RTG @ Northeastern - GPRT Seminar

Palace of Catalan Music. Photo by Micha Weber.

Geometry, Physics, and Representation Theory Seminar

Spring 2026

Meeting weekly on Thursdays 3:00-4:00pm in 509/511 Lake Hall at Northeastern.
When available, abstracts, slides, and links to recordings can be found by clicking on the entries.
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If you have questions or would like to speak at the seminar, please email do.hoang [at] northeastern.edu.

Organizers: Pablo Boixeda Alvarez, Do Kien Hoang, Iva Halacheva, Sasha Pevzner, Valerio Toledano Laredo.

Affine Temperley–Lieb algebras and projectors, quotients and generalisations

Abstract: The affine and periodic Temperley–Lieb algebras are families of infinite-dimensional algebras with a diagrammatic presentation. They have been studied in the last 30 years, mostly for their physical applications in statistical mechanics, where the diagrammatic presentation encodes the connectivity property of the models. Most of the relevant representations for physics are finite-dimensional. In this work, we define finite-dimensional quotients of these algebras that we name uncoiled algebras in reference to the diagrammatic interpretation of the quotient and construct a family of Jones–Wenzl idempotents, each of which projects onto one of the one-dimensional modules these algebras admit. We also prove that, most of the time, the uncoiled algebras are affine cellular and we define a notion of skew sandwich cellularity for the remaining cases. This is joint work with Alexi Morin-Duchesne.

Time permitting, I will also cover future generalisations on diagrammatic calculus on surfaces via cobordisms.

Jan 22: Daoji Huang

Dual affine Robinson-schensted correspondence via growth diagrams

Abstract: The Robinson--Schensted (RS) correspondence admits diagrammatic interpretations via Fomin's growth diagrams and Viennot's shadow line construction. Works of Spaltenstein, Springer, Steinberg, and van Leeuwen connected this combinatorial construction to the relative position map of Springer fibers. Motivated by Kazhdan--Lusztig cell theory, various generalizations of the Robinson--Schensted correspondence into the affine type A setting have been studied. Prominent examples include Shi's insertion algorithm and the affine matrix ball construction by Chmutov--Pylyavskyy--Yudovina. In particular, using the affine matrix ball construction, Boixeda--Ying--Yue showed that the two-sided cells and S-cells agree when the nilpotent is of rectangular type.

In this talk, we introduce a new combinatorial construction of the affine RS correspondence via growth diagrams and shadow lines that is in a sense dual to Shi's insertion and the affine matrix ball construction, and geometrically natural in terms of relative positions of affine flags.

Ongoing joint work with Sylvester Zhang.

Jan 29: Mengwei Hu

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Feb 5: Mini course by Sergey Fomin

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Feb 12: Raj Gandhi

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Feb 19:

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Feb 26:

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Mar 5: Spring break