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Showing 1 to 16 of 16 for “"categorification"”.
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Odd symmetric functions and categorification
… odd analogue of the nilHecke algebra, we give a categorification of the integral divided powers form of U_q^+(sl_2) inequivalent to the one due to Khovanov-Lauda. Along the way, we develop a graphical calculus for indecomposable modules for the odd nilHecke algebra.
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Knot Floer Homology and Categorification
… between knot homology theories arising from categorification and from Heegaard Floer homology, we present a self-contained construction of knot Floer homology in the language of HOMFLY-PT homology. Using the cube of resolutions for knot Floer homology defined by Ozsváth and Szabó;, we first …
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Categorification of the Kirwan map
Given a Hamiltonian action of a group on a scheme we can consider the Hamiltonian reduction. This furnishes us with a notion of quotient. From the construction it follows that we have a map from the equivariant cohomology of the scheme to the cohomology of the quotient. It is natural to ask if this …
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A Coherent Categorification of the Asymptotic Affine Hecke Algebra
Kazhdan–Lusztig categorified the affine Hecke algebra H in terms of equivariant coherent sheaves on the Steinberg variety. Recently, Ben-Zvi–Chen–Helm–Nadler have applied the formalism of categorical traces to construct a "coherent Springer sheaf" on a moduli stack of Deligne–Langlands parameters …
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Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras
… thesis, we examine three different versions of "categorification" of the affine Hecke algebra and its periodic module: the first is by equivariant coherent sheaves on the Grothendieck resolution (and related objects), the second is by certain classes on bimodules over polynomial rings, called …
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Coherence for categorified operadic theories
… P, we propose a definition of the weakening (or categorification) of the theory, in which equations that hold strictly for P -algebras hold only up to coherent isomorphism. This generalizes the theories of monoidal categories and symmetric monoidal categories, and several related notions defined …
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The K-theoretic Hall Algebra On Surfaces and Categorifications
… that it was associative. I also made a naive categorification of the elliptic Hall algebra.
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Hopfological Algebra
… classes of examples that appear naturally in categorification.
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On motivic Donaldson-Thomas invariants on the local projective plane
Motivic Donaldson-Thomas (DT) invariant is a categorification of the classical DT invariant which contains more information of the local structure of a moduli space. In this thesis, we give three (partial) studies on the motivic DT invariants for various moduli spaces associated to the local …
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Categorifications of Cluster Varieties
In this thesis we study additive categorifications of algebraic varieties whose coordinate rings admit a cluster algebra structure. The presence of a cluster structure has important implications for the geometry of a variety including the existence of canonical linearly independent sets of regular …
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Tripos models of Internal Set Theory
… started by A. Kock and C. J. Mikkelsen on the categorification of Transfer. We then elaborate upon one particular kind of model of each type: the ultrapower models, which are Nelson models obtained from a choice of adequate ultrafilter and that mirror the constructions of classical Robinson …
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Loop Spaces and Iterated Higher Dimensional Enrichment
… just a part of the broad undertaking known as categorification as described by Baez and Dolan. This effort has as a partial goal that of understanding the categories and functors that correspond to loop spaces and their associated topological functors. Progress towards this goal has been …
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Semisimple filtrations of tilting modules for algebraic groups
… understand this behavior we describe an explicit categorification of higher-order linkage using the language of Soergel bimodules. Along the way we also develop the algebra and combinatorics of higher-order linkage at the de-categorified level. We hope that this will provide a foundation for a …
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A graphical calculus for shifted symmetric functions
The goal of this thesis is twofold. The fi rst goal is to describe three categori cations of the algebra of symmetric functions and establish relationships between them all. The second goal is to establish an isomorphism between the centre of Khovanov's Heisenberg category [Kho14] and the algebra …
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A graphical calculus for shifted symmetric functions
The goal of this thesis is twofold. The fi rst goal is to describe three categori cations of the algebra of symmetric functions and establish relationships between them all. The second goal is to establish an isomorphism between the centre of Khovanov's Heisenberg category [Kho14] and the algebra …
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On a Heegaard Floer theory for tangles
… homology HFT^ for tangles in the 3-ball. The decategorification of HFL^ is the classical Alexander polynomial for links; likewise, the decategorification of HFT^ gives a local version ∇ˢ of the Alexander polynomial. In the first chapter of this thesis, we give a purely combinatorial definition …