Our Interactions in AGT - User contributions [en]

Workshops

2026-01-19T13:21:34Z

Admin: /* Workshop 1 */

== Workshop 1 ==

Original workshop file can be found here [[:File:Workshop1.pdf]].

File:Workshop1.pdf

2026-01-19T13:21:05Z

Admin: Question sheet for Workshop 1

== Summary ==
Question sheet for Workshop 1

Books

2026-01-19T13:19:38Z

Admin: added more file paths to books

== Books ==

Here is the list of books from the reading list at the start of the course. Links to PDFs and suchlike will be added in due course. Hopefully as the semester progresses, the field will narrow down.

* Tu, Loring, Differential Geometry : Connections, Curvature, and Characteristic Classes. 1st ed. 2017
* [[:File:Taubes_-_Differential_geometry_-_Bundles%2C_connections%2C_metrics_and_curvature.pdf|Taubes, Clifford, Differential geometry : bundles, connections, metrics and curvature. 2011]]
* [[:File:Schmidt_and_Rudolph_-_Differential_Geometry_and_Mathematical_Physics_I.pdf|Rudolph, Gerd, Schmidt, Matthias., Differential geometry and mathematical physics. Part I, Manifolds, Lie groups and Hamiltonian systems. 2013]]
* [[:File:Schmidt_and_Rudolph_-_Differential_Geometry_and_Mathematical_Physics_II.pdf|Rudolph, Gerd, Schmidt, Matthias.Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields. 1st ed. 2017]]
* [[:File:Frenkel_-_the-geometry-of-physics.pdf|Frankel, Theodore, The geometry of physics : an introduction, 3rd edition. 2012]]
* [[:File:Nakahara_-_Geometry,_Topology,_and_Physics.pdf|Nakahara, Mikio, Geometry, topology, and physics, Second edition. 2003]]
* Nash, Charles, Sen, Siddhartha, Topology and geometry for physicists. 1987
* [[:File:Hamilton_-_Mathematical_Gauge_Theory.pdf|Hamilton, Mark J.D. Mathematical Gauge Theory : With Applications to the Standard Model of Particle Physics, 1st ed. 2017]]
* [[:File:Naber_-_Topology_Geometry_and_Gauge_Fields_-_Foundations.pdf|Naber, Gregory L., Topology, geometry and Gauge fields: foundations, Second edition. 2011]]
* [[:File:Naber_-_Topology_Geometry_and_Gauge_Fields_-_Interactions.pdf|Naber, Gregory L., Topology, geometry and gauge fields: interactions, Second edition. 2011]]
* [[:File:Sontz_-_Principal_Bundles_-_The_Classical_Case.pdf|Sontz, S. B., Principal bundles : the classical case. 2015]]
* Husemöller, Dale, Fibre Bundles, 3rd ed. 1994

Books

2026-01-19T13:17:05Z

Admin: added file links for naber

== Books ==

Here is the list of books from the reading list at the start of the course. Links to PDFs and suchlike will be added in due course. Hopefully as the semester progresses, the field will narrow down.

* Tu, Loring, Differential Geometry : Connections, Curvature, and Characteristic Classes. 1st ed. 2017
* [[:File:Taubes_-_Differential_geometry_-_Bundles%2C_connections%2C_metrics_and_curvature.pdf|Taubes, Clifford, Differential geometry : bundles, connections, metrics and curvature. 2011]]
* Rudolph, Gerd, Schmidt, Matthias., Differential geometry and mathematical physics. Part I, Manifolds, Lie groups and Hamiltonian systems. 2013
* Rudolph, Gerd, Schmidt, Matthias.Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields. 1st ed. 2017
* Frankel, Theodore, The geometry of physics : an introduction, 3rd edition. 2012
* Nakahara, Mikio, Geometry, topology, and physics, Second edition. 2003
* Nash, Charles, Sen, Siddhartha, Topology and geometry for physicists. 1987
* Hamilton, Mark J.D. Mathematical Gauge Theory : With Applications to the Standard Model of Particle Physics, 1st ed. 2017
* [[:File:Naber_-_Topology_Geometry_and_Gauge_Fields_-_Foundations.pdf|Naber, Gregory L., Topology, geometry and Gauge fields: foundations, Second edition. 2011]]
* [[:File:Naber_-_Topology_Geometry_and_Gauge_Fields_-_Interactions.pdf|Naber, Gregory L., Topology, geometry and gauge fields: interactions, Second edition. 2011]]
* Sontz, S. B., Principal bundles : the classical case. 2015
* Husemöller, Dale, Fibre Bundles, 3rd ed. 1994

File:Sontz - Principal Bundles - The Classical Case.pdf

2026-01-19T13:12:08Z

Admin:

Books

2026-01-19T13:02:12Z

Admin: /* Books */

== Books ==

Here is the list of books from the reading list at the start of the course. Links to PDFs and suchlike will be added in due course. Hopefully as the semester progresses, the field will narrow down.

* Tu, Loring, Differential Geometry : Connections, Curvature, and Characteristic Classes. 1st ed. 2017
* [[:File:Taubes_-_Differential_geometry_-_Bundles%2C_connections%2C_metrics_and_curvature.pdf|Taubes, Clifford, Differential geometry : bundles, connections, metrics and curvature. 2011]]
* Rudolph, Gerd, Schmidt, Matthias., Differential geometry and mathematical physics. Part I, Manifolds, Lie groups and Hamiltonian systems. 2013
* Rudolph, Gerd, Schmidt, Matthias.Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields. 1st ed. 2017
* Frankel, Theodore, The geometry of physics : an introduction, 3rd edition. 2012
* Nakahara, Mikio, Geometry, topology, and physics, Second edition. 2003
* Nash, Charles, Sen, Siddhartha, Topology and geometry for physicists. 1987
* Hamilton, Mark J.D. Mathematical Gauge Theory : With Applications to the Standard Model of Particle Physics, 1st ed. 2017
* Naber, Gregory L., Topology, geometry and Gauge fields: foundations, Second edition. 2011
* Naber, Gregory L., Topology, geometry and gauge fields: interactions, Second edition. 2011
* Sontz, S. B., Principal bundles : the classical case. 2015
* Husemöller, Dale, Fibre Bundles, 3rd ed. 1994

File:Naber - Topology Geometry and Gauge Fields - Interactions.pdf

2026-01-19T12:58:38Z

Admin:

File:Naber - Topology Geometry and Gauge Fields - Foundations.pdf

2026-01-19T12:58:28Z

Admin:

File:Taubes - Differential geometry - Bundles, connections, metrics and curvature.pdf

2026-01-19T12:58:20Z

Admin:

File:Hamilton - Mathematical Gauge Theory.pdf

2026-01-19T12:58:01Z

Admin:

File:Nakahara - Geometry, Topology, and Physics.pdf

2026-01-19T12:57:50Z

Admin:

File:Frenkel - the-geometry-of-physics.pdf

2026-01-19T12:57:40Z

Admin:

File:Schmidt and Rudolph - Differential Geometry and Mathematical Physics II.pdf

2026-01-19T12:57:28Z

Admin:

File:Schmidt and Rudolph - Differential Geometry and Mathematical Physics I.pdf

2026-01-19T12:57:03Z

Admin:

Workshops

2026-01-18T17:34:12Z

Admin: Created page with " == Workshop 1 =="

== Workshop 1 ==

Main Page

2026-01-18T17:30:00Z

Admin:

Welcome to the collaborative wiki for Interactions in Algebra, Geometry, and Topology; a reading course in the School of Mathematics at the University of Edinburgh. The topic of this year's incarnation is the differential geometry of gauge theory: vector and principal bundles, connections, Chern-Weil theory, and instantons.

This wiki is an experiment in collaborative mathematical learning. Since there are no course notes and many course textbooks this is an opportunity to pool our resources. as the saying goes, “differential geometry is the study of notation under invariance”.

== Getting started ==
* [[Lecture Schedule]]
* [[Books]]
* [[Workshops]]

Books

2026-01-18T17:13:57Z

Admin: /* Books */

Books

2026-01-18T17:10:19Z

Admin:

Books

2026-01-18T17:09:39Z

Admin: /* Books */

Books

2026-01-18T17:09:29Z

Admin:

== Books ==

Here is the list of books from the reading list at the start of the course. Links to PDFs and suchlike will be added in due course. Hopefully as the semester progresses, the field will narrow down.

<nowiki><math> E = mc^2 </math></nowiki>
* Tu, Loring, Differential Geometry : Connections, Curvature, and Characteristic Classes. 1st ed. 2017
* Taubes, Clifford, Differential geometry : bundles, connections, metrics and curvature. 2011
* Rudolph, Gerd, Schmidt, Matthias., Differential geometry and mathematical physics. Part I, Manifolds, Lie groups and Hamiltonian systems. 2013
* Rudolph, Gerd, Schmidt, Matthias.Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields. 1st ed. 2017
* Frankel, Theodore, The geometry of physics : an introduction, 3rd edition. 2012
* Nakahara, Mikio, Geometry, topology, and physics, Second edition. 2003
* Nash, Charles, Sen, Siddhartha, Topology and geometry for physicists. 1987
* Hamilton, Mark J.D. Mathematical Gauge Theory : With Applications to the Standard Model of Particle Physics, 1st ed. 2017
* Naber, Gregory L., Topology, geometry and Gauge fields: foundations, Second edition. 2011
* Naber, Gregory L., Topology, geometry and gauge fields: interactions, Second edition. 2011
* Sontz, S. B., Principal bundles : the classical case. 2015
* Husemöller, Dale, Fibre Bundles, 3rd ed. 1994

Books

2026-01-18T17:08:48Z

Admin: Created page with "== Books == Here is the list of books from the reading list at the start of the course. Links to PDFs and suchlike will be added in due course. Hopefully as the semester progresses, the field will narrow down. * Tu, Loring, Differential Geometry : Connections, Curvature, and Characteristic Classes. 1st ed. 2017 * Taubes, Clifford, Differential geometry : bundles, connections, metrics and curvature. 2011 * Rudolph, Gerd, Schmidt, Matthias., Differential geometry and m..."

Lecture Schedule

2026-01-18T17:07:43Z

Admin: /* Week 5 = */

== Lectures ==
Tentative lecture plan is as follows:

=== Week 1 ===
Topics: Review of differential geometry

* Topological and smooth manifolds,
* Vector and tensor fields,
* Algebra of differential forms,
* De Rham Cohomology

Reading:

* Taubes Ch 1
* Frenkel Sections 1-3
* Nakahara Sections 5.1, 5.2, 5.4. 6.
* Sontz Chapters 2, 3, 5

=== Week 2 ===
Topics: Review of differential geometry

* vector fields
* Lie brackets
* diffeomorphisms
* Lie derivatives
* Lie groups and Lie algebras.
* Exponential maps
* adjoint representation
* Basics of Symplectic Geometry
* Hamiltonian vector fields
* Hamiltonian group actions
* Moment maps and co-moment maps.

Reading:

* Rudolph-Schmidt (Differential Geometry and Mathematical Physics. Part I) Section 5

=== Week 3 ===
Topics:

* Further details on smooth actions,
* Symplectic structure on cotangent bundles
* Quotients of free, proper, smooth actions
* Principal bundles.
* Frame bundles.
* Associated fibre bundles.

Reading:

=== Week 4 ===
Topics:

* Associated fibre bundles: vector bundles, adjoint bundle.
* Reduction and extension of structure group.
* Group of gauge transformations.
* Linear connections.

Reading:

=== Week 5===
Topics:

* Connections: Koszul connections, principal connections, Ehresmann connections.
* Equivalences between them.
* Atiyah sequence and differential operators.

Reading:

Lecture Schedule

2026-01-18T17:07:31Z

Admin:

== Lectures ==
Tentative lecture plan is as follows:

=== Week 1 ===
Topics: Review of differential geometry

* Topological and smooth manifolds,
* Vector and tensor fields,
* Algebra of differential forms,
* De Rham Cohomology

Reading:

* Taubes Ch 1
* Frenkel Sections 1-3
* Nakahara Sections 5.1, 5.2, 5.4. 6.
* Sontz Chapters 2, 3, 5

=== Week 2 ===
Topics: Review of differential geometry

* vector fields
* Lie brackets
* diffeomorphisms
* Lie derivatives
* Lie groups and Lie algebras.
* Exponential maps
* adjoint representation
* Basics of Symplectic Geometry
* Hamiltonian vector fields
* Hamiltonian group actions
* Moment maps and co-moment maps.

Reading:

* Rudolph-Schmidt (Differential Geometry and Mathematical Physics. Part I) Section 5

=== Week 3 ===
Topics:

* Further details on smooth actions,
* Symplectic structure on cotangent bundles
* Quotients of free, proper, smooth actions
* Principal bundles.
* Frame bundles.
* Associated fibre bundles.

Reading:

=== Week 4 ===
Topics:

* Associated fibre bundles: vector bundles, adjoint bundle.
* Reduction and extension of structure group.
* Group of gauge transformations.
* Linear connections.

Reading:

=== Week 5 ====
Topics:

* Connections: Koszul connections, principal connections, Ehresmann connections.
* Equivalences between them.
* Atiyah sequence and differential operators.

Reading:

Lecture Schedule

2026-01-18T17:06:49Z

Admin:

== Lectures ==
Tentative lecture plan is as follows:

=== Week 1 ===
Topics: Review of differential geometry

* Topological and smooth manifolds,
* Vector and tensor fields,
* Algebra of differential forms,
* De Rham Cohomology

Reading:

* Taubes Ch 1
* Frenkel Sections 1-3
* Nakahara Sections 5.1, 5.2, 5.4. 6.
* Sontz Chapters 2, 3, 5

=== Week 2 ===
Topics: Review of differential geometry

* vector fields
* Lie brackets
* diffeomorphisms
* Lie derivatives
* Lie groups and Lie algebras.
* Exponential maps
* adjoint representation
* Basics of Symplectic Geometry
* Hamiltonian vector fields
* Hamiltonian group actions
* Moment maps and co-moment maps.

Reading:

* Rudolph-Schmidt (Differential Geometry and Mathematical Physics. Part I) Section 5

=== Week 3 ===
Topics:

* Further details on smooth actions,
* Symplectic structure on cotangent bundles
* Quotients of free, proper, smooth actions
* Principal bundles.
* Frame bundles.
* Associated fibre bundles.

Reading:

=== Week 4 ===
Topics:

* Associated fibre bundles: vector bundles, adjoint bundle.
* Reduction and extension of structure group.
* Group of gauge transformations.
* Linear connections.

Reading:

=== Week 5 ====
Topics:

* Connections: Koszul connections, principal connections, Ehresmann connections.
* Equivalences between them.
* Atiyah sequence and differential operators.

Reading:

Lecture Schedule

2026-01-18T17:06:04Z

Admin:

====== Lectures =======

Tentative lecture plan is as follows:

=== Week 1 ===
Topics: Review of differential geometry

* Topological and smooth manifolds,
* Vector and tensor fields,
* Algebra of differential forms,
* De Rham Cohomology

Reading:

* Taubes Ch 1
* Frenkel Sections 1-3
* Nakahara Sections 5.1, 5.2, 5.4. 6.
* Sontz Chapters 2, 3, 5

=== Week 2 ===
Topics: Review of differential geometry

* vector fields
* Lie brackets
* diffeomorphisms
* Lie derivatives
* Lie groups and Lie algebras.
* Exponential maps
* adjoint representation
* Basics of Symplectic Geometry
* Hamiltonian vector fields
* Hamiltonian group actions
* Moment maps and co-moment maps.

Reading:

* Rudolph-Schmidt (Differential Geometry and Mathematical Physics. Part I) Section 5

=== Week 3 ===
Topics:

* Further details on smooth actions,
* Symplectic structure on cotangent bundles
* Quotients of free, proper, smooth actions
* Principal bundles.
* Frame bundles.
* Associated fibre bundles.

Reading:

=== Week 4 ===
Topics:

* Associated fibre bundles: vector bundles, adjoint bundle.
* Reduction and extension of structure group.
* Group of gauge transformations.
* Linear connections.

Reading:

=== Week 5 ====
Topics:

* Connections: Koszul connections, principal connections, Ehresmann connections.
* Equivalences between them.
* Atiyah sequence and differential operators.

Reading:

Lecture Schedule

2026-01-18T17:05:49Z

Admin: Created page with "====== Lectures ======= Tentative lecture plan is as follows: === Week 1 === Topics: Review of differential geometry * Topological and smooth manifolds, * Vector and tensor fields, * Algebra of differential forms, * De Rham Cohomology Reading: * Taubes Ch 1 * Frenkel Sections 1-3 * Nakahara Sections 5.1, 5.2, 5.4. 6. * Sontz Chapters 2, 3, 5 === Week 2 === Topics: Review of differential geometry * vector fields * Lie brackets * diffeomorphism..."

====== Lectures =======

Tentative lecture plan is as follows:

=== Week 1 ===
Topics: Review of differential geometry
* Topological and smooth manifolds,
* Vector and tensor fields,
* Algebra of differential forms,
* De Rham Cohomology

Reading:
* Taubes Ch 1
* Frenkel Sections 1-3
* Nakahara Sections 5.1, 5.2, 5.4. 6.
* Sontz Chapters 2, 3, 5

=== Week 2 ===
Topics: Review of differential geometry
* vector fields
* Lie brackets
* diffeomorphisms
* Lie derivatives
* Lie groups and Lie algebras.
* Exponential maps
* adjoint representation
* Basics of Symplectic Geometry
* Hamiltonian vector fields
* Hamiltonian group actions
* Moment maps and co-moment maps.

Reading:
* Rudolph-Schmidt (Differential Geometry and Mathematical Physics. Part I) Section 5

=== Week 3 ===
Topics:
* Further details on smooth actions,
* Symplectic structure on cotangent bundles
* Quotients of free, proper, smooth actions
* Principal bundles.
* Frame bundles.
* Associated fibre bundles.

Reading:

=== Week 4 ===
Topics:
* Associated fibre bundles: vector bundles, adjoint bundle.
* Reduction and extension of structure group.
* Group of gauge transformations.
* Linear connections.

Reading:

=== Week 5 ====
Topics:
* Connections: Koszul connections, principal connections, Ehresmann connections.
* Equivalences between them.
* Atiyah sequence and differential operators.

Reading:

Main Page

2026-01-18T17:05:29Z

Admin:

Welcome to the collaborative wiki for Interactions in Algebra, Geometry, and Topology; a reading course in the School of Mathematics at the University of Edinburgh. The topic of this year's incarnation is the differential geometry of gauge theory: vector and principal bundles, connections, Chern-Weil theory, and instantons.

This wiki is an experiment in collaborative mathematical learning. Since there are no course notes and many course textbooks this is an opportunity to pool our resources. as the saying goes, “Differential geometry is the study of notiation under invariance” .

== Getting started ==
* [[Lecture Schedule]]
* [[Books]]
* [[Workshops]]

Main Page

2026-01-18T17:04:23Z

Admin:

MediaWiki has been installed.

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

In this world $E = mc^2$.

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2026-01-18T17:02:37Z

Admin:

MediaWiki has been installed.

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

<math>x^2+3x=5</math>

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2026-01-18T17:02:30Z

Admin:

MediaWiki has been installed.

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

<math>x^2+3x=5</math<

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

Main Page

2026-01-18T16:47:08Z

Admin:

MediaWiki has been installed.

Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.

$$x^2+3x=5$$

== Getting started ==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/postorius/lists/mediawiki-announce.lists.wikimedia.org/ MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]