
|-<br />
|12/12<br />
|Yunfeng Jiang<br />
| an introduction on the geometry of spin equations<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all compact toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
'''Yunfeng Jiang''' ''an introduction on the geometry of spin equations''<br />
<br />
Abstract:<br />
<br />
I will talk about the recent progress on the study of witten equation, including the precise definition, the analysis especially the compactifications.<br />
abstract: witten equation,orbifold structure , compactifications<br />
<br />
References:<br />
<br />
http://arxiv.org/abs/1209.3045<br />
<br />
http://arxiv.org/abs/0812.4781<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Fall_2012_Symplectic_Geometry_Seminar&diff=5005Fall 2012 Symplectic Geometry Seminar2013-02-04T18:39:02Z<p>Dwang: New page: Wednesday 3:30pm-5:00pm VV B139 *If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang] ...</p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|12/05<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group(continued)<br />
|<br />
|-<br />
|12/12<br />
|Yunfeng Jiang<br />
| an introduction on the geometry of spin equations<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all compact toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
'''Yunfeng Jiang''' ''an introduction on the geometry of spin equations''<br />
<br />
Abstract:<br />
<br />
I will talk about the recent progress on the study of witten equation, including the precise definition, the analysis especially the compactifications.<br />
abstract: witten equation,orbifold structure , compactifications<br />
<br />
References:<br />
<br />
http://arxiv.org/abs/1209.3045<br />
<br />
http://arxiv.org/abs/0812.4781<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]<br />
*[[ Fall 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=5004Symplectic Geometry Seminar2013-02-04T18:38:49Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|date<br />
| name<br />
|Title<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''name''' ''title ''<br />
<br />
Abstract:<br />
<br />
???<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]<br />
*[[ Fall 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4782Symplectic Geometry Seminar2012-12-07T20:14:07Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|12/05<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group(continued)<br />
|<br />
|-<br />
|12/12<br />
|Yunfeng Jiang<br />
| an introduction on the geometry of spin equations<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all compact toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
'''Yunfeng Jiang''' ''an introduction on the geometry of spin equations''<br />
<br />
Abstract:<br />
<br />
I will talk about the recent progress on the study of witten equation, including the precise definition, the analysis especially the compactifications.<br />
abstract: witten equation,orbifold structure , compactifications<br />
<br />
References:<br />
<br />
http://arxiv.org/abs/1209.3045<br />
<br />
http://arxiv.org/abs/0812.4781<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4781Symplectic Geometry Seminar2012-12-07T20:13:27Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|12/05<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group(continued)<br />
|<br />
|-<br />
|12/12<br />
|Yunfeng Jiang<br />
| an introduction on the geometry of spin equations<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
'''Yunfeng Jiang''' ''an introduction on the geometry of spin equations''<br />
<br />
Abstract:<br />
<br />
I will talk about the recent progress on the study of witten equation, including the precise definition, the analysis especially the compactifications.<br />
abstract: witten equation,orbifold structure , compactifications<br />
<br />
References:<br />
<br />
http://arxiv.org/abs/1209.3045<br />
<br />
http://arxiv.org/abs/0812.4781<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4780Symplectic Geometry Seminar2012-12-07T20:12:24Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|10/24<br />
|Wenfeng Jiang<br />
|Classification of Free Hamitolnian-its mathematics foundation<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|12/05<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group(continued)<br />
|<br />
|-<br />
|12/12<br />
|Yunfeng Jiang<br />
| an introduction on the geometry of spin equations<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
'''Yunfeng Jiang''' ''an introduction on the geometry of spin equations''<br />
<br />
Abstract:<br />
<br />
I will talk about the recent progress on the study of witten equation, including the precise definition, the analysis especially the compactifications.<br />
abstract: witten equation,orbifold structure , compactifications<br />
<br />
References:<br />
<br />
http://arxiv.org/abs/1209.3045<br />
<br />
http://arxiv.org/abs/0812.4781<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4779Symplectic Geometry Seminar2012-12-07T20:11:59Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|10/24<br />
|Wenfeng Jiang<br />
|Classification of Free Hamitolnian-its mathematics foundation<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|12/05<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group(continued)<br />
|<br />
|-<br />
|12/12<br />
|Erkao Bao<br />
| an introduction on the geometry of spin equations<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
'''Yunfeng Jiang''' ''an introduction on the geometry of spin equations''<br />
<br />
Abstract:<br />
<br />
I will talk about the recent progress on the study of witten equation, including the precise definition, the analysis especially the compactifications.<br />
abstract: witten equation,orbifold structure , compactifications<br />
<br />
References:<br />
<br />
http://arxiv.org/abs/1209.3045<br />
<br />
http://arxiv.org/abs/0812.4781<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4749Symplectic Geometry Seminar2012-11-27T23:28:43Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|10/24<br />
|Wenfeng Jiang<br />
|Classification of Free Hamitolnian-its mathematics foundation<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|12/05<br />
|<br />
| Title<br />
|-<br />
|-<br />
|12/12<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4748Symplectic Geometry Seminar2012-11-27T23:23:13Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|10/24<br />
|Wenfeng Jiang<br />
|Classification of Free Hamitolnian-its mathematics foundation<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4747Symplectic Geometry Seminar2012-11-27T23:22:37Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|The canonical connection on contact manifolds<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|10/24<br />
|Wenfeng Jiang<br />
|Classification of Free Hamitolnian-its mathematics foundation<br />
|-<br />
|-<br />
|10/31<br />
|<br />
| Title<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|11/28<br />
|Yoosik Kim<br />
|Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Rui Wang''' ''The canonical connection on contact manifolds and an tensorial proof of exponential decay ''<br />
<br />
Abstract:<br />
<br />
We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh. <br />
<br />
'''Dongning Wang''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
'''Yoosik Kim''' ''Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group''<br />
<br />
Abstract:<br />
<br />
I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4534Symplectic Geometry Seminar2012-10-13T14:42:13Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|on Canonical Connection<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|Exponential decay<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
| 10/17<br />
|<br />
|no seminar this week<br />
|-<br />
|-<br />
|10/24<br />
|Wenfeng Jiang<br />
|Classification of Free Hamitolnian-its mathematics foundation<br />
|-<br />
|-<br />
|10/31<br />
|<br />
| Title<br />
|-<br />
|-<br />
|11/07<br />
|Dongning Wang<br />
|Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation<br />
|-<br />
|-<br />
|date<br />
|name<br />
|title<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wabg''' ''Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation''<br />
<br />
Abstract:<br />
<br />
We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4312Symplectic Geometry Seminar2012-09-14T16:09:56Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|09/19<br />
| Rui Wang<br />
|on Canonical Connection<br />
|-<br />
|-<br />
|09/26<br />
|Rui Wang<br />
|Exponential decay<br />
|-<br />
|-<br />
|10/03<br />
|Erkao Bao, Jaeho Lee<br />
|Symplectic Homology1<br />
|-<br />
|-<br />
| 10/10<br />
|Dongning Wang, Jie Zhao<br />
|Symplectic HomologyII<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|date<br />
|name<br />
|title<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract:<br />
<br />
Abstract<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4213Symplectic Geometry Seminar2012-09-06T00:26:15Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-5:00pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
<br />
|-<br />
| date<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|date<br />
|name<br />
|title<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| Title<br />
|-<br />
|-<br />
|<br />
|<br />
| <br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract:<br />
<br />
Abstract<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Spring_2012_Symplectic_Geometry_Seminar&diff=4212Spring 2012 Symplectic Geometry Seminar2012-09-06T00:22:38Z<p>Dwang: New page: Wednesday 2:15pm-4:30pm VV B139 *If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang] ...</p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 22st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 29th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|-<br />
|-<br />
|March. 7th<br />
|Jie Zhao<br />
| Title<br />
|-<br />
|-<br />
|March. 14th<br />
|Peng Zhou<br />
| Title<br />
|-<br />
|-<br />
|March. 21th<br />
|Jae-ho Lee<br />
| Title<br />
|-<br />
|-<br />
|March. 28th<br />
|Dongning Wang<br />
|Proof of the Triviality Axiom and Composition Axiom of Seidel Representation<br />
|-<br />
|April. 11th<br />
|Cheol-Hyun Cho<br />
| Title<br />
|-<br />
|-<br />
|April. 18th<br />
|Louis Lau<br />
| Title<br />
|-<br />
|-<br />
|April. 25th<br />
|Erkao Bao<br />
| On the Fukaya categories of higher genus surfaces.<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wang''' ''Seidel elements and mirror transformations''<br />
<br />
Abstract:<br />
<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
<br />
Seidel elements and mirror transformations<br />
<br />
http://arxiv.org/abs/1103.4171<br />
<br />
'''Dongning Wang''' "Proof of the Triviality Axiom and Composition Axiom of Seidel Representation"<br />
<br />
Abstract:<br />
<br />
I will briefly review the definition of Seidel representation, then introduce parametrized group action, Kuranishi structure, equivariant Kuranishi structure and parametrized equivariant Kuranishi structure, and use these to prove the triviality axiom of Seidel representation. To prove the composition axiom, I will construct a Lefschetz fibration, then consider then moduli spaces this space and their Kuranishi structures. Finally, if time permitted, I will mention the extra ingredients needed for orbifold Seidel representation.<br />
<br />
<br />
'''Erkao Bao''' ''On the Fukaya categories of higher genus surfaces''<br />
<br />
I will present Abouzaid's paper: http://arxiv.org/abs/math/0606598. In this paper he proved that the Grothendieck group of the derived Fukaya category of a surface <math>\Sigma </math> with Euler characteristic <math>\chi (\Sigma)<0 </math> is isomorphic to <math>H_1(\Sigma,\mathbb{Z})\oplus {\mathbb{Z}/ \chi (\Sigma) \mathbb{Z}} \oplus \mathbb{R}</math>.<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=4211Symplectic Geometry Seminar2012-09-06T00:22:30Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 22st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 29th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|-<br />
|-<br />
|March. 7th<br />
|Jie Zhao<br />
| Title<br />
|-<br />
|-<br />
|March. 14th<br />
|Peng Zhou<br />
| Title<br />
|-<br />
|-<br />
|March. 21th<br />
|Jae-ho Lee<br />
| Title<br />
|-<br />
|-<br />
|March. 28th<br />
|Dongning Wang<br />
|Proof of the Triviality Axiom and Composition Axiom of Seidel Representation<br />
|-<br />
|April. 11th<br />
|Cheol-Hyun Cho<br />
| Title<br />
|-<br />
|-<br />
|April. 18th<br />
|Louis Lau<br />
| Title<br />
|-<br />
|-<br />
|April. 25th<br />
|Erkao Bao<br />
| On the Fukaya categories of higher genus surfaces.<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wang''' ''Seidel elements and mirror transformations''<br />
<br />
Abstract:<br />
<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
<br />
Seidel elements and mirror transformations<br />
<br />
http://arxiv.org/abs/1103.4171<br />
<br />
'''Dongning Wang''' "Proof of the Triviality Axiom and Composition Axiom of Seidel Representation"<br />
<br />
Abstract:<br />
<br />
I will briefly review the definition of Seidel representation, then introduce parametrized group action, Kuranishi structure, equivariant Kuranishi structure and parametrized equivariant Kuranishi structure, and use these to prove the triviality axiom of Seidel representation. To prove the composition axiom, I will construct a Lefschetz fibration, then consider then moduli spaces this space and their Kuranishi structures. Finally, if time permitted, I will mention the extra ingredients needed for orbifold Seidel representation.<br />
<br />
<br />
'''Erkao Bao''' ''On the Fukaya categories of higher genus surfaces''<br />
<br />
I will present Abouzaid's paper: http://arxiv.org/abs/math/0606598. In this paper he proved that the Grothendieck group of the derived Fukaya category of a surface <math>\Sigma </math> with Euler characteristic <math>\chi (\Sigma)<0 </math> is isomorphic to <math>H_1(\Sigma,\mathbb{Z})\oplus {\mathbb{Z}/ \chi (\Sigma) \mathbb{Z}} \oplus \mathbb{R}</math>.<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]<br />
*[[ Spring 2012 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Summer_stacks&diff=3924Summer stacks2012-05-30T09:51:24Z<p>Dwang: /* Introduction */</p>
<hr />
<div>This is the page for the 2012 Summer stacks reading group. <br />
<br />
== Resources ==<br />
<br />
The book in progress of Behrend, Fulton, Kresch and other people is available here: [http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1] <br />
<br />
Thanks to Sukhendu we have a copy of Champs algebriques" by Laumon and Moret-Bailly, currently in Ed's office.<br />
<br />
The Stacks Project: [http://www.math.columbia.edu/algebraic_geometry/stacks-git/]<br />
<br />
== Milestones ==<br />
<br />
6/1 Finish Chapter 1<br />
<br />
6/14 Finish Chapter 2<br />
<br />
6/29 Finish Chapter 3<br />
<br />
7/14 Finish Chapter 4<br />
<br />
7/28 Finish Chapter 5<br />
<br />
== Comments, Questions and (hopefully) Answers ==<br />
<br />
=== Introduction ===<br />
Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle<br />
<br />
A: I figured it out myself :) The fiber product is along s (source) and t (target), which I assume means that the elements of the fiber product are pairs (f,g) such that target(f)=source(g). Thus it's okay for m to only be defined on those elements because that's all there is.<br />
<br />
Q: I'm finding the <math>\tilde{S}</math> construction in the segment on moduli space of triangles pretty confusing. Is it just (non-canonically) isomorphic to a disjoint union of 6 copies of <math>S</math>? (I'm emphasizing the non-canonicity thing since despite the notation it looks as though <math>\tilde{S}</math> ought to depend on <math>T</math> as well as <math>S</math> but I don't quite grok how that works) [[User:Dewey|Dewey]] 21:23, 26 May 2012 (UTC)<br />
<br />
A: <math>\tilde{S}</math> might be not isomorphic to a disjoint union of 6 copies of <math>S</math> at all. Take the example in the previous page: <math>S</math> being a circle, and X being a family of equilateral triangles which rotates by 120 in one revolution around the circle. The corresponding <math>\tilde{S}</math> is a NON-TRIVIAL principal <math>\mathfrak{S}_3</math> bundle over <math>S^1</math>. Imagine that you start from the point <math>(e^{0i},123)\in\tilde{S}</math> and walk along the base, when you return, you will arrive at <math>(e^{0i},231)</math>. Continue for another round, you get <math>(e^{0i},312)</math>. Yet another round you return to the starting point <math>(e^{0i},123)</math>. If you start with <math>(e^{0i},213)</math>, then you get the other three points in the fiber of the principal bundle. So <math>\tilde{S}</math> has two connected component, each is a 3-cover of the base circle. This is also consistent with your feeling that <math>\tilde{S}</math> should depend on <math>T</math> and <math>S</math>. -[http://www.math.wisc.edu/~dwang Dongning] 05:13, 29 May 2012 (UTC)<br />
<br />
Q: This question is sort of tangential, but working on the "moduli space of triangles section" now and I noticed something kind of funny. Usually saying that <math>\tilde{T}</math> is the moduli space of ordered triangles would just mean that there is a natural isomorphism from the functor <math>S \to \{X \to S\}</math> where <math>X \to S</math> is a family of ordered triangles on S, to the functor <math>Hom(-,\tilde{T})</math>. But here this is more structure. Since the morphisms in <math>\tilde{\mathfrak{T}}</math> are required to be isometries on each fiber there is actually a functor from <math>\tilde{\mathfrak{T}}</math> to the category <math>\tilde{T}-Top</math> of spaces over <math>\tilde{T}</math>, that is, the objects spaces with a specified maps to <math>\tilde{T}</math> and the morphisms are commutative triangles. Is there some way to phrase this in a way that is more like the traditional definition of a moduli space? Like, maybe replace <math>Hom(-,\tilde{T})</math> with the functor Top --> Cat sending <math>S</math> to the fully subcategory of <math>\tilde{T}-Top</math> consisting of morphisms <math>S \to \tilde{T}</math>? [[User:Dewey|Dewey]] 22:42, 27 May 2012 (UTC)<br />
<br />
Something similar is going on in the section on elliptic curves. Rather than look at a moduli functor we look at a category of families of elliptic curves. Interestingly the morphisms are all required to be ''cartesian'' commutative squares. This should somehow correspond to the fact that in the moduli functor setup, the map on hom-sets is defined using pullback. Maybe what is really giong on in the moduli space of triangles section is not that the map on fibers is required to be an isometry, but that this makes all the morphisms into Cartesian squares. <br />
<br />
A: I've been thinking about the fact that the diagrams have to be Cartesian too. Here is an elliptic curve example: Say you have a morphism from <math> E \to Spec(K) </math> to <math> E' \to Spec(K') </math>, by the Cartesian property this means that <math> E \times_{Spec(K)} Spec(K') </math> is isomorphic to <math>E'</math>. In other words, <math>E</math> and <math>E'</math> are the "same" elliptic curve, all we've done is a base change. It makes sense that in a moduli space there would be a map between an elliptic curve and the same elliptic curve over a field extension. In the case of triangles, requiring that the map be an isometry should similarly makes sure that it's the "same" triangle (okay, this is vague. but that's my feeling)--[[User:Vincent|Vincent]] 21:39, 29 May 2012 (UTC)<br />
<br />
<br />
Q: I think I'm confused about the groupoid coming from an atlas for an orbifold. On page 23 the book says that the map <math>R \to U \times U</math> is never injective unless X is just a manifold with its trivial orbifold structure. But consider the case <math> X = \mathbf{C}</math>, with a single patch. In that case R is given by triples <math>(z_1,z_2,\phi)</math> with <math>\phi</math> a germ of a holomorphic map from a neighbourhood of the first point to a neighbourhood of the second. But complex discs have a whole <math>SL_2(\mathbf{R})</math> of automorphisms, so the fiber of R over any point of <math>U \times U</math> should be a whole <math>SL_2(\mathbf{R})</math>, rather than a point. [[User:Dewey|Dewey]] 16:58, 28 May 2012 (UTC)<br />
<br />
A: Key point is that <math>\phi</math> is a map over X. In this case, where the coordinate patches are given by the identity <math>X \to X</math>, <math>\phi</math> is necessarily the identity map.<br />
<br />
Q: I (think I) solved problem 1.15, but to do it I needed to use the fact that the groups <math>G_\alpha</math> from the orbifold data are all finite. If you relax that condition and let them be infinite does anyone have a counterexample? I'm interested in this because supposedly orbifolds are analagous to DM stacks and when you relax the condition on the groups being infinit, but require them to be algebraic, you should get something like an Artin stack, so this infinite vs finite groups thing could be a big deal. Note: as far as the DM and Artin stacks thing goes, I have no idea what I am talking about.<br />
<br />
C: I think a lot of the problems where you find a map of groupoids satisfying conditions i and ii boil down to the following statement: Let A and B be two groups acting on a space X such that the actions of A and B commute and B acts faithfully. Then A acts on Y, the quotient of X by B, and there is a map of groupoids <math>(A \times B \times X \rightrightarrows X) \to (A \times Y \rightrightarrows Y)</math> satisfying conditions i and ii<br />
<br />
C: A note for those who have not messed around with the j-invariant before: at least over an algebraically closed field, the j invariant for a polynomial <math>y^2 = f(x)^3</math> depends only on the roots of f and their multiplicities.<br />
<br />
Q: On page 17 in the definition of a "modular family" the text says that the condition that any first order deformation of any fiber in one of the families C --> S is captured by a tangent vector on the base S, and goes on to say that this is like requiring that the map from S to the (nonexistent) moduli space of curves be etale. If the moduli space M existed, then a deformation of <math>C_s</math>, the fiber of C over <math>s\in S</math>, should correspond to a family <math>C' \to \mathrm{spec} k[\epsilon]/(\epsilon^2)</math> whose fiber over 0 is <math>C_s</math>. Saying that this deformation is captured by a tangent vector to S should be saying that this family over <math>k[\epsilon]/(\epsilon^2)</math> can be obtained by fibering <math>C \to S</math> with a map <math>\mathrm{spec}\, k[\epsilon]/(\epsilon^2) \to S</math>. On the other hand, a family over <math>k[\epsilon]/(\epsilon^2)</math> is the same thing as a tangent vector v in M, and saying that such a fiber can be captured by a tangent vector to S should mean that v is in the image of the map of tangent spaces induced by the map <math> S \to M </math> corresponding to the family <math> C \to S</math> (phew!). '''So:''' this claim sort of makes sense if asking for a map to be etale is like asking for it to induce a surjection on tangent spaces. Can someone who knows about etale maps say if that's right?<br />
<br />
C: Etale morphisms between finite type schemes are maps whose Jacobians are nonsingular (see Milne Etale Cohomology, Corollary 2.2). However this is much weaker than being surjective. If you knew some more information like what the dimension of the schemes was, you would be in business. --[[User:Jain|Jain]] 01:14, 30 May 2012 (UTC)<br />
<br />
=== Chapter 1 ===<br />
<br />
Q:<br />
<br />
A:<br />
<br />
=== Chapter 2 ===<br />
<br />
=== Chapter 3 ===<br />
<br />
=== Chapter 4 ===<br />
<br />
=== Chapter 5 ===<br />
<br />
== Summer plans ==<br />
<br />
If you feel like telling us your general plans for the summer, so that we'll know when you are around Madison, please do so here:<br />
<br />
Ed: Leaving June 2, back around August 1.<br />
<br />
Jeff: Leaving June 17, back July 8.<br />
<br />
Evan: Leaving May 22, back June 20.<br />
<br />
Christelle: Leaving June 24, back July 20, leaving August 4.<br />
<br />
David: Leaving June 17, back July 8. Leaving July 31, back August 14th.</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Summer_stacks&diff=3919Summer stacks2012-05-29T10:20:20Z<p>Dwang: /* Introduction */</p>
<hr />
<div>This is the page for the 2012 Summer stacks reading group. <br />
<br />
== Resources ==<br />
<br />
The book in progress of Behrend, Fulton, Kresch and other people is available here: [http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1] <br />
<br />
Thanks to Sukhendu we have a copy of Champs algebriques" by Laumon and Moret-Bailly, currently in Ed's office.<br />
<br />
The Stacks Project: [http://www.math.columbia.edu/algebraic_geometry/stacks-git/]<br />
<br />
== Milestones ==<br />
<br />
6/1 Finish Chapter 1<br />
<br />
6/14 Finish Chapter 2<br />
<br />
6/29 Finish Chapter 3<br />
<br />
7/14 Finish Chapter 4<br />
<br />
7/28 Finish Chapter 5<br />
<br />
== Comments, Questions and (hopefully) Answers ==<br />
<br />
=== Introduction ===<br />
Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle<br />
<br />
A: I figured it out myself :) The fiber product is along s (source) and t (target), which I assume means that the elements of the fiber product are pairs (f,g) such that target(f)=source(g). Thus it's okay for m to only be defined on those elements because that's all there is.<br />
<br />
Q: I'm finding the <math>\tilde{S}</math> construction in the segment on moduli space of triangles pretty confusing. Is it just (non-canonically) isomorphic to a disjoint union of 6 copies of <math>S</math>? (I'm emphasizing the non-canonicity thing since despite the notation it looks as though <math>\tilde{S}</math> ought to depend on <math>T</math> as well as <math>S</math> but I don't quite grok how that works) [[User:Dewey|Dewey]] 21:23, 26 May 2012 (UTC)<br />
<br />
A: <math>\tilde{S}</math> might be not isomorphic to a disjoint union of 6 copies of <math>S</math> at all. Take the example in the previous page: <math>S</math> being a circle, and X being a family of equilateral triangles which rotates by 120 in one revolution around the circle. The corresponding <math>\tilde{S}</math> is a NON-TRIVIAL principal <math>\mathfrak{S}_3</math> bundle over <math>S^1</math>. Imagine that you start from the point <math>(e^{0i},123)\in\mathfrak{S}_3</math> and walk along the base, when you return, you will arrive at <math>(e^{0i},231)</math>. Continue for another round, you get <math>(e^{0i},312)</math>. Yet another round you return to the starting point <math>(e^{0i},123)</math>. If you start with <math>(e^{0i},213)</math>, then you get the other three points in the fiber of the principal bundle. So <math>\tilde{S}</math> has two connected component, each is a 3-cover of the base circle. This is also consistent with your feeling that <math>\tilde{S}</math> should depend on <math>T</math> and <math>S</math>. -[http://www.math.wisc.edu/~dwang Dongning] 05:13, 29 May 2012 (UTC)<br />
<br />
Q: This question is sort of tangential, but working on the "moduli space of triangles section" now and I noticed something kind of funny. Usually saying that <math>\tilde{T}</math> is the moduli space of ordered triangles would just mean that there is a natural isomorphism from the functor <math>S \to \{X \to S\}</math> where <math>X \to S</math> is a family of ordered triangles on S, to the functor <math>Hom(-,\tilde{T})</math>. But here this is more structure. Since the morphisms in <math>\tilde{\mathfrak{T}}</math> are required to be isometries on each fiber there is actually a functor from <math>\tilde{\mathfrak{T}}</math> to the category <math>\tilde{T}-Top</math> of spaces over <math>\tilde{T}</math>, that is, the objects spaces with a specified maps to <math>\tilde{T}</math> and the morphisms are commutative triangles. Is there some way to phrase this in a way that is more like the traditional definition of a moduli space? Like, maybe replace <math>Hom(-,\tilde{T})</math> with the functor Top --> Cat sending <math>S</math> to the fully subcategory of <math>\tilde{T}-Top</math> consisting of morphisms <math>S \to \tilde{T}</math>? [[User:Dewey|Dewey]] 22:42, 27 May 2012 (UTC)<br />
<br />
Something similar is going on in the section on elliptic curves. Rather than look at a moduli functor we look at a category of families of elliptic curves. Interestingly the morphisms are all required to be ''cartesian'' commutative squares. This should somehow correspond to the fact that in the moduli functor setup, the map on hom-sets is defined using pullback. Maybe what is really giong on in the moduli space of triangles section is not that the map on fibers is required to be an isometry, but that this makes all the morphisms into Cartesian squares. <br />
<br />
<br />
Q: I think I'm confused about the groupoid coming from an atlas for an orbifold. On page 23 the book says that the map <math>R \to U \times U</math> is never injective unless X is just a manifold with its trivial orbifold structure. But consider the case <math> X = \mathbf{C}</math>, with a single patch. In that case R is given by triples <math>(z_1,z_2,\phi)</math> with <math>\phi</math> a germ of a holomorphic map from a neighbourhood of the first point to a neighbourhood of the second. But complex discs have a whole <math>SL_2(\mathbf{R})</math> of automorphisms, so the fiber of R over any point of <math>U \times U</math> should be a whole <math>SL_2(\mathbf{R})</math>, rather than a point. [[User:Dewey|Dewey]] 16:58, 28 May 2012 (UTC)<br />
<br />
A: Key point is that <math>\phi</math> is a map over X. In this case, where the coordinate patches are given by the identity <math>X \to X</math>, <math>\phi</math> is necessarily the identity map.<br />
<br />
Q: I (think I) solved problem 1.15, but to do it I needed to use the fact that the groups <math>G_\alpha</math> from the orbifold data are all finite. If you relax that condition and let them be infinite does anyone have a counterexample? I'm interested in this because supposedly orbifolds are analagous to DM stacks and when you relax the condition on the groups being infinit, but require them to be algebraic, you should get something like an Artin stack, so this infinite vs finite groups thing could be a big deal. Note: as far as the DM and Artin stacks thing goes, I have no idea what I am talking about.<br />
<br />
C: I think a lot of the problems where you find a map of groupoids satisfying conditions i and ii boil down to the following statement: Let A and B be two groups acting on a space X such that the actions of A and B commute and B acts faithfully. Then A acts on Y, the quotient of X by B, and there is a map of groupoids <math>(A \times B \times X \rightrightarrows X) \to (A \times Y \rightrightarrows Y)</math> satisfying conditions i and ii<br />
<br />
C: A note for those who have not messed around with the j-invariant before: at least over an algebraically closed field, the j invariant for a polynomial <math>y^2 = f(x)^3</math> depends only on the roots of f and their multiplicities.<br />
<br />
Q: On page 17 in the definition of a "modular family" the text says that the condition that any first order deformation of any fiber in one of the families C --> S is captured by a tangent vector on the base S, and goes on to say that this is like requiring that the map from S to the (nonexistent) moduli space of curves be etale. If the moduli space M existed, then a deformation of <math>C_s</math>, the fiber of C over <math>s\in S</math>, should correspond to a family <math>C' \to \mathrm{spec} k[\epsilon]/(\epsilon^2)</math> whose fiber over 0 is <math>C_s</math>. Saying that this deformation is captured by a tangent vector to S should be saying that this family over <math>k[\epsilon]/(\epsilon^2)</math> can be obtained by fibering <math>C \to S</math> with a map <math>\mathrm{spec}\, k[\epsilon]/(\epsilon^2) \to S</math>. On the other hand, a family over <math>k[\epsilon]/(\epsilon^2)</math> is the same thing as a tangent vector v in M, and saying that such a fiber can be captured by a tangent vector to S should mean that v is in the image of the map of tangent spaces induced by the map <math> S \to M </math> corresponding to the family <math> C \to S</math> (phew!). '''So:''' this claim sort of makes sense if asking for a map to be etale is like asking for it to induce a surjection on tangent spaces. Can someone who knows about etale maps say if that's right?<br />
<br />
=== Chapter 1 ===<br />
<br />
Q:<br />
<br />
A:<br />
<br />
=== Chapter 2 ===<br />
<br />
=== Chapter 3 ===<br />
<br />
=== Chapter 4 ===<br />
<br />
=== Chapter 5 ===<br />
<br />
== Summer plans ==<br />
<br />
If you feel like telling us your general plans for the summer, so that we'll know when you are around Madison, please do so here:<br />
<br />
Ed: Leaving June 2, back around August 1.<br />
<br />
Jeff: Leaving June 17, back July 8.<br />
<br />
Evan: Leaving May 22, back June 20.<br />
<br />
Christelle: Leaving June 24, back July 20, leaving August 4.<br />
<br />
David: Leaving June 17, back July 8. Leaving July 31, back August 14th.</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Summer_stacks&diff=3918Summer stacks2012-05-29T10:17:23Z<p>Dwang: /* Introduction */</p>
<hr />
<div>This is the page for the 2012 Summer stacks reading group. <br />
<br />
== Resources ==<br />
<br />
The book in progress of Behrend, Fulton, Kresch and other people is available here: [http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1] <br />
<br />
Thanks to Sukhendu we have a copy of Champs algebriques" by Laumon and Moret-Bailly, currently in Ed's office.<br />
<br />
The Stacks Project: [http://www.math.columbia.edu/algebraic_geometry/stacks-git/]<br />
<br />
== Milestones ==<br />
<br />
6/1 Finish Chapter 1<br />
<br />
6/14 Finish Chapter 2<br />
<br />
6/29 Finish Chapter 3<br />
<br />
7/14 Finish Chapter 4<br />
<br />
7/28 Finish Chapter 5<br />
<br />
== Comments, Questions and (hopefully) Answers ==<br />
<br />
=== Introduction ===<br />
Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle<br />
<br />
A: I figured it out myself :) The fiber product is along s (source) and t (target), which I assume means that the elements of the fiber product are pairs (f,g) such that target(f)=source(g). Thus it's okay for m to only be defined on those elements because that's all there is.<br />
<br />
Q: I'm finding the <math>\tilde{S}</math> construction in the segment on moduli space of triangles pretty confusing. Is it just (non-canonically) isomorphic to a disjoint union of 6 copies of <math>S</math>? (I'm emphasizing the non-canonicity thing since despite the notation it looks as though <math>\tilde{S}</math> ought to depend on <math>T</math> as well as <math>S</math> but I don't quite grok how that works) [[User:Dewey|Dewey]] 21:23, 26 May 2012 (UTC)<br />
<br />
A: <math>\tilde{S}</math> might be not isomorphic to a disjoint union of 6 copies of <math>S</math> at all. Take the example in the previous page: <math>S</math> being a circle, and X being a family of equilateral triangles which rotates by 120 in one revolution around the circle. The corresponding <math>\tilde{S}</math> is a NON-TRIVIAL principal <math>\mathfrak{S}_3</math> bundle over <math>S^1</math>. Imagine that you start from the point <math>(e^{0i},123)\in\mathfrak{S}_3</math> and walk along the base, when you return, you will arrive at <math>(e^{0i},231)</math>. Continue for another round, you get <math>(e^{0i},312)</math>. Yet another round you return to the starting point <math>(e^{0i},123)</math>. If you start with <math>(e^{0i},213)</math>, then you get the other three points in the fiber of the principal bundle. So <math>\tilde{S}</math> has two connected component, each is a 3-cover of the base circle. [http://www.math.wisc.edu/~dwang Dongning] 05:13, 29 May 2012 (UTC)<br />
<br />
Q: This question is sort of tangential, but working on the "moduli space of triangles section" now and I noticed something kind of funny. Usually saying that <math>\tilde{T}</math> is the moduli space of ordered triangles would just mean that there is a natural isomorphism from the functor <math>S \to \{X \to S\}</math> where <math>X \to S</math> is a family of ordered triangles on S, to the functor <math>Hom(-,\tilde{T})</math>. But here this is more structure. Since the morphisms in <math>\tilde{\mathfrak{T}}</math> are required to be isometries on each fiber there is actually a functor from <math>\tilde{\mathfrak{T}}</math> to the category <math>\tilde{T}-Top</math> of spaces over <math>\tilde{T}</math>, that is, the objects spaces with a specified maps to <math>\tilde{T}</math> and the morphisms are commutative triangles. Is there some way to phrase this in a way that is more like the traditional definition of a moduli space? Like, maybe replace <math>Hom(-,\tilde{T})</math> with the functor Top --> Cat sending <math>S</math> to the fully subcategory of <math>\tilde{T}-Top</math> consisting of morphisms <math>S \to \tilde{T}</math>? [[User:Dewey|Dewey]] 22:42, 27 May 2012 (UTC)<br />
<br />
Something similar is going on in the section on elliptic curves. Rather than look at a moduli functor we look at a category of families of elliptic curves. Interestingly the morphisms are all required to be ''cartesian'' commutative squares. This should somehow correspond to the fact that in the moduli functor setup, the map on hom-sets is defined using pullback. Maybe what is really giong on in the moduli space of triangles section is not that the map on fibers is required to be an isometry, but that this makes all the morphisms into Cartesian squares. <br />
<br />
<br />
Q: I think I'm confused about the groupoid coming from an atlas for an orbifold. On page 23 the book says that the map <math>R \to U \times U</math> is never injective unless X is just a manifold with its trivial orbifold structure. But consider the case <math> X = \mathbf{C}</math>, with a single patch. In that case R is given by triples <math>(z_1,z_2,\phi)</math> with <math>\phi</math> a germ of a holomorphic map from a neighbourhood of the first point to a neighbourhood of the second. But complex discs have a whole <math>SL_2(\mathbf{R})</math> of automorphisms, so the fiber of R over any point of <math>U \times U</math> should be a whole <math>SL_2(\mathbf{R})</math>, rather than a point. [[User:Dewey|Dewey]] 16:58, 28 May 2012 (UTC)<br />
<br />
A: Key point is that <math>\phi</math> is a map over X. In this case, where the coordinate patches are given by the identity <math>X \to X</math>, <math>\phi</math> is necessarily the identity map.<br />
<br />
Q: I (think I) solved problem 1.15, but to do it I needed to use the fact that the groups <math>G_\alpha</math> from the orbifold data are all finite. If you relax that condition and let them be infinite does anyone have a counterexample? I'm interested in this because supposedly orbifolds are analagous to DM stacks and when you relax the condition on the groups being infinit, but require them to be algebraic, you should get something like an Artin stack, so this infinite vs finite groups thing could be a big deal. Note: as far as the DM and Artin stacks thing goes, I have no idea what I am talking about.<br />
<br />
C: I think a lot of the problems where you find a map of groupoids satisfying conditions i and ii boil down to the following statement: Let A and B be two groups acting on a space X such that the actions of A and B commute and B acts faithfully. Then A acts on Y, the quotient of X by B, and there is a map of groupoids <math>(A \times B \times X \rightrightarrows X) \to (A \times Y \rightrightarrows Y)</math> satisfying conditions i and ii<br />
<br />
C: A note for those who have not messed around with the j-invariant before: at least over an algebraically closed field, the j invariant for a polynomial <math>y^2 = f(x)^3</math> depends only on the roots of f and their multiplicities.<br />
<br />
Q: On page 17 in the definition of a "modular family" the text says that the condition that any first order deformation of any fiber in one of the families C --> S is captured by a tangent vector on the base S, and goes on to say that this is like requiring that the map from S to the (nonexistent) moduli space of curves be etale. If the moduli space M existed, then a deformation of <math>C_s</math>, the fiber of C over <math>s\in S</math>, should correspond to a family <math>C' \to \mathrm{spec} k[\epsilon]/(\epsilon^2)</math> whose fiber over 0 is <math>C_s</math>. Saying that this deformation is captured by a tangent vector to S should be saying that this family over <math>k[\epsilon]/(\epsilon^2)</math> can be obtained by fibering <math>C \to S</math> with a map <math>\mathrm{spec}\, k[\epsilon]/(\epsilon^2) \to S</math>. On the other hand, a family over <math>k[\epsilon]/(\epsilon^2)</math> is the same thing as a tangent vector v in M, and saying that such a fiber can be captured by a tangent vector to S should mean that v is in the image of the map of tangent spaces induced by the map <math> S \to M </math> corresponding to the family <math> C \to S</math> (phew!). '''So:''' this claim sort of makes sense if asking for a map to be etale is like asking for it to induce a surjection on tangent spaces. Can someone who knows about etale maps say if that's right?<br />
<br />
=== Chapter 1 ===<br />
<br />
Q:<br />
<br />
A:<br />
<br />
=== Chapter 2 ===<br />
<br />
=== Chapter 3 ===<br />
<br />
=== Chapter 4 ===<br />
<br />
=== Chapter 5 ===<br />
<br />
== Summer plans ==<br />
<br />
If you feel like telling us your general plans for the summer, so that we'll know when you are around Madison, please do so here:<br />
<br />
Ed: Leaving June 2, back around August 1.<br />
<br />
Jeff: Leaving June 17, back July 8.<br />
<br />
Evan: Leaving May 22, back June 20.<br />
<br />
Christelle: Leaving June 24, back July 20, leaving August 4.<br />
<br />
David: Leaving June 17, back July 8. Leaving July 31, back August 14th.</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Summer_stacks&diff=3917Summer stacks2012-05-29T10:14:06Z<p>Dwang: /* Introduction */</p>
<hr />
<div>This is the page for the 2012 Summer stacks reading group. <br />
<br />
== Resources ==<br />
<br />
The book in progress of Behrend, Fulton, Kresch and other people is available here: [http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1] <br />
<br />
Thanks to Sukhendu we have a copy of Champs algebriques" by Laumon and Moret-Bailly, currently in Ed's office.<br />
<br />
The Stacks Project: [http://www.math.columbia.edu/algebraic_geometry/stacks-git/]<br />
<br />
== Milestones ==<br />
<br />
6/1 Finish Chapter 1<br />
<br />
6/14 Finish Chapter 2<br />
<br />
6/29 Finish Chapter 3<br />
<br />
7/14 Finish Chapter 4<br />
<br />
7/28 Finish Chapter 5<br />
<br />
== Comments, Questions and (hopefully) Answers ==<br />
<br />
=== Introduction ===<br />
Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle<br />
<br />
A: I figured it out myself :) The fiber product is along s (source) and t (target), which I assume means that the elements of the fiber product are pairs (f,g) such that target(f)=source(g). Thus it's okay for m to only be defined on those elements because that's all there is.<br />
<br />
Q: I'm finding the <math>\tilde{S}</math> construction in the segment on moduli space of triangles pretty confusing. Is it just (non-canonically) isomorphic to a disjoint union of 6 copies of <math>S</math>? (I'm emphasizing the non-canonicity thing since despite the notation it looks as though <math>\tilde{S}</math> ought to depend on <math>T</math> as well as <math>S</math> but I don't quite grok how that works) [[User:Dewey|Dewey]] 21:23, 26 May 2012 (UTC)<br />
<br />
A: <math>\tilde{S}</math> might be not isomorphic to a disjoint union of 6 copies of <math>S</math> at all. Take the example in the previous page: <math>S</math> being a circle, and X being a family of equilateral triangles which rotates by 120 in one revolution around the circle. The corresponding <math>\tilde{S}</math> is a NON-TRIVIAL principal <math>\mathfrak{S}_3</math> bundle over <math>S^1</math>. Imagine that you start from the point <math>(e^{0i},123)\in\mathfrak{S}_3</math> and walk along the base, when you return, you will arrive at <math>(e^{0i},231)</math>. Continue for another round, you get <math>(e^{0i},312)</math>. Yet another round you return to the starting point <math>(e^{0i},123)</math>. If you start with <math>(e^{0i},213)</math>, then you get the other three points in the fiber of the principal bundle. So <math>\tilde{S}</math> has two connected component, each is a 3-cover of the base circle.[[User:Dwang|Dwang]] 05:13, 29 May 2012 (UTC)<br />
<br />
Q: This question is sort of tangential, but working on the "moduli space of triangles section" now and I noticed something kind of funny. Usually saying that <math>\tilde{T}</math> is the moduli space of ordered triangles would just mean that there is a natural isomorphism from the functor <math>S \to \{X \to S\}</math> where <math>X \to S</math> is a family of ordered triangles on S, to the functor <math>Hom(-,\tilde{T})</math>. But here this is more structure. Since the morphisms in <math>\tilde{\mathfrak{T}}</math> are required to be isometries on each fiber there is actually a functor from <math>\tilde{\mathfrak{T}}</math> to the category <math>\tilde{T}-Top</math> of spaces over <math>\tilde{T}</math>, that is, the objects spaces with a specified maps to <math>\tilde{T}</math> and the morphisms are commutative triangles. Is there some way to phrase this in a way that is more like the traditional definition of a moduli space? Like, maybe replace <math>Hom(-,\tilde{T})</math> with the functor Top --> Cat sending <math>S</math> to the fully subcategory of <math>\tilde{T}-Top</math> consisting of morphisms <math>S \to \tilde{T}</math>? [[User:Dewey|Dewey]] 22:42, 27 May 2012 (UTC)<br />
<br />
Something similar is going on in the section on elliptic curves. Rather than look at a moduli functor we look at a category of families of elliptic curves. Interestingly the morphisms are all required to be ''cartesian'' commutative squares. This should somehow correspond to the fact that in the moduli functor setup, the map on hom-sets is defined using pullback. Maybe what is really giong on in the moduli space of triangles section is not that the map on fibers is required to be an isometry, but that this makes all the morphisms into Cartesian squares. <br />
<br />
<br />
Q: I think I'm confused about the groupoid coming from an atlas for an orbifold. On page 23 the book says that the map <math>R \to U \times U</math> is never injective unless X is just a manifold with its trivial orbifold structure. But consider the case <math> X = \mathbf{C}</math>, with a single patch. In that case R is given by triples <math>(z_1,z_2,\phi)</math> with <math>\phi</math> a germ of a holomorphic map from a neighbourhood of the first point to a neighbourhood of the second. But complex discs have a whole <math>SL_2(\mathbf{R})</math> of automorphisms, so the fiber of R over any point of <math>U \times U</math> should be a whole <math>SL_2(\mathbf{R})</math>, rather than a point. [[User:Dewey|Dewey]] 16:58, 28 May 2012 (UTC)<br />
<br />
A: Key point is that <math>\phi</math> is a map over X. In this case, where the coordinate patches are given by the identity <math>X \to X</math>, <math>\phi</math> is necessarily the identity map.<br />
<br />
Q: I (think I) solved problem 1.15, but to do it I needed to use the fact that the groups <math>G_\alpha</math> from the orbifold data are all finite. If you relax that condition and let them be infinite does anyone have a counterexample? I'm interested in this because supposedly orbifolds are analagous to DM stacks and when you relax the condition on the groups being infinit, but require them to be algebraic, you should get something like an Artin stack, so this infinite vs finite groups thing could be a big deal. Note: as far as the DM and Artin stacks thing goes, I have no idea what I am talking about.<br />
<br />
C: I think a lot of the problems where you find a map of groupoids satisfying conditions i and ii boil down to the following statement: Let A and B be two groups acting on a space X such that the actions of A and B commute and B acts faithfully. Then A acts on Y, the quotient of X by B, and there is a map of groupoids <math>(A \times B \times X \rightrightarrows X) \to (A \times Y \rightrightarrows Y)</math> satisfying conditions i and ii<br />
<br />
C: A note for those who have not messed around with the j-invariant before: at least over an algebraically closed field, the j invariant for a polynomial <math>y^2 = f(x)^3</math> depends only on the roots of f and their multiplicities.<br />
<br />
Q: On page 17 in the definition of a "modular family" the text says that the condition that any first order deformation of any fiber in one of the families C --> S is captured by a tangent vector on the base S, and goes on to say that this is like requiring that the map from S to the (nonexistent) moduli space of curves be etale. If the moduli space M existed, then a deformation of <math>C_s</math>, the fiber of C over <math>s\in S</math>, should correspond to a family <math>C' \to \mathrm{spec} k[\epsilon]/(\epsilon^2)</math> whose fiber over 0 is <math>C_s</math>. Saying that this deformation is captured by a tangent vector to S should be saying that this family over <math>k[\epsilon]/(\epsilon^2)</math> can be obtained by fibering <math>C \to S</math> with a map <math>\mathrm{spec}\, k[\epsilon]/(\epsilon^2) \to S</math>. On the other hand, a family over <math>k[\epsilon]/(\epsilon^2)</math> is the same thing as a tangent vector v in M, and saying that such a fiber can be captured by a tangent vector to S should mean that v is in the image of the map of tangent spaces induced by the map <math> S \to M </math> corresponding to the family <math> C \to S</math> (phew!). '''So:''' this claim sort of makes sense if asking for a map to be etale is like asking for it to induce a surjection on tangent spaces. Can someone who knows about etale maps say if that's right?<br />
<br />
=== Chapter 1 ===<br />
<br />
Q:<br />
<br />
A:<br />
<br />
=== Chapter 2 ===<br />
<br />
=== Chapter 3 ===<br />
<br />
=== Chapter 4 ===<br />
<br />
=== Chapter 5 ===<br />
<br />
== Summer plans ==<br />
<br />
If you feel like telling us your general plans for the summer, so that we'll know when you are around Madison, please do so here:<br />
<br />
Ed: Leaving June 2, back around August 1.<br />
<br />
Jeff: Leaving June 17, back July 8.<br />
<br />
Evan: Leaving May 22, back June 20.<br />
<br />
Christelle: Leaving June 24, back July 20, leaving August 4.<br />
<br />
David: Leaving June 17, back July 8. Leaving July 31, back August 14th.</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Summer_stacks&diff=3916Summer stacks2012-05-29T10:13:33Z<p>Dwang: /* Introduction */</p>
<hr />
<div>This is the page for the 2012 Summer stacks reading group. <br />
<br />
== Resources ==<br />
<br />
The book in progress of Behrend, Fulton, Kresch and other people is available here: [http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1] <br />
<br />
Thanks to Sukhendu we have a copy of Champs algebriques" by Laumon and Moret-Bailly, currently in Ed's office.<br />
<br />
The Stacks Project: [http://www.math.columbia.edu/algebraic_geometry/stacks-git/]<br />
<br />
== Milestones ==<br />
<br />
6/1 Finish Chapter 1<br />
<br />
6/14 Finish Chapter 2<br />
<br />
6/29 Finish Chapter 3<br />
<br />
7/14 Finish Chapter 4<br />
<br />
7/28 Finish Chapter 5<br />
<br />
== Comments, Questions and (hopefully) Answers ==<br />
<br />
=== Introduction ===<br />
Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle<br />
<br />
A: I figured it out myself :) The fiber product is along s (source) and t (target), which I assume means that the elements of the fiber product are pairs (f,g) such that target(f)=source(g). Thus it's okay for m to only be defined on those elements because that's all there is.<br />
<br />
Q: I'm finding the <math>\tilde{S}</math> construction in the segment on moduli space of triangles pretty confusing. Is it just (non-canonically) isomorphic to a disjoint union of 6 copies of <math>S</math>? (I'm emphasizing the non-canonicity thing since despite the notation it looks as though <math>\tilde{S}</math> ought to depend on <math>T</math> as well as <math>S</math> but I don't quite grok how that works) [[User:Dewey|Dewey]] 21:23, 26 May 2012 (UTC)<br />
<br />
A: <math>\tilde{S}</math> might be not isomorphic to a disjoint union of 6 copies of <math>S</math> at all. Take the example in the previous page: <math>S</math> being a circle, and X be a family of equilateral triangles which rotates by 120 in one revolution around the circle. The corresponding <math>\tilde{S}</math> is a NON-TRIVIAL principal <math>\mathfrak{S}_3</math> bundle over <math>S^1</math>. Imagine that you start from the point <math>(e^{0i},123)\in\mathfrak{S}_3</math> and walk along the base, when you return, you will arrive at <math>(e^{0i},231)</math>. Continue for another round, you get <math>(e^{0i},312)</math>. Yet another round you return to the starting point <math>(e^{0i},123)</math>. If you start with <math>(e^{0i},213)</math>, then you get the other three points in the fiber of the principal bundle. So <math>\tilde{S}</math> has two connected component, each is a 3-cover of the base circle.[[User:Dwang|Dwang]] 05:13, 29 May 2012 (UTC)<br />
<br />
Q: This question is sort of tangential, but working on the "moduli space of triangles section" now and I noticed something kind of funny. Usually saying that <math>\tilde{T}</math> is the moduli space of ordered triangles would just mean that there is a natural isomorphism from the functor <math>S \to \{X \to S\}</math> where <math>X \to S</math> is a family of ordered triangles on S, to the functor <math>Hom(-,\tilde{T})</math>. But here this is more structure. Since the morphisms in <math>\tilde{\mathfrak{T}}</math> are required to be isometries on each fiber there is actually a functor from <math>\tilde{\mathfrak{T}}</math> to the category <math>\tilde{T}-Top</math> of spaces over <math>\tilde{T}</math>, that is, the objects spaces with a specified maps to <math>\tilde{T}</math> and the morphisms are commutative triangles. Is there some way to phrase this in a way that is more like the traditional definition of a moduli space? Like, maybe replace <math>Hom(-,\tilde{T})</math> with the functor Top --> Cat sending <math>S</math> to the fully subcategory of <math>\tilde{T}-Top</math> consisting of morphisms <math>S \to \tilde{T}</math>? [[User:Dewey|Dewey]] 22:42, 27 May 2012 (UTC)<br />
<br />
Something similar is going on in the section on elliptic curves. Rather than look at a moduli functor we look at a category of families of elliptic curves. Interestingly the morphisms are all required to be ''cartesian'' commutative squares. This should somehow correspond to the fact that in the moduli functor setup, the map on hom-sets is defined using pullback. Maybe what is really giong on in the moduli space of triangles section is not that the map on fibers is required to be an isometry, but that this makes all the morphisms into Cartesian squares. <br />
<br />
<br />
Q: I think I'm confused about the groupoid coming from an atlas for an orbifold. On page 23 the book says that the map <math>R \to U \times U</math> is never injective unless X is just a manifold with its trivial orbifold structure. But consider the case <math> X = \mathbf{C}</math>, with a single patch. In that case R is given by triples <math>(z_1,z_2,\phi)</math> with <math>\phi</math> a germ of a holomorphic map from a neighbourhood of the first point to a neighbourhood of the second. But complex discs have a whole <math>SL_2(\mathbf{R})</math> of automorphisms, so the fiber of R over any point of <math>U \times U</math> should be a whole <math>SL_2(\mathbf{R})</math>, rather than a point. [[User:Dewey|Dewey]] 16:58, 28 May 2012 (UTC)<br />
<br />
A: Key point is that <math>\phi</math> is a map over X. In this case, where the coordinate patches are given by the identity <math>X \to X</math>, <math>\phi</math> is necessarily the identity map.<br />
<br />
Q: I (think I) solved problem 1.15, but to do it I needed to use the fact that the groups <math>G_\alpha</math> from the orbifold data are all finite. If you relax that condition and let them be infinite does anyone have a counterexample? I'm interested in this because supposedly orbifolds are analagous to DM stacks and when you relax the condition on the groups being infinit, but require them to be algebraic, you should get something like an Artin stack, so this infinite vs finite groups thing could be a big deal. Note: as far as the DM and Artin stacks thing goes, I have no idea what I am talking about.<br />
<br />
C: I think a lot of the problems where you find a map of groupoids satisfying conditions i and ii boil down to the following statement: Let A and B be two groups acting on a space X such that the actions of A and B commute and B acts faithfully. Then A acts on Y, the quotient of X by B, and there is a map of groupoids <math>(A \times B \times X \rightrightarrows X) \to (A \times Y \rightrightarrows Y)</math> satisfying conditions i and ii<br />
<br />
C: A note for those who have not messed around with the j-invariant before: at least over an algebraically closed field, the j invariant for a polynomial <math>y^2 = f(x)^3</math> depends only on the roots of f and their multiplicities.<br />
<br />
Q: On page 17 in the definition of a "modular family" the text says that the condition that any first order deformation of any fiber in one of the families C --> S is captured by a tangent vector on the base S, and goes on to say that this is like requiring that the map from S to the (nonexistent) moduli space of curves be etale. If the moduli space M existed, then a deformation of <math>C_s</math>, the fiber of C over <math>s\in S</math>, should correspond to a family <math>C' \to \mathrm{spec} k[\epsilon]/(\epsilon^2)</math> whose fiber over 0 is <math>C_s</math>. Saying that this deformation is captured by a tangent vector to S should be saying that this family over <math>k[\epsilon]/(\epsilon^2)</math> can be obtained by fibering <math>C \to S</math> with a map <math>\mathrm{spec}\, k[\epsilon]/(\epsilon^2) \to S</math>. On the other hand, a family over <math>k[\epsilon]/(\epsilon^2)</math> is the same thing as a tangent vector v in M, and saying that such a fiber can be captured by a tangent vector to S should mean that v is in the image of the map of tangent spaces induced by the map <math> S \to M </math> corresponding to the family <math> C \to S</math> (phew!). '''So:''' this claim sort of makes sense if asking for a map to be etale is like asking for it to induce a surjection on tangent spaces. Can someone who knows about etale maps say if that's right?<br />
<br />
=== Chapter 1 ===<br />
<br />
Q:<br />
<br />
A:<br />
<br />
=== Chapter 2 ===<br />
<br />
=== Chapter 3 ===<br />
<br />
=== Chapter 4 ===<br />
<br />
=== Chapter 5 ===<br />
<br />
== Summer plans ==<br />
<br />
If you feel like telling us your general plans for the summer, so that we'll know when you are around Madison, please do so here:<br />
<br />
Ed: Leaving June 2, back around August 1.<br />
<br />
Jeff: Leaving June 17, back July 8.<br />
<br />
Evan: Leaving May 22, back June 20.<br />
<br />
Christelle: Leaving June 24, back July 20, leaving August 4.<br />
<br />
David: Leaving June 17, back July 8. Leaving July 31, back August 14th.</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Summer_stacks&diff=3915Summer stacks2012-05-29T10:12:02Z<p>Dwang: /* Introduction */</p>
<hr />
<div>This is the page for the 2012 Summer stacks reading group. <br />
<br />
== Resources ==<br />
<br />
The book in progress of Behrend, Fulton, Kresch and other people is available here: [http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1] <br />
<br />
Thanks to Sukhendu we have a copy of Champs algebriques" by Laumon and Moret-Bailly, currently in Ed's office.<br />
<br />
The Stacks Project: [http://www.math.columbia.edu/algebraic_geometry/stacks-git/]<br />
<br />
== Milestones ==<br />
<br />
6/1 Finish Chapter 1<br />
<br />
6/14 Finish Chapter 2<br />
<br />
6/29 Finish Chapter 3<br />
<br />
7/14 Finish Chapter 4<br />
<br />
7/28 Finish Chapter 5<br />
<br />
== Comments, Questions and (hopefully) Answers ==<br />
<br />
=== Introduction ===<br />
Q: On page 5, the authors talk about the fundamental groupoid of a topological space. I'm not excellent with fiber products, so I'm having trouble seeing how the map m they exhibit really is a map m as in the definition of a groupoid. More precisely, why is it okay that it's only defined when we can concatenate the paths? I'm assuming that this is the whole point of the definition of groupoid, and I'm missing it... -Christelle<br />
<br />
A: I figured it out myself :) The fiber product is along s (source) and t (target), which I assume means that the elements of the fiber product are pairs (f,g) such that target(f)=source(g). Thus it's okay for m to only be defined on those elements because that's all there is.<br />
<br />
Q: I'm finding the <math>\tilde{S}</math> construction in the segment on moduli space of triangles pretty confusing. Is it just (non-canonically) isomorphic to a disjoint union of 6 copies of <math>S</math>? (I'm emphasizing the non-canonicity thing since despite the notation it looks as though <math>\tilde{S}</math> ought to depend on <math>T</math> as well as <math>S</math> but I don't quite grok how that works) [[User:Dewey|Dewey]] 21:23, 26 May 2012 (UTC)<br />
A: <math>\tilde{S}</math> might be not isomorphic to a disjoint union of 6 copies of <math>S</math> at all. Take the example in the previous page: <math>S</math> being a circle, and X be a family of equilateral triangles which rotates by 120 in one revolution around the circle. The corresponding <math>\tilde{S}</math> is a NON-TRIVIAL principal <math>\mathfrak{S}_3</math> bundle over <math>S^1</math>. Imagine that you start from the point <math>(e^{0i},123)\in\mathfrak{S}_3</math> and walk along the base, when you return, you will arrive at <math>(e^{0i},231)</math>. Continue for another round, you get <math>(e^{0i},312)</math>. Yet another round you return to the starting point <math>(e^{0i},123)</math>. If you start with <math>(e^{0i},213)</math>, then you get the other three points in the fiber of the principal bundle. So <math>\tilde{S}</math> has two connected component, each is a 3-cover of the base circle.<br />
<br />
Q: This question is sort of tangential, but working on the "moduli space of triangles section" now and I noticed something kind of funny. Usually saying that <math>\tilde{T}</math> is the moduli space of ordered triangles would just mean that there is a natural isomorphism from the functor <math>S \to \{X \to S\}</math> where <math>X \to S</math> is a family of ordered triangles on S, to the functor <math>Hom(-,\tilde{T})</math>. But here this is more structure. Since the morphisms in <math>\tilde{\mathfrak{T}}</math> are required to be isometries on each fiber there is actually a functor from <math>\tilde{\mathfrak{T}}</math> to the category <math>\tilde{T}-Top</math> of spaces over <math>\tilde{T}</math>, that is, the objects spaces with a specified maps to <math>\tilde{T}</math> and the morphisms are commutative triangles. Is there some way to phrase this in a way that is more like the traditional definition of a moduli space? Like, maybe replace <math>Hom(-,\tilde{T})</math> with the functor Top --> Cat sending <math>S</math> to the fully subcategory of <math>\tilde{T}-Top</math> consisting of morphisms <math>S \to \tilde{T}</math>? [[User:Dewey|Dewey]] 22:42, 27 May 2012 (UTC)<br />
<br />
Something similar is going on in the section on elliptic curves. Rather than look at a moduli functor we look at a category of families of elliptic curves. Interestingly the morphisms are all required to be ''cartesian'' commutative squares. This should somehow correspond to the fact that in the moduli functor setup, the map on hom-sets is defined using pullback. Maybe what is really giong on in the moduli space of triangles section is not that the map on fibers is required to be an isometry, but that this makes all the morphisms into Cartesian squares. <br />
<br />
<br />
Q: I think I'm confused about the groupoid coming from an atlas for an orbifold. On page 23 the book says that the map <math>R \to U \times U</math> is never injective unless X is just a manifold with its trivial orbifold structure. But consider the case <math> X = \mathbf{C}</math>, with a single patch. In that case R is given by triples <math>(z_1,z_2,\phi)</math> with <math>\phi</math> a germ of a holomorphic map from a neighbourhood of the first point to a neighbourhood of the second. But complex discs have a whole <math>SL_2(\mathbf{R})</math> of automorphisms, so the fiber of R over any point of <math>U \times U</math> should be a whole <math>SL_2(\mathbf{R})</math>, rather than a point. [[User:Dewey|Dewey]] 16:58, 28 May 2012 (UTC)<br />
<br />
A: Key point is that <math>\phi</math> is a map over X. In this case, where the coordinate patches are given by the identity <math>X \to X</math>, <math>\phi</math> is necessarily the identity map.<br />
<br />
Q: I (think I) solved problem 1.15, but to do it I needed to use the fact that the groups <math>G_\alpha</math> from the orbifold data are all finite. If you relax that condition and let them be infinite does anyone have a counterexample? I'm interested in this because supposedly orbifolds are analagous to DM stacks and when you relax the condition on the groups being infinit, but require them to be algebraic, you should get something like an Artin stack, so this infinite vs finite groups thing could be a big deal. Note: as far as the DM and Artin stacks thing goes, I have no idea what I am talking about.<br />
<br />
C: I think a lot of the problems where you find a map of groupoids satisfying conditions i and ii boil down to the following statement: Let A and B be two groups acting on a space X such that the actions of A and B commute and B acts faithfully. Then A acts on Y, the quotient of X by B, and there is a map of groupoids <math>(A \times B \times X \rightrightarrows X) \to (A \times Y \rightrightarrows Y)</math> satisfying conditions i and ii<br />
<br />
C: A note for those who have not messed around with the j-invariant before: at least over an algebraically closed field, the j invariant for a polynomial <math>y^2 = f(x)^3</math> depends only on the roots of f and their multiplicities.<br />
<br />
Q: On page 17 in the definition of a "modular family" the text says that the condition that any first order deformation of any fiber in one of the families C --> S is captured by a tangent vector on the base S, and goes on to say that this is like requiring that the map from S to the (nonexistent) moduli space of curves be etale. If the moduli space M existed, then a deformation of <math>C_s</math>, the fiber of C over <math>s\in S</math>, should correspond to a family <math>C' \to \mathrm{spec} k[\epsilon]/(\epsilon^2)</math> whose fiber over 0 is <math>C_s</math>. Saying that this deformation is captured by a tangent vector to S should be saying that this family over <math>k[\epsilon]/(\epsilon^2)</math> can be obtained by fibering <math>C \to S</math> with a map <math>\mathrm{spec}\, k[\epsilon]/(\epsilon^2) \to S</math>. On the other hand, a family over <math>k[\epsilon]/(\epsilon^2)</math> is the same thing as a tangent vector v in M, and saying that such a fiber can be captured by a tangent vector to S should mean that v is in the image of the map of tangent spaces induced by the map <math> S \to M </math> corresponding to the family <math> C \to S</math> (phew!). '''So:''' this claim sort of makes sense if asking for a map to be etale is like asking for it to induce a surjection on tangent spaces. Can someone who knows about etale maps say if that's right?<br />
<br />
=== Chapter 1 ===<br />
<br />
Q:<br />
<br />
A:<br />
<br />
=== Chapter 2 ===<br />
<br />
=== Chapter 3 ===<br />
<br />
=== Chapter 4 ===<br />
<br />
=== Chapter 5 ===<br />
<br />
== Summer plans ==<br />
<br />
If you feel like telling us your general plans for the summer, so that we'll know when you are around Madison, please do so here:<br />
<br />
Ed: Leaving June 2, back around August 1.<br />
<br />
Jeff: Leaving June 17, back July 8.<br />
<br />
Evan: Leaving May 22, back June 20.<br />
<br />
Christelle: Leaving June 24, back July 20, leaving August 4.<br />
<br />
David: Leaving June 17, back July 8. Leaving July 31, back August 14th.</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3711Symplectic Geometry Seminar2012-03-28T12:19:04Z<p>Dwang: /* Abstracts */</p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 22st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 29th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|-<br />
|-<br />
|March. 7th<br />
|Jie Zhao<br />
| Title<br />
|-<br />
|-<br />
|March. 14th<br />
|Peng Zhou<br />
| Title<br />
|-<br />
|-<br />
|March. 21th<br />
|Jae-ho Lee<br />
| Title<br />
|-<br />
|-<br />
|March. 28th<br />
|Dongning Wang<br />
|Proof of the Triviality Axiom and Composition Axiom of Seidel Representation<br />
|-<br />
|April. 11th<br />
|Cheol-Hyun Cho<br />
| Title<br />
|-<br />
|-<br />
|April. 18th<br />
|Louis Lau<br />
| Title<br />
|-<br />
|-<br />
|April. 25th<br />
|Erkao Bao<br />
| Title<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wang''' ''Seidel elements and mirror transformations''<br />
<br />
Abstract:<br />
<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
<br />
Seidel elements and mirror transformations<br />
<br />
http://arxiv.org/abs/1103.4171<br />
<br />
'''Dongning Wang''' "Proof of the Triviality Axiom and Composition Axiom of Seidel Representation"<br />
<br />
Abstract:<br />
<br />
I will briefly review the definition of Seidel representation, then introduce parametrized group action, Kuranishi structure, equivariant Kuranishi structure and parametrized equivariant Kuranishi structure, and use these to prove the triviality axiom of Seidel representation. To prove the composition axiom, I will construct a Lefschetz fibration, then consider then moduli spaces this space and their Kuranishi structures. Finally, if time permitted, I will mention the extra ingredients needed for orbifold Seidel representation.<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3682Symplectic Geometry Seminar2012-03-21T02:02:11Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 22st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 29th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|-<br />
|-<br />
|March. 7th<br />
|Jie Zhao<br />
| Title<br />
|-<br />
|-<br />
|March. 14th<br />
|Peng Zhou<br />
| Title<br />
|-<br />
|-<br />
|March. 21th<br />
|Jae-ho Lee<br />
| Title<br />
|-<br />
|-<br />
|March. 28th<br />
|Dongning Wang<br />
|Proof of the Triviality Axiom and Composition Axiom of Seidel Representation<br />
|-<br />
|April. 11th<br />
|Cheol-Hyun Cho<br />
| Title<br />
|-<br />
|-<br />
|April. 18th<br />
|Louis Lau<br />
| Title<br />
|-<br />
|-<br />
|April. 25th<br />
|Erkao Bao<br />
| Title<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wang''' ''Seidel elements and mirror transformations''<br />
<br />
Abstract:<br />
<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
<br />
Seidel elements and mirror transformations<br />
<br />
http://arxiv.org/abs/1103.4171<br />
<br />
'''Dongning Wang''' "Proof of the Triviality Axiom and Composition Axiom of Seidel Representation"<br />
<br />
Abstract:<br />
<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3604Symplectic Geometry Seminar2012-03-02T08:18:49Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 22st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 29th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|-<br />
|-<br />
|March. 7th<br />
|Jie Zhao<br />
| Title<br />
|-<br />
|-<br />
|March. 14th<br />
|Peng Zhou<br />
| Title<br />
|-<br />
|-<br />
|March. 21th<br />
|Jae-ho Lee<br />
| Title<br />
|-<br />
|-<br />
|March. 28th<br />
|??<br />
| Title<br />
|-<br />
|April. 11th<br />
|Louis Lau<br />
| Title<br />
|-<br />
|-<br />
|April. 18th<br />
|??<br />
| Title<br />
|-<br />
|-<br />
|April. 25th<br />
|??<br />
| Title<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wang''' ''Seidel elements and mirror transformations''<br />
<br />
Abstract:<br />
<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
<br />
Seidel elements and mirror transformations<br />
<br />
http://arxiv.org/abs/1103.4171<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3558Symplectic Geometry Seminar2012-02-24T05:17:50Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 21st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 28th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wang''' ''Seidel elements and mirror transformations''<br />
<br />
Abstract:<br />
<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
<br />
Seidel elements and mirror transformations<br />
<br />
http://arxiv.org/abs/1103.4171<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3557Symplectic Geometry Seminar2012-02-24T05:17:30Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 21st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 28th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wang''' ''Seidel elements and mirror transformations''<br />
<br />
Abstract<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
<br />
Seidel elements and mirror transformations<br />
<br />
http://arxiv.org/abs/1103.4171<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3556Symplectic Geometry Seminar2012-02-24T05:17:05Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 21st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 28th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Dongning Wang''' ''Seidel elements and mirror transformations''<br />
<br />
Abstract<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
Seidel elements and mirror transformations<br />
http://arxiv.org/abs/1103.4171<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3555Symplectic Geometry Seminar2012-02-24T05:16:21Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 21st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 28th<br />
|Dongning Wang<br />
|Seidel elements and mirror transformations<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
Seidel elements and mirror transformations<br />
http://arxiv.org/abs/1103.4171<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3554Symplectic Geometry Seminar2012-02-24T05:15:47Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 21st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 28th<br />
|Dongning Wang<br />
|Seidel element and mirror transformation<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract<br />
I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:<br />
[Seidel elements and mirror transformations]<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3553Symplectic Geometry Seminar2012-02-24T05:13:31Z<p>Dwang: /* Abstracts */</p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 21st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 28th<br />
|Dongning Wang<br />
|Seidel element and mirror map<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3552Symplectic Geometry Seminar2012-02-24T05:12:23Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
|-<br />
|Feb. 15th<br />
|Kaileung Chan<br />
| Title<br />
|-<br />
|-<br />
|Feb. 21st<br />
|Chit Ma<br />
| Title<br />
|-<br />
<br />
|-<br />
|Feb. 28th<br />
|Dongning Wang<br />
|Seidel element and mirror map<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3415Symplectic Geometry Seminar2012-02-01T23:55:12Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 8th<br />
|Lino<br />
| Title<br />
|-<br />
<br />
|-<br />
|date<br />
|name<br />
|title<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3331Symplectic Geometry Seminar2012-01-26T00:10:19Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan. ??<br />
|Name<br />
| Title<br />
|-<br />
<br />
|-<br />
|date<br />
|name<br />
|title<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3330Symplectic Geometry Seminar2012-01-26T00:08:35Z<p>Dwang: </p>
<hr />
<div>Wednesday 2:15pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan. 21st<br />
|Name<br />
| Title<br />
|-<br />
<br />
|-<br />
|date<br />
|name<br />
|title<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Name''' ''title''<br />
<br />
Abstract<br />
<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Fall_2011_Symplectic_Geometry_Seminar&diff=3329Fall 2011 Symplectic Geometry Seminar2012-01-26T00:05:51Z<p>Dwang: New page: Wednesday 3:30pm-4:30pm VV B139 *If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang] ...</p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|-<br />
|Oct. 12th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds(continued)<br />
|-<br />
|-<br />
|Oct. 26th<br />
|Jie Zhao<br />
| Mirror Symmetry and Quantum Correction<br />
|-<br />
|-<br />
|Nov. 23th<br />
|Jaeho Lee<br />
|Tropical curves and Toric varieties(continued)<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, one would like to compute quantum cohomology of symplectic orbifolds defined by Chen and Ruan for many reasons, for example, to verify mirror symmetry between orbifolds and its mirror. With this motivation, we generalize Seidel representation to the orbifold cases. To do that, we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loops of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds. This is a joint work with Hsian-Hua Tseng.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=3328Symplectic Geometry Seminar2012-01-26T00:04:20Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|-<br />
|Oct. 12th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds(continued)<br />
|-<br />
|-<br />
|Oct. 26th<br />
|Jie Zhao<br />
| Mirror Symmetry and Quantum Correction<br />
|-<br />
|-<br />
|Nov. 23th<br />
|Jaeho Lee<br />
|Tropical curves and Toric varieties(continued)<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, one would like to compute quantum cohomology of symplectic orbifolds defined by Chen and Ruan for many reasons, for example, to verify mirror symmetry between orbifolds and its mirror. With this motivation, we generalize Seidel representation to the orbifold cases. To do that, we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loops of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds. This is a joint work with Hsian-Hua Tseng.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]<br />
*[[ Fall 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2883Symplectic Geometry Seminar2011-10-18T21:25:17Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|-<br />
|Oct. 12th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds(continued)<br />
|-<br />
|-<br />
|Oct. 26th<br />
|Jie Zhao<br />
| Mirror Symmetry and Quantum Correction<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, one would like to compute quantum cohomology of symplectic orbifolds defined by Chen and Ruan for many reasons, for example, to verify mirror symmetry between orbifolds and its mirror. With this motivation, we generalize Seidel representation to the orbifold cases. To do that, we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loops of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds. This is a joint work with Hsian-Hua Tseng.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2860Symplectic Geometry Seminar2011-10-17T04:03:57Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|-<br />
|Oct. 12th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds(continued)<br />
|-<br />
|-<br />
|Oct. 19th<br />
|Jie Zhao<br />
| Mirror Symmetry and Quantum Correction<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, one would like to compute quantum cohomology of symplectic orbifolds defined by Chen and Ruan for many reasons, for example, to verify mirror symmetry between orbifolds and its mirror. With this motivation, we generalize Seidel representation to the orbifold cases. To do that, we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loops of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds. This is a joint work with Hsian-Hua Tseng.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2823Symplectic Geometry Seminar2011-10-09T06:13:30Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|-<br />
|Oct. 12th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds(continued)<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, one would like to compute quantum cohomology of symplectic orbifolds defined by Chen and Ruan for many reasons, for example, to verify mirror symmetry between orbifolds and its mirror. With this motivation, we generalize Seidel representation to the orbifold cases. To do that, we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loops of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds. This is a joint work with Hsian-Hua Tseng.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2819Symplectic Geometry Seminar2011-10-07T05:51:47Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|-<br />
|Oct. 12th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds(continued)<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, one would like to compute quantum cohomology of symplectic orbifolds defined by Chen and Ruan for many reasons, for example, to verify mirror symmetry between orbifolds and its mirror. With this motivation, we generalize Seidel representation to the orbifold cases. To do that, we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loops of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2765Symplectic Geometry Seminar2011-09-30T08:44:00Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, one would like to compute quantum cohomology of symplectic orbifolds defined by Chen and Ruan for many reasons, for example, to verify mirror symmetry between orbifolds and its mirror. With this motivation, we generalize Seidel representation to the orbifold cases. To do that, we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loops of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2764Symplectic Geometry Seminar2011-09-30T08:43:38Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
Abstract<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, one would like to compute quantum cohomology of symplectic orbifolds defined by Chen and Ruan for many reasons, for example, to verify mirror symmetry between orbifolds and its mirror. With this motivation, we generalize Seidel representation to the orbifold cases. To do that, we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loops of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2763Symplectic Geometry Seminar2011-09-30T08:38:45Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
Abstract<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, as suggested by physicists, there is mirror symmetry between orbifolds and its mirror. To check this, one would like to compute the quantum cohomology of symplectic orbifolds which is defined by Chen and Ruan. We generalize Seidel representation in order to compute quantum cohomology for symplectic orbifolds. Thus we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define loop of Hamiltonian diffeomorphisms, <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2762Symplectic Geometry Seminar2011-09-30T08:37:08Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
Abstract<br />
<br />
For a symplectic manifold <math>(M,\omega)</math>, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, as suggested by physicists, there is mirror symmetry between orbifolds and its mirror. To check this, one would like to compute the quantum cohomology of symplectic orbifolds which is defined by Chen and Ruan. We generalize Seidel representation in order to compute quantum cohomology for symplectic orbifolds. Thus we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2761Symplectic Geometry Seminar2011-09-30T08:35:07Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
Abstract<br />
<br />
For a symplectic manifold, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, as suggested by physicists, there is mirror symmetry between orbifolds and its mirror. To check this, one would like to compute the quantum cohomology of symplectic orbifolds which is defined by Chen and Ruan. We generalize Seidel representation in order to compute quantum cohomology for symplectic orbifolds. Thus we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation for orbifolds.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2760Symplectic Geometry Seminar2011-09-30T08:34:35Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
Abstract<br />
<br />
For a symplectic manifold, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, as suggested by physicists, there is mirror symmetry between orbifolds and its mirror. To check this, one would like to compute the quantum cohomology of symplectic orbifolds which is defined by Chen and Ruan. We generalize Seidel representation in order to compute quantum cohomology for symplectic orbifolds. Thus we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)</math>, we define <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2759Symplectic Geometry Seminar2011-09-30T08:34:05Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
Abstract<br />
<br />
For a symplectic manifold, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, as suggested by physicists, there is mirror symmetry between orbifolds and its mirror. To check this, one would like to compute the quantum cohomology of symplectic orbifolds which is defined by Chen and Ruan. We generalize Seidel representation in order to compute quantum cohomology for symplectic orbifolds. Thus we need to generalize all the terminologies used to construct Seidel representation. For a symplectic orbifold <math>(\mathcal{X},\omega)<math>, we define <math>\pi_1(Ham(\mathcal{X},\omega))</math>, Hamiltonian orbifiber bundles, and sectional pseudoholomorphic orbicurves into the bundle. In this talk, I will explain these definitions and use them to construct Seidel representation.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2758Symplectic Geometry Seminar2011-09-30T08:25:26Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
'''Dongning Wang''' ''Seidel Representation for Symplectic Orbifolds''<br />
<br />
Abstract<br />
<br />
For a symplectic manifold, Seidel representation is a group morphism from <math>\pi_1(Ham(M,\omega))</math> to the multiplication group of the quantum cohomology ring <math>QH^*(M,\omega)</math>. With this morphism, once given enough information about <math>\pi_1(Ham(M,\omega))</math>, one can get compute <math>QH^*(M,\omega)</math>. On the other side, as suggested by physicists, there is mirror symmetry between orbifolds and its mirror. To check this, one would like to compute the quantum cohomology of symplectic orbifolds which is defined by Chen and Ruan. In this talk, I will explain how to generalize Seidel representation to the orbifold case: for a symplectic orbifold <math>(\mathcal{X},\omega)<math>, we define '''<math>\pi_1(Ham(\mathcal{X},\omega))</math>''', Hamiltonian orbifiber bundle, and count sectional pseudoholomorphic orbicurves into the bundle.<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2725Symplectic Geometry Seminar2011-09-23T19:13:51Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties<br />
|-<br />
|-<br />
|Sept. 28st<br />
|Ruifang Song<br />
| The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties(continued)<br />
|-<br />
|-<br />
|Oct. 5th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''The Picard-Fuchs equations of Calabi-Yau hypersurfaces in partial flag varieties ''<br />
<br />
Abstract<br />
<br />
We introduce a system of differential equations associated to a smooth algebraic variety X acted by a complex Lie group G and a G-linearlized line bundle L on X. We show that this system is holonomic and thus has finite dimensional solution space assuming G acts on X with finitely many orbits. When X is a partial flag variety, we show that this system gives the Picard-Fuchs system of Calabi-Yau hypersurfaces in X. In particular, when X is a toric variety, our construction recovers GKZ systems and extended GKZ systems, which have played important roles in studying periods of Calabi-Yau hypersurfaces/complete intersections in toric varieties. In general, if X is a Fano variety, L is the anticanonical line bundle and G=Aut(X), this construction can be used to study the Picard-Fuchs system of Calabi-Yau hypersurfaces/complete intersections in X.<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwanghttps://www.math.wisc.edu/wiki/index.php?title=Symplectic_Geometry_Seminar&diff=2613Symplectic Geometry Seminar2011-09-14T21:03:41Z<p>Dwang: </p>
<hr />
<div>Wednesday 3:30pm-4:30pm VV B139<br />
<br />
*If you would like to talk in the seminar but have difficulty with adding information here, please contact [http://www.math.wisc.edu/~dwang Dongning Wang]<br />
<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 21st<br />
|Ruifang Song<br />
|Title1<br />
|-<br />
|-<br />
|Sept. 28th<br />
|Dongning Wang<br />
|Seidel Representation for Symplectic Orbifolds<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
'''Ruifang Song''' ''Title''<br />
<br />
Abstract<br />
<br />
==Past Semesters ==<br />
*[[ Spring 2011 Symplectic Geometry Seminar]]</div>Dwang