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Time: Mondays, 4:30 - 5:30 pm.
Room: Gilman 219.
Contact: Cesar Bardomiano Martinez and Colton Sandvik.
Faculty Contact: David Gepner, Mee Seong Im, Mikhail Khovanov, Nitu Kitchloo, Emily Riehl.
Weekly Social Events
Department Afternoon Tea: Mondays, Tuesdays, and Thursdays, 4 - 5pm, Krieger 413
Department Wine and Cheese: Wednesdays, 4 - 5pm, Krieger 413
Aug 31: Ishan Levy (Institute for Advanced Study, Princeton, NJ)
Title: What we know about the telescopic categories
Abstract: The stable homotopy category naturally breaks up into indecomposable building blocks, the telescopic (or T(n)-local) stable categories. These pieces are not well understood in general, rather much attention has been given to their computationally tractable close relatives, the K(n)-local categories. I will give an overview of some of the recent advances in understanding the T(n)-local category, explaining what we understand about its difference with the K(n)-local category, some consequences, and some of the new tools we have for working with the T(n)-local category.
This comes from projects joint with Burklund, Carmeli, Clausen, Hahn, Schlank, and Yanovski.
Sept 14: Colton Sandvik (Johns Hopkins University, Baltimore, MD)
Title: Modular Character Sheaves and Monodromic Hecke Categories
Abstract: Character sheaves provide a geometric framework for studying characters of finite groups of Lie type. Introduced by Lusztig in the 1980s, they played a central role in the classification of irreducible complex representations of these groups and in the computation of their characters. Although the definition of character sheaves can be formulated with modular coefficients, much of Lusztig's characteristic-zero machinery breaks down in this setting.
In this talk, I will give a streamlined overview of the theory of character sheaves using modern language from categorical representation theory. From this perspective, categorical traces allow one to study character sheaves through monodromic Hecke categories. I will describe two models for these categories: a geometric categorification in terms of parity sheaves and an algebraic categorification in terms of Soergel bimodules. A key advantage of these models is that they are tightly controlled by p-Kazhdan–Lusztig combinatorics. This paves the way for a combinatorial approach to the study of modular character sheaves.
Sept 21: Cesar Bardomiano Martinez (Johns Hopkins University, Baltimore, MD)
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Sept 28: Logan Hyslop (Harvard University, Cambridge, MA)
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Oct 5: Kush Singhal (Harvard University, Cambridge, MA)
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Oct 13 (Tuesday): Dahye Cho (G-LAMP AI-Bio Convergence Research Institute, Soongsil University, Seoul, Korea)
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Oct 19: Luke Conners (Universität Zürich, Institute of Mathematics, Zürich, Switzerland)
Title: HOMFLY Homology for Oriented Tangles
Abstract: We introduce an extension of Khovanov and Rozansky's categorification of the HOMFLY polynomial to oriented tangles. Unlike previous such extensions, ours is invariant under the full suite of oriented Reidemeister moves, including the "misoriented" Reidemeister IIb. For oriented links L, this removes the preliminary step of presenting L as a braid closure. Our construction admits an interpretation in terms of Bar-Natan's "canopoly" framework, allowing for local computations. Time permitting, we will briefly discuss potential consequences for functoriality under (non-compact) oriented tangle cobordisms and extracting smooth 4-manifold invariants. Based on forthcoming joint work with William Ballinger.
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