ORCID Profile
0000-0002-2517-7924
Current Organisations
University of California Santa Cruz
,
Universität Hamburg
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Category Theory, K Theory, Homological Algebra | Pure Mathematics | Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory | Topology
Expanding Knowledge in the Physical Sciences | Expanding Knowledge in the Mathematical Sciences |
Publisher: Elsevier BV
Date: 09-2019
Publisher: Cambridge University Press (CUP)
Date: 05-03-2021
DOI: 10.1017/S001708952100001X
Abstract: In this note, we compute the centers of the categories of tilting modules for G = SL 2 in prime characteristic, of tilting modules for the corresponding quantum group at a complex root of unity, and of projective G g T -modules when g = 1, 2.
Publisher: Mathematical Sciences Publishers
Date: 04-10-2017
Publisher: Mathematical Sciences Publishers
Date: 31-12-2022
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 17-03-2021
DOI: 10.4171/QT/148
Publisher: Mathematical Sciences Publishers
Date: 23-02-2016
Publisher: Elsevier BV
Date: 04-2019
Publisher: Wiley
Date: 18-01-2021
DOI: 10.1112/JLMS.12433
Publisher: Wiley
Date: 28-07-2022
DOI: 10.1111/REC.13743
Abstract: Scientists who identify as lesbian, gay, bisexual, transgender, queer, or members of other marginalized sexual orientations and gender identities (LGBTQ+) face serious disparities compared to their non‐LGBTQ+ peers. Restoration science presents additional risks for LGBTQ+ researchers, including extensive time in the field—sometimes in locations that are hostile to LGBTQ+ people or create discomfort around gender expression and sexual orientation. At the same time, restoration science is uniquely positioned to create change: the same principles that shape ecosystem restoration also provide a blueprint for cultivating inclusion in science. We present 10 recommendations for LGBTQ+ inclusion based on four guiding restoration principles: (1) Context is key (2) Healthy environments require support (3) Success needs to be defined and (4) A erse future is worth striving for. We provide concrete actions that in iduals and institutions can take and emphasize the positive outcomes that LGBTQ+ inclusion can generate for a healthier restoration community.
Publisher: Springer Science and Business Media LLC
Date: 19-12-2022
DOI: 10.1007/S00209-022-03163-9
Abstract: We describe the universal target of annular Khovanov–Rozansky link homology functors as the homotopy category of a free symmetric monoidal linear category generated by one object and one endomorphism. This categorifies the ring of symmetric functions and admits categorical analogues of plethystic transformations, which we use to characterize the annular invariants of Coxeter braids. Further, we prove the existence of symmetric group actions on the Khovanov–Rozansky invariants of cabled tangles and we introduce spectral sequences that aid in computing the homologies of generalized Hopf links. Finally, we conjecture a characterization of the horizontal traces of Rouquier complexes of Coxeter braids in other types.
Publisher: International Press of Boston
Date: 2018
Publisher: IOP Publishing
Date: 13-08-2020
Abstract: The Hamiltonian of the N -state superintegrable chiral Potts (SICP) model is written in terms of a coupled algebra defined by N − 1 types of Temperley–Lieb generators. This generalises a previous result for N = 3 obtained by Fjelstad and Månsson (2012 J. Phys. A: Math. Theor. 45 155208). A pictorial representation of a related coupled algebra is given for the N = 3 case which involves a generalisation of the pictorial presentation of the Temperley–Lieb algebra to include a pole around which loops can become entangled. For the two known representations of this algebra, the N = 3 SICP chain and the staggered spin-1/2 XX chain, closed (contractible) loops have weight 3 and weight 2, respectively. For both representations closed (non-contractible) loops around the pole have weight zero. The pictorial representation provides a graphical interpretation of the algebraic relations. A key ingredient in the resolution of diagrams is a crossing relation for loops encircling a pole which involves the parameter ρ = e 2 π i/3 for the SICP chain and ρ = 1 for the staggered XX chain. These ρ values are derived assuming the Kauffman bracket skein relation.
Publisher: Springer Science and Business Media LLC
Date: 04-05-2023
DOI: 10.1007/S00029-023-00835-0
Abstract: Using the non-semisimple Temperley–Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for $$\\textrm{SL}_{2}$$ SL 2 in the mixed case. This simultaneously generalizes the semisimple situation, the case of the complex quantum group at a root of unity, and the algebraic group case in positive characteristic. We describe character formulas and give a presentation of the category of tilting modules as an additive category via a quiver with relations. Turning to the monoidal structure, we describe fusion rules and obtain an explicit recursive description of the appropriate analog of Jones–Wenzl projectors.
Publisher: Wiley
Date: 21-06-2018
DOI: 10.1112/PLMS.12154
Publisher: Elsevier BV
Date: 07-2023
Publisher: Mathematical Sciences Publishers
Date: 21-12-2016
Publisher: Oxford University Press (OUP)
Date: 13-04-2021
DOI: 10.1093/IMRN/RNAB019
Abstract: We study two kinds of categorical traces of (monoidal) dg categories, with particular interest in categories of Soergel bimodules. First, we explicitly compute the usual Hochschild homology, or derived vertical trace, of the category of Soergel bimodules in arbitrary types. Secondly, we introduce the notion of derived horizontal trace of a monoidal dg category and compute the derived horizontal trace of Soergel bimodules in type $A$. As an application we obtain a derived annular Khovanov–Rozansky link invariant with an action of full twist insertion, and thus a categorification of the HOMFLY-PT skein module of the solid torus.
Publisher: Oxford University Press (OUP)
Date: 14-01-2019
DOI: 10.1093/IMRN/RNY289
Abstract: We prove that the generating functions for the colored HOMFLY-PT polynomials of rational links are specializations of the generating functions of the motivic Donaldson–Thomas invariants of appropriate quivers that we naturally associate with these links. This shows that the conjectural links–quivers correspondence of Kucharski–Reineke–Stošić–Sułkowski as well as the LMOV conjecture holds for all rational links. Along the way, we extend the links–quivers correspondence to tangles and, thus, explore elements of a skein theory for motivic Donaldson–Thomas invariants.
Publisher: American Mathematical Society (AMS)
Date: 03-06-2021
DOI: 10.1090/ERT/569
Abstract: Using diagrammatic methods, we define a quiver with relations depending on a prime p \\mathsf {p} and show that the associated path algebra describes the category of tilting modules for S L 2 \\mathrm {SL}_{2} in characteristic p \\mathsf {p} . Along the way we obtain a presentation for morphisms between p \\mathsf {p} -Jones–Wenzl projectors.
Location: United States of America
Location: United States of America
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Location: United States of America
Start Date: 2020
End Date: 2022
Funder: Australian Research Council
View Funded ActivityStart Date: 12-2020
End Date: 12-2020
Amount: $427,066.00
Funder: Australian Research Council
View Funded Activity