Symplectic duality

Workshop on Algebra and Representation Theory, Held on Oregonian Grounds

7-11 August 2017
University of Oregon
Eugene, OR


Timing is still tentative.
Exercises and lecture notes will be linked from this webpage when available.
Pastries and Coffee will be available in the lecture room starting at 8:30AM each morning.

All talks will be held in Straub 145.


900-1000: Introduction. Notes. (Ben Webster)
1020-1120: The hypertoric enveloping algebra I: Higgs description. Notes. Reference: HCO, Sections 3.1-2. (Nick Proudfoot)
1120-1200: Exercise.

1200-130: Lunch.

130-230: The hypertoric enveloping algebra II: Coulomb description. Notes. Reference: BFN 2, Section 4. (Ben Webster)
230-310: Exercise.
330-430: Weight functors and representing projectives. Notes. Reference: MvdB, Section 3.1. (Ben Webster).
430-510: Exercise.


900-1000: Category O (describe simples, standards, projectives). Reference: HCO, Section 3.3 & 4. (Justin Hilburn)
1000-1040: Exercise.
1100-1200: Quiver presentation, highest weightness. Notes. Reference: HCO, Sections 3.4 & 4.2. (Ben Webster)
1200-1240: Exercise.

1240-200: Lunch.

200-300: Intro to Koszul duality. Notes. References: BGS, Section 2; and MOS, Sections 3 and 4. (Ben Elias)
300-340: Exercise.
400-500: More Kozsul duality. Notes. References: same as above. (Ben Webster)
500-540: Exercise.


900-1000: The Farkas Lemma. Notes. References: Ziegler, Sections 1.3 & 1.4; and GDKD, Section 2.3. (Nick Proudfoot)
1000-1040: Exercise.
1100-1200: Gale duality and Koszul duality. Notes. Reference: GDKD, Section 3. (Ben Webster)
1200-1240: Exercise.

1240-200: Lunch.

207: 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.

600-900: Evening Pizza Party at University Park


900-1000: More Koszul duality. (continued) (Ben Webster)
1000-1040: Exercise.
1100-1200 Hypertoric varieties and their Lagrangians. Notes. Reference: HCO, Section 5. (Nick Proudfoot)
1200-1240: Exercise.

1230-200: Lunch.

200-300: Quantizations. Reference: QCSR 1. (Justin Hilburn)
300-340: Exercise.
Previous stuff:
130-230: DQ-Modules. Reference: QCSR 1. (Ben Webster)
300-400: The Kirwan functor and a second proof of Koszul duality. Reference: GCOQV, Section 3. (Ben Webster)
430-530: Justin's perspective on duality. (Justin Hilburn)


900-1000: The nonabelian Higgs and Coulomb branches. Reference: HnC, Section 3.1-2. (Alex Weekes)
1000-1040: Exercise.
1100-1200: Weight functors and the homogeneous presentation. Reference: HnC, Section 3.3. (Ben Webster)
1200-1240: Exercise.

1240-200: Lunch.

200-300: Simples on the Higgs side, Steinbergs and the KLR algebra. Reference: HnC, Section 2. (Ben Webster)
300-340: Exercise.
400-500: The isomorphism and Koszul duality. Reference: HnC, Section 4. (Ben Webster)

The End