Graduate Geometric Analysis Reading Seminar: Difference between revisions

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The graduate reading seminar in differential geometry / geometric analysis meets '''Tuesdays 4-6pm''' in '''Van Vleck B211'''. Students will give literature talks over the semester with participation by several faculty (Sean Paul, Alex Waldron, Ruobing Zhang, and Sigurd Angenent).


The topic for Fall 2024 is '''Ricci flow'''. We will cover the fundamentals in the fall and try to get through most of Perelman's proof of the Poincaré conjecture before the end of the year. We may also dip into the proof of Thurston's geometrization conjecture.


To join the mailing list, send an email to: math-geom-reading+subscribe@g-groups.wisc.edu.
=== Fall 2024 Schedule ===
=== Fall 2024 Schedule ===
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!Speaker
!Speaker
!Title
!Title
!Comments
!Reference
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|9/10
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|Sigurd Angenent
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|Introduction to the Ricci flow
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|9/17
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|Alex Waldron
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|Rapid course in Riemannian geometry
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|[https://people.math.wisc.edu/~awaldron3/Notes/Crash%20course%20091724 Notes]
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|9/24
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|Ruocheng Yang
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|Evolution equations under Ricci flow
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|Topping Ch. 2, [https://people.math.wisc.edu/~awaldron3/Notes/Ruocheng%20Ch.%202%20notes.pdf Notes]
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|10/1
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|Kaiyi Huang
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|The maximum principle
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|Topping Ch. 3, [https://people.math.wisc.edu/~awaldron3/Notes/Kaiyi%20maximum%20principle Notes]
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|10/8
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|Anuk Dayaprema
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|Short-time existence for the Ricci flow
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|Topping Ch. 4-5
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|10/15
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|Yijie He
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|Ricci flow as a gradient flow
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|Topping Ch. 6
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|10/22
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|Ruobing Zhang
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|The compactness theorem for the Ricci flow
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|Topping Ch. 7
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|10/29
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|Alex Waldron
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|Curvature pinching and preserved curvature properties
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|Topping Ch. 9
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|11/05
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|Andoni Royo-Abrego (Tübingen)
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|Ricci flow and sphere theorems
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|[https://people.math.wisc.edu/~awaldron3/Notes/Andoni%20sphere%20theorems%20talk Notes]
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|11/12
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|Anuk Dayaprema
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|Perelman's W-functional
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|Topping Ch. 8
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|}


==== September 11. [https://sites.google.com/view/jakefiedler Jake Fiedler], ''Projection theorems in geometric measure theory.'' ====
=== Past topics: ===
Abstract: Geometric measure theory (GMT) investigates how certain geometric properties of sets or operations on sets affect their size. Orthogonal projections are one such operation, and have been closely studied in this context for many years. Marstrand's projection theorem is the most prominent result of this type and states that for any (reasonable) set, the projections of that set in almost every direction have maximal Hausdorff dimension. We will introduce some of the main ideas of GMT, discuss Marstrand's projection theorem and other projection results, and begin to explore some new tools that have enabled recent progress in this area. This is the first of two talks.
Spring '24: Heat-kernel approach to the Atiyah-Singer index theorem
 
The second talk will happen on September 13th, at 1:20pm-2:10pm in VV B235 during the Graduate Analysis Seminar:
 
Title: Universal sets for projections
 
Abstract: In this talk, we will consider certain variants of Marstrand's projection theorem that hold for ''classes'' of sets in the plane. In particular, we will examine the class of sets with optimal oracles, the class of weakly regular sets, and the class of Ahlfors-David regular sets. This is the second of two talks and is based on joint work with Don Stull.
 
==== September 18. [https://people.math.wisc.edu/~secraig2/ Sam Craig], ''TBA.'' ====
Abstract: TBA.
 
==== September 25. Kaiyi Huang, ''TBA.'' ====
Abstract: TBA.
 
==== October 2. Kaiwen Jin, ''TBA.'' ====
Abstract: TBA.
 
==== October 9. TBA, ''TBA.'' ====
Abstract: TBA.
 
==== October 9. TBA, ''TBA.'' ====
Abstract: TBA.
 
==== October 16. TBA, ''TBA.'' ====
Abstract: TBA.
 
==== October 23. TBA, ''TBA.'' ====
Abstract: TBA.
 
==== October 30. TBA, ''TBA.'' ====
Abstract: TBA.
 
==== November 6. TBA, ''TBA.'' ====
Abstract: TBA.
 
==== November 13. TBA, ''TBA.'' ====
Abstract: TBA.
 
==== November 20. TBA, ''TBA.'' ====
Abstract: TBA.


==== November 27. TBA, ''TBA.'' ====
Fall '23: G<sub>2</sub> geometry
Abstract: TBA.


==== December 4. TBA, ''TBA.'' ====
Spring '23: Yau's proof of the Calabi conjecture
Abstract: TBA.


==== December 11. TBA, ''TBA.'' ====
Fall '22: Spin geometry and the index theorem
Abstract: TBA.


=== Previous Semesters ===
Spring '22: Differential-geometric approach to GIT.
[[GAPS Previous Semesters|Click here]] to view of all previous semesters' speakers and abstracts.

Latest revision as of 02:56, 10 November 2024

The graduate reading seminar in differential geometry / geometric analysis meets Tuesdays 4-6pm in Van Vleck B211. Students will give literature talks over the semester with participation by several faculty (Sean Paul, Alex Waldron, Ruobing Zhang, and Sigurd Angenent).

The topic for Fall 2024 is Ricci flow. We will cover the fundamentals in the fall and try to get through most of Perelman's proof of the Poincaré conjecture before the end of the year. We may also dip into the proof of Thurston's geometrization conjecture.

To join the mailing list, send an email to: math-geom-reading+subscribe@g-groups.wisc.edu.

Fall 2024 Schedule

Date Speaker Title Reference
9/10 Sigurd Angenent Introduction to the Ricci flow
9/17 Alex Waldron Rapid course in Riemannian geometry Notes
9/24 Ruocheng Yang Evolution equations under Ricci flow Topping Ch. 2, Notes
10/1 Kaiyi Huang The maximum principle Topping Ch. 3, Notes
10/8 Anuk Dayaprema Short-time existence for the Ricci flow Topping Ch. 4-5
10/15 Yijie He Ricci flow as a gradient flow Topping Ch. 6
10/22 Ruobing Zhang The compactness theorem for the Ricci flow Topping Ch. 7
10/29 Alex Waldron Curvature pinching and preserved curvature properties Topping Ch. 9
11/05 Andoni Royo-Abrego (Tübingen) Ricci flow and sphere theorems Notes
11/12 Anuk Dayaprema Perelman's W-functional Topping Ch. 8

Past topics:

Spring '24: Heat-kernel approach to the Atiyah-Singer index theorem

Fall '23: G2 geometry

Spring '23: Yau's proof of the Calabi conjecture

Fall '22: Spin geometry and the index theorem

Spring '22: Differential-geometric approach to GIT.

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