WARTHOG 2025
Braid Varieties and Cluster Structures
Workshop on Algebra and Representation Theory, Held on Oregonian Grounds
August 18-22, 2025
University of Oregon
Eugene, OR
Schedule
The schedule and timing are subject to change.
Exercises and lecture notes will be linked from this webpage when available.
Pastries and Coffee will be available in the lecture room starting at 830AM each morning.
All talks will be held in Tykeson 032.
Some mornings have time alotted for triage, where the main speaker gets to emphasize certain ideas and make sure everyone is on the same page, depending on how the exercises go. If triage runs short the first lecture will start earlier to give more time for lunch later. TL;DR: make sure you're in the lecture room at 9!
Here is a lovely flowchart of the lectures!
Monday:
900-910: Opening Remarks
915-1015: Background on Flag Varieties, Definition of Braid Varieties (Jose) Notes
1015-1055: Exercise
1115-1215: More on Braid Varieties (Melissa) Notes
1215-1255: Exercise
1255-200: Lunch.
200-300: Cluster Algebras (Eugene) Notes
300-340: Exercise
400-500: Cluster varieties and the Starfish Lemma (Jose) Notes
500-540: Exercise
Tuesday:
900-910: Triage
915-1015: Demazure products and weaves (Eugene) Notes
1015-1055: Exercise
1115-1215: Local acyclicity and sink recurrence (Eugene) Notes
1215-1255: Exercise
1255-200: Lunch.
200-300: The Deodhar torus (Jose) Notes
300-340: Exercise
400-500: Cluster variables on the Deodhar torus (Jose)
500-540: Exercise (finish exercise 7.1, compute cluster variables)
Wednesday:
900-1000: 3D plabic graphs (Melissa) Notes
1000-1040: Exercise
1100-1200: Double Bott-Samelson varieties (Jose)Notes
1200-1230: Exercise
1230-207: Lunch.
No later than 207PM: Take the number 28 bus at 14th and Kincaid, to Martin St and Amazon (arriving 225), for an afternoon hike up Spencer Butte. Bring water! Bring change for the bus (two dollars each way, or a buck seventy-five exact change), or buy your fare in advance using their Umo app, see here and here. Don't be late or you have to wait until 237.
600-900: Evening Pizza Party on lawn outside Tykeson Hall
Thursday:
900-910: Triage
915-1015: GLSBS - the quiver, the statement (Melissa) Notes
1015-1055: Exercise
1115-1215: GLSBS - rotation, braid moves (Melissa) Notes
1215-1255: Exercise
1255-200: Lunch.
200-300: CGGLSS - Lusztig cycles (Eugene) Notes
300-340: Exercise
400-500: CGGLSS - Cluster coordinates (Eugene) Notes
500-540: Exercise
Friday:
900-910: Triage
915-1015: Proof of CGGLSS (Eugene) Notes
1015-1055: Exercise
1115-1215: Comparisons (Jose) Notes
1215-1255: Exercise
1255-200: Lunch.
200-300: Leclerc's construction for Richardson varieties (Melissa) Notes
300-330: Exercise
330-430: Open questions (Eugene, Jose, Melissa) and Exercise
The End