Workshop on Algebra and Representation Theory, Held on Oregonian Grounds

25 July - 29 July 2016

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 the Lokey Education Center, room 276.

900-945: Introduction and overview; what we do and don't know about HHH.

1000-1100: First definition of HHH. MOY diagrams and cubes of resolutions.

1115-1200: Interlude: informal discussion of cancellation and spectral sequences.

LECTURES ARE HERE.

EXERCISES ARE HERE.

1200-130: Eat lunch, discussing the exercises between bites.

130-200: Exercises in the lecture room. Some will be done on the board near the end.

215-315: Second definition of HHH. Hecke algebra and Soergel bimodules.

330-430: Basics of the rational Cherednik algebra; Dunkl operators, the polynomial representation.

EXERCISES ARE HERE.

430-500: Exercises and questions in the lecture room.

Later that night: Exercises at a bar/restaurant, TBD.

900-930: Triage

945-1045: Cherednik algebras II: filtrations, Gordon-Stafford.

1100-1200: Projectors (uncategorified). The full twist operator, and colored polynomials.

LECTURES ARE HERE.

EXERCISES ARE HERE.

1200-200: Lunch and exercises, like monday.

215-315: The infinite torus braid as a categorified projector.

330-430: Introduction to Hilbert schemes; equivariant K-theory and localization.

EXERCISES ARE HERE.

430-500: Exercises and questions in the lecture room.

Later: Dinner and exercises.

900-1000: Building other projectors, colored homology. (Paul Wedrich)

1015-1115: Colored homology and Cherednik algebras. (Eugene Gorsky)

1130-1230: Oblomkov-Shende. Compactified Jacobians.

EXERCISES ARE HERE.

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

900-930: Triage

945-1045: Diagonal harmonics and the n! conjecture. Comparison with T(kn+1,n). (Eugene Gorsky)

11-12: Cherednik algebras and Hilbert Schemes / Cherednik algebras and the compactified Jacobian.

EXERCISES ARE HERE.

12-2: Lunch and exercises, like Monday

215-315: Knots and sheaves on Hilbert schemes.

330-430: Double Shuffle Algebras. (Eugene Gorsky)

430-500: Question and answer in the exercise room.

Later: Dinner and exercises.

900-930: Triage

945-1045: Categorical diagonalization I. (Matt Hogancamp and Ben Elias)

1100-1200: Categorical diagonalization II. (Matt Hogancamp and Ben Elias)

1200-200: Lunch and exercises, like Monday.

215-315: Hilbert schemes and the homology of projectors. (Eugene Gorsky)

330-430: What we know and don't know (reprise). Where to next?