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Geometry, Physics, and Representation Theory Seminar

RTG Group Seminar

Spring 2021, Northeastern

Meeting weekly on Thursdays 2:50-3:50pm via Zoom.

If you are not at Northeastern but would like to recieve announcements, join the mailing list.

If you have questions or would like to speak at the seminar, please email v.blankers [at] northeastern.edu.

Organizers: Peter Crooks, Iva Halacheva, Vance Blankers, Christopher Beasley, Valerio Toledano Laredo.

Schedule

Date Speaker Title
Jan 28 Joshua Wen (Northeastern University) Towards wreath Macdonald theory

Wreath Macdonald polynomials are generalizations of Macdonald polynomials wherein the symmetric groups are replaced with their wreath products with a cyclic group of order $\ell$. They were defined by Haiman, and mirroring the usual Macdonald theory, it is not obvious that they exist. Haiman also conjectured for them a generalization of his celebrated proof of Macdonald positivity where the Hilbert scheme of points on the plane is replaced with certain cyclic Nakajima quiver varieties. This conjecture was proven by Bezrukavnikov and Finkelberg, which also implies the existence of the polynomials. Analogues of standard formulas and results of usual Macdonald theory remain to be explored. I will present an approach to the study of the wreath variants via the quantum toroidal algebra of $\mathfrak{sl}_\ell$, generalizing the fruitful interactions between the usual Macdonald theory and the quantum toroidal algebra of $\mathfrak{gl}_1$. As applications, I'll present an analogue of the norm formula and a conjectural path towards "wreath Macdonald operators" that makes contact with the spin Ruijsenaars-Schneider integrable system.

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Feb 4 Martha Precup (Washington University) TBD

No abstract available at this time. Please contact the organizers or check back later!

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Feb 11 TBD TBD

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Feb 18 TBD TBD

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Feb 25 TBD TBD

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Mar 4 TBD TBD

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Mar 11 TBD TBD

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Mar 18 TBD TBD

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Mar 25 TBD TBD

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Apr 1 TBD TBD

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Apr 8 TBD TBD

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Apr 15 TBD TBD

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Apr 22 TBD TBD

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End of Semester (Seminar resumes Fall 2021)




Previous Semesters

Fall 2020
Spring 2020
Fall 2019
Spring 2019
Fall 2018
Spring 2018
Fall 2017
Spring 2017
Fall 2016
Spring 2016
Fall 2015
Spring 2015