**Date:** July 26-30, 2021 (Zoom details are at the bottom of the page.)

**Speaker:** Mahir Bilen Can (Tulane University)

**Title:** Lie Groups and Algebraic Groups in Action

**Abstract:** The purpose of our lectures is to give a short but self-contained overview of some well-known results about the geometry of algebraic group actions. We will focus mainly on the actions of connected reductive groups. Our main goals are 1) introducing some interesting examples of equivariant completions of homogeneous spaces, 2) explaining several combinatorial gadgets such as valuation cones, weight monoids, colors, etc. that are not only useful for classifying algebraic actions of low complexity but also essential for understanding these equivariant completions. Along the way, we will review some representation theory. In addition, we will analyze some concrete examples of combinatorial varieties such as toric and Schubert varieties.   

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**Slack workspace [[https://join.slack.com/t/ggtiworkspace/shared_invite/zt-tjxz56ie-vl5JfDMT2Nq~ve9NrCH3HQ|link]]** for discussions. (Let us know if the link is expired.)

**Lecture 1** Monday, July 26 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT) 
  * {{ :lecture:2021:mahir-lectures-1.pdf |Lecture Note}}
  * {{ :lecture:2021:mahir-exercises-1.pdf |Exercises}}

**Lecture 2** Tuesday, July 27 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)
  * [[https://www.youtube.com/watch?v=RXcOmsWBImY|Lecture Video]]
  * {{ :lecture:2021:mahir-lectures-2.pdf |Lecture Note}}
  * {{ :lecture:2021:mahir-exercises-2.pdf |Exercises}}

**Lecture 3** Wednesday, July 28 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)
  * [[https://www.youtube.com/watch?v=cs78Kz9QWV4|Lecture Video]]
  * {{ :lecture:2021:mahir-lectures-3.pdf |Lecture Note}}
  * {{ :lecture:2021:mahir-exercises-3.pdf |Exercises}}

**Lecture 4** Thursday, July 29 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)
  * [[https://www.youtube.com/watch?v=q3HXzgjIAGo|Lecture Video]]
  * {{ :lecture:2021:mahir-lectures-4.pdf |Lecture Note}}
  * {{ :lecture:2021:mahir-exercises-4.pdf |Exercises}}

**Lecture 5** Friday, July 30 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)
  * [[https://www.youtube.com/watch?v=PQaeGRLjmKI|Lecture Video]]
  * {{ :lecture:2021:mahir-lectures-5.pdf |Lecture Note}}


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**Zoom Meeting ID** 974 3685 2246

**Password** Initials of the speaker's name (use capitals)

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