# overview
My research focuses on topological phases of matter, their mathematical models and applications to quantum information.

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4009 Electronics, Sensors And Digital Hardware

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Networking And Information Technology R&d (nitrd)

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Indiana University Bloomington - (Bloomington, Indiana, United States)

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University of California, San Diego - (San Diego, California, United States)

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University of California, San Diego - (San Diego, California, United States)

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Fermionic Modular Categories and the 16-fold Way

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A quaternionic braid representation (after Goldschmidt and Jones)

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Mini-Workshop: The YangBaxter Equation and Representations of Braid Groups

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European Mathematical Society - EMS - Publishing House

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Solutions to the constant YangBaxter equation: additive charge conservation in three dimensions

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Two paradigms for topological quantum computation

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On a family of non-unitarizable ribbon categories

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EXTRASPECIAL TWO-GROUPS, GENERALIZED YANG-BAXTER EQUATIONS AND BRAIDING QUANTUM GATES

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Local unitary representations of the braid group and their applications to quantum computing

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Classification of super-modular categories by rank

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Braid group representations from twisted tensor products of algebras

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RANK-FINITENESS FOR G-CROSSED BRAIDED FUSION CATEGORIES

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Low-dimensional representations of the three component loop braid group

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Low-dimensional indecomposable representations of the braid group $B_3$

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MODULAR CATEGORIES, INTEGRALITY AND EGYPTIAN FRACTIONS

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Modular categories, integrality and Egyptian fractions

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On the Classification of Weakly Integral Modular Categories

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On the classification of the Grothendieck rings of non-self-dual modular categories

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Braid Representations from Unitary Braided Vector Spaces

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FINITE LINEAR QUOTIENTS OF B₃ OF LOW DIMENSION

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Generating functions for ranks of pre-modular categories

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From quantum groups to unitary modular tensor categories

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From Quantum Groups to Unitary Modular Tensor Categories

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Integral non-group-theoretical modular categories of dimension $p^2q^2$

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On the classification of weakly integral modular categories

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Braided Zestings of Verlinde Modular Categories and Their Modular Data

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On invariants of modular categories beyond modular data

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Unitary braid representations with finite image

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Braid group representations from twisted quantum doubles of finite groups

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The Witt classes of so(2r)2r

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Classification of metaplectic modular categories

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On invariants of Modular categories beyond modular data

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Braid representations from unitary braided vector spaces

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Dimension as a quantum statistic and the classification of metaplectic categories

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Fermionic modular categories and the 16-fold way

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Finite Linear Quotients of $B_3$ of Low Dimension

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Braid representations from quantum groups of exceptional Lie type

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Reconstructing braided subcategories of SU(N)k

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Modular categories, integrality and Egyptian fractions

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Classification of integral modular categories of Frobenius-Perron dimension pq^4 and p^2q^2

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Reconstruction of modular data from $SL_2(mathbb{Z})$ representations

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An Invitation to the Mathematics of Topological Quantum Computation

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G-crossed braided zesting

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Classification of Super-Modular Categories by Rank

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GENERALISATIONS OF HECKE ALGEBRAS FROM LOOP BRAID GROUPS

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Localization of Unitary Braid Group Representations

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The -eigenvalue problem and two applications

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Braid group representations from twisted quantum doubles of finite groups

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Unitary Braid Representations with Finite Image

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An Invitation to the Mathematics of Topological Quantum Computation

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Generalisations of Hecke algebras from Loop Braid Groups

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A note on tensor categories of Lie type $E_9$

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The N-eigenvalue problem and two applications

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Reconstruction of Modular Data from SL₂(Z) Representations

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Rank-finiteness for G-crossed braided fusion categories

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Generalized and Quasi-Localizations of Braid Group Representations

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A quaternionic braid representation (after Goldschmidt and Jones)

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European Mathematical Society - EMS - Publishing House

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Metaplectic Categories, Gauging and Property F

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On classification of super-modular categories of rank 8

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Symplectic Level-Rank Duality via Tensor Categories

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Extraspecial Two-Groups, Generalized Yang-Baxter Equations and Braiding   Quantum Gates

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On Tensor Categories Arising from Quantum Groups and BMW-algebras at Odd Roots of Unity

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On the classification of non-self-dual modular categories

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Extraspecial 2-groups and images of braid group representations

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Symplectic level-rank duality via tensor categories

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Braids, Motions and Topological Quantum Computing

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Classification of Metaplectic Modular Categories

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On near-group centers and super-modular categories

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Dimension as a quantum statistic and the classification of metaplectic categories

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Modular Categories of Dimension $p^3m$ with $m$ Square-Free

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Local representations of the loop braid group

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Two paradigms for topological quantum computation

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Generalized and quasi-localizations of braid group representations

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BRAID REPRESENTATIONS FROM QUANTUM GROUPS OF EXCEPTIONAL LIE TYPE

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A Categorical Perspective on Braid Representations

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LOCAL REPRESENTATIONS OF THE LOOP BRAID GROUP

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On a Family of Non-Unitarizable Ribbon Categories

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Braid Group Representations from Twisted Tensor Products of Algebras

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Extraspecial 2-groups and images of braid group representations

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PARAMETER-DEPENDENT GAUSSIAN (N, z)-GENERALIZED YANG-BAXTER OPERATORS

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$SO(N)_2$ Braid group representations are Gaussian

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Classification of modular data up to rank 12

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Representations of the Necklace Braid Group: Topological and Combinatorial Approaches

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Local unitary representations of the braid group and their applications to quantum computing

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A finiteness property for braided fusion categories

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Mathematics of Topological Quantum Computing

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Dimension as a quantum statistic and the classification of metaplectic categories

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Localization of unitary braid group representations

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On classification of modular categories by rank

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Low-dimensional representations of the three component loop braid group

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An algebra-level version of a link-polynomial identity of Lickorish

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Representations of the Necklace Braid Group: Topological and Combinatorial Approaches

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On Classification of Modular Tensor Categories

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MATHEMATICS OF TOPOLOGICAL QUANTUM COMPUTING

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A Finiteness Property for Braided Fusion Categories

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An algebra-level version of a link-polynomial identity of Lickorish

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SO(N)₂ braid group representations are Gaussian

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European Mathematical Society - EMS - Publishing House

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Acyclic anyon models, thermal anyon error corrections, and braiding   universality

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The N-eigenvalue Problem and Two Applications

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A note on tensor categories of Lie type E ₉

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METAPLECTIC CATEGORIES, GAUGING AND PROPERTY F

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Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions

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On Classification of Modular Categories by Rank

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MODULAR CATEGORIES OF DIMENSION p³m WITH m SQUARE-FREE

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Classification of Integral Modular Categories of Frobenius-Perron Dimension pq ⁴ and P ² q ²

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On classification of modular tensor categories

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Topological Phases of Matter and Their Application To Quantum Computing

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

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Collaborative Research:  Mathematical Foundations of Topological Quantum Computation

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National Science Foundation - (Arlington, Virginia, United States)

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Quantum Symmetries of Topological Phases of Matter

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National Science Foundation - (Arlington, Virginia, United States)

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FRG: cQIS: Collaborative Research: Mathematical Foundations of Topological Quantum Computation and Its Applications

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National Science Foundation - (Arlington, Virginia, United States)

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Texas A&M University; Mathematics; 3368 TAMU

# etdChairOf[].label
Bruillard, Paul Joseph (2013-08). On the Classification of Low-Rank Braided Fusion Categories. Doctoral Dissertation.

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Ganesan, Priyanga (2022-05). Quantum Coloring of Quantum Graphs. Doctoral Dissertation.

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Gustafson, Paul Prem (2018-08). On the Property F Conjecture. Doctoral Dissertation.

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Weeks, John Munroe (2022-08). Property of Rapid Decay and Free Wreath Products. Doctoral Dissertation.

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Kimball, Andrew M. (2019-05). Representations of the Necklace Braid Group. Doctoral Dissertation.

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Zhang, Qing (2019-12). SUPER-MODULAR CATEGORIES. Doctoral Dissertation.

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Deaton, Adam Paul (2024-05). De-Equivariantization in Fusion Categories from Quantum Groups at Roots of Unity. Master's Thesis.

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Creamer, Daniel Edward (2018-08). A Computational Approach to Classifying Low Rank Modular Tensor Categories. Doctoral Dissertation.