GAPS: Difference between revisions
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|September 11 | |September 11 | ||
|Jake Fiedler | |Jake Fiedler | ||
|Universal sets for projections | |Projection theorems in geometric measure theory | ||
|A continuation of this talk, "Universal sets for projections," will happen on September 13th in the Graduate Analysis Seminar (Fridays @ 1:20pm-2:10pm in VV B235). | |||
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|September 18 | |September 18 | ||
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==== September 11. [https://sites.google.com/view/jakefiedler Jake Fiedler], '' | ==== September 11. [https://sites.google.com/view/jakefiedler Jake Fiedler], ''Projection theorems in geometric measure theory.'' ==== | ||
Abstract: | 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. | ||
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.'' ==== | ==== September 18. [https://people.math.wisc.edu/~secraig2/ Sam Craig], ''TBA.'' ==== | ||
Revision as of 02:44, 31 August 2024
The Graduate Analysis and PDEs Seminar (GAPS) is intended to build community for graduate students in the different subfields of analysis and PDEs. The goal is to give accessible talks about your current research projects, papers you found interesting on the arXiv, or even just a theorem/result that you use and think is really cool!
We currently meet Wednesdays, 1:20pm-2:10pm, in Van Vleck 901. Cookies are provided. If you have any questions, please email the organizers: Summer Al Hamdani (alhamdani (at) wisc.edu) and Allison Byars (abyars (at) wisc.edu).
To join the mailing list, send an email to: gaps+subscribe@g-groups.wisc.edu.
Fall 2024 Schedule
| Date | Speaker | Title | Comments |
|---|---|---|---|
| September 4 | Summer & Allison | Planning / Social! | |
| September 11 | Jake Fiedler | Projection theorems in geometric measure theory | A continuation of this talk, "Universal sets for projections," will happen on September 13th in the Graduate Analysis Seminar (Fridays @ 1:20pm-2:10pm in VV B235). |
| September 18 | Sam Craig | TBA | |
| September 25 | Kaiyi Huang | TBA | |
| October 2 | |||
| October 9 | |||
| October 16 | |||
| October 23 | |||
| October 30 | |||
| November 6 | |||
| November 13 | |||
| November 20 | |||
| November 27 | Day before Thanksgiving | ||
| December 4 | |||
| December 11 |
September 11. Jake Fiedler, Projection theorems in geometric measure theory.
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.
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. Sam Craig, TBA.
Abstract: TBA.
September 25. Kaiyi Huang, TBA.
Abstract: TBA.
Previous Semesters
Click here to view of all previous semesters' speakers and abstracts.