David E. Evans
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
David E. Evans has a total of 9 co-authors. Here are the top co-authors by number of shared publications:
- Mathew Pugh
Cardiff University
4 shared publications - Andreas Næs Aaserud
University of California Los Angeles
3 shared publications - Ulrich Pennig
Cardiff University, School of Mathematics, Senghennydd Road, Cardiff, CF24 4AG Wales, United Kingdom
3 shared publications - Yasuyuki Kawahigashi
Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan
2 shared publications - Böckenhauer1 shared publication
- Corey Jones
Department of Mathematics, North Carolina State University, Raleigh, USA
1 shared publication
Latest Publications
- Open Access
- 12 December 2025
- Published by American Mathematical Society (AMS) in Communications of the American Mathematical Society
- Vol. 5 (15) , 897-942
Spectral sequence computation of higher twisted 𝐾-groups of 𝑆𝑈(𝑛)
Motivated by the Freed-Hopkins-Teleman theorem we study graded equivariant higher twists of K K -theory for the groups G = S U ( n ) G = SU(n) induced by exponential functors. We compute the rationalisation of these groups for all n n and all non-trivial functors. Classical twists use the determinant functor and yield equivariant bundles of compact operators that are classified by Dixmier-Douady theory. Their equivariant K K -theory reproduces the Verlinde ring of conformal field theory. Higher twists give equivariant bundles of stable uniformly hyperfinite algebras, which can be classified using stable homotopy theory. Rationally, only the K K -theory in degree dim ( G ) \dim (G) is again non-trivial. The non-vanishing group is a quotient of a localisation of the representation ring R ( G ) ⊗ Q R(G) \otimes \mathbb {Q} by a higher fusion ideal J F , Q J_{F,\mathbb {Q}} . We give generators for this ideal and prove that these can be obtained as derivatives of a potential. For the exterior algebra functor, which is exponential, we show that the determinant bundle over L S U ( n ) LSU(n) has a non-commutative counterpart where the fibre is the unitary group of the UHF algebra.
- 12 December 2025
- Published by American Mathematical Society (AMS) in Communications of the American Mathematical Society
- Vol. 5 (15) , 897-942
Open AccessSpectral sequence computation of higher twisted 𝐾-groups of 𝑆𝑈(𝑛)
Motivated by the Freed-Hopkins-Teleman theorem we study graded equivariant higher twists of K K -theory for the groups G = S U ( n ) G = SU(n) induced by exponential functors. We compute the rationalisation of these groups for all n n and all non-trivial functors. Classical twists use the determinant functor and yield equivariant bundles of compact operators that are classified by Dixmier-Douady theory. Their equivariant K K -theory reproduces the Verlinde ring of conformal field theory. Higher twists give equivariant bundles of stable uniformly hyperfinite algebras, which can be classified using stable homotopy theory. Rationally, only the K K -theory in degree dim ( G ) \dim (G) is again non-trivial. The non-vanishing group is a quotient of a localisation of the representation ring R ( G ) ⊗ Q R(G) \otimes \mathbb {Q} by a higher fusion ideal J F , Q J_{F,\mathbb {Q}} . We give generators for this ideal and prove that these can be obtained as derivatives of a potential. For the exterior algebra functor, which is exponential, we show that the determinant bundle over L S U ( n ) LSU(n) has a non-commutative counterpart where the fibre is the unitary group of the UHF algebra.
- Open Access
- 4 June 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (7) , 1-23
Quantum Symmetries of Noncommutative Tori
We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the $$E_{8}$$ subfactor on a noncommutative 3-torus, and of $$\text {PSU}(2)_{15}$$ on a noncommutative 4-torus.- 4 June 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (7) , 1-23
Open AccessQuantum Symmetries of Noncommutative Tori
We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the $$E_{8}$$ subfactor on a noncommutative 3-torus, and of $$\text {PSU}(2)_{15}$$ on a noncommutative 4-torus. - Open Access
- 1 January 2025
- Published by American Mathematical Society (AMS) in Communications of the American Mathematical Society
- Vol. 5 (15) , 897-942
Spectral sequence computation of higher twisted 𝐾-groups of 𝑆𝑈(𝑛)
Motivated by the Freed-Hopkins-Teleman theorem we study graded equivariant higher twists of $K$-theory for the groups $G = SU(n)$ induced by exponential functors. We compute the rationalisation of these groups for all $n$ and all non-trivial functors. Classical twists use the determinant functor and yield equivariant bundles of compact operators that are classified by Dixmier-Douady theory. Their equivariant $K$-theory reproduces the Verlinde ring of conformal field theory. Higher twists give equivariant bundles of stable uniformly hyperfinite algebras, which can be classified using stable homotopy theory. Rationally, only the $K$-theory in degree $\dim (G)$ is again non-trivial. The non-vanishing group is a quotient of a localisation of the representation ring $R(G) \otimes \mathbb {Q}$ by a higher fusion ideal $J_{F,\mathbb {Q}}$. We give generators for this ideal and prove that these can be obtained as derivatives of a potential. For the exterior algebra functor, which is exponential, we show that the determinant bundle over $LSU(n)$ has a non-commutative counterpart where the fibre is the unitary group of the UHF algebra.- 1 January 2025
- Published by American Mathematical Society (AMS) in Communications of the American Mathematical Society
- Vol. 5 (15) , 897-942
Open AccessSpectral sequence computation of higher twisted 𝐾-groups of 𝑆𝑈(𝑛)
Motivated by the Freed-Hopkins-Teleman theorem we study graded equivariant higher twists of $K$-theory for the groups $G = SU(n)$ induced by exponential functors. We compute the rationalisation of these groups for all $n$ and all non-trivial functors. Classical twists use the determinant functor and yield equivariant bundles of compact operators that are classified by Dixmier-Douady theory. Their equivariant $K$-theory reproduces the Verlinde ring of conformal field theory. Higher twists give equivariant bundles of stable uniformly hyperfinite algebras, which can be classified using stable homotopy theory. Rationally, only the $K$-theory in degree $\dim (G)$ is again non-trivial. The non-vanishing group is a quotient of a localisation of the representation ring $R(G) \otimes \mathbb {Q}$ by a higher fusion ideal $J_{F,\mathbb {Q}}$. We give generators for this ideal and prove that these can be obtained as derivatives of a potential. For the exterior algebra functor, which is exponential, we show that the determinant bundle over $LSU(n)$ has a non-commutative counterpart where the fibre is the unitary group of the UHF algebra. - Open Access
Equivariant higher Dixmier-Douady Theory for circle actions on UHF-algebras
We develop an equivariant Dixmier-Douady theory for locally trivial bundles of $C^*$-algebras with fibre $D \otimes \mathbb{K}$ equipped with a fibrewise $\mathbb{T}$-action, where $\mathbb{T}$ denotes the circle group and $D = \operatorname{End}\left(V\right)^{\otimes \infty}$ for a $\mathbb{T}$-representation $V$. In particular, we show that the group of $\mathbb{T}$-equivariant $*$-automorphisms $\operatorname{Aut}_{\mathbb{T}}(D \otimes \mathbb{K})$ is an infinite loop space giving rise to a cohomology theory $E^*_{D,\mathbb{T}}(X)$. Isomorphism classes of equivariant bundles then form a group with respect to the fibrewise tensor product that is isomorphic to $E^1_{D,\mathbb{T}}(X) \cong [X, B\operatorname{Aut}_{\mathbb{T}}(D \otimes \mathbb{K})]$. We compute this group for tori and compare the case $D = \mathbb{C}$ to the equivariant Brauer group for trivial actions on the base space.Open AccessEquivariant higher Dixmier-Douady Theory for circle actions on UHF-algebras
We develop an equivariant Dixmier-Douady theory for locally trivial bundles of $C^*$-algebras with fibre $D \otimes \mathbb{K}$ equipped with a fibrewise $\mathbb{T}$-action, where $\mathbb{T}$ denotes the circle group and $D = \operatorname{End}\left(V\right)^{\otimes \infty}$ for a $\mathbb{T}$-representation $V$. In particular, we show that the group of $\mathbb{T}$-equivariant $*$-automorphisms $\operatorname{Aut}_{\mathbb{T}}(D \otimes \mathbb{K})$ is an infinite loop space giving rise to a cohomology theory $E^*_{D,\mathbb{T}}(X)$. Isomorphism classes of equivariant bundles then form a group with respect to the fibrewise tensor product that is isomorphic to $E^1_{D,\mathbb{T}}(X) \cong [X, B\operatorname{Aut}_{\mathbb{T}}(D \otimes \mathbb{K})]$. We compute this group for tori and compare the case $D = \mathbb{C}$ to the equivariant Brauer group for trivial actions on the base space. - Open Access
- 1 June 2023
- Published by American Mathematical Society (AMS) in Bulletin of the American Mathematical Society
- Vol. 60 (4) , 459-482
Subfactors and mathematical physics
This paper surveys the long-standing connections and impact between Vaughan Jones’s theory of subfactors and various topics in mathematical physics, namely statistical mechanics, quantum field theory, quantum information, and two-dimensional conformal field theory.
- 1 June 2023
- Published by American Mathematical Society (AMS) in Bulletin of the American Mathematical Society
- Vol. 60 (4) , 459-482
Open AccessSubfactors and mathematical physics
This paper surveys the long-standing connections and impact between Vaughan Jones’s theory of subfactors and various topics in mathematical physics, namely statistical mechanics, quantum field theory, quantum information, and two-dimensional conformal field theory.
- Open Access
Subfactors and Mathematical Physics
This paper surveys the long-standing connections and impact between Vaughan Jones's theory of subfactors and various topics in mathematical physics, namely statistical mechanics,quantum field theory,quantum information and two-dimensional conformal field theory.
Open AccessSubfactors and Mathematical Physics
This paper surveys the long-standing connections and impact between Vaughan Jones's theory of subfactors and various topics in mathematical physics, namely statistical mechanics,quantum field theory,quantum information and two-dimensional conformal field theory.
- Open Access
Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules
We associate to each Temperley-Lieb-Jones C*-tensor category $\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ with parameter $\delta$ in the discrete range $\{2\cos(\pi/(k+2))\,:\,k=1,2,\ldots\}\cup\{2\}$ a certain C*-algebra $\mathcal{B}$ of compact operators. We use the unitary braiding on $\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ to equip the category $\mathrm{Mod}_{\mathcal{B}}$ of (right) Hilbert $\mathcal{B}$-modules with the structure of a braided C*-tensor category. We show that $\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ is equivalent, as a braided C*-tensor category, to the full subcategory $\mathrm{Mod}_{\mathcal{B}}^f$ of $\mathrm{Mod}_{\mathcal{B}}$ whose objects are those modules which admit a finite orthonormal basis. Finally, we indicate how these considerations generalize to arbitrary finitely generated rigid braided C*-tensor categories.Open AccessRealizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules
We associate to each Temperley-Lieb-Jones C*-tensor category $\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ with parameter $\delta$ in the discrete range $\{2\cos(\pi/(k+2))\,:\,k=1,2,\ldots\}\cup\{2\}$ a certain C*-algebra $\mathcal{B}$ of compact operators. We use the unitary braiding on $\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ to equip the category $\mathrm{Mod}_{\mathcal{B}}$ of (right) Hilbert $\mathcal{B}$-modules with the structure of a braided C*-tensor category. We show that $\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ is equivalent, as a braided C*-tensor category, to the full subcategory $\mathrm{Mod}_{\mathcal{B}}^f$ of $\mathrm{Mod}_{\mathcal{B}}$ whose objects are those modules which admit a finite orthonormal basis. Finally, we indicate how these considerations generalize to arbitrary finitely generated rigid braided C*-tensor categories. - Open Access
- 23 May 2020
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 380 (1) , 103-130
Realizing the Braided Temperley–Lieb–Jones C*-Tensor Categories as Hilbert C*-Modules
We associate to each Temperley–Lieb–Jones C*-tensor category $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ with parameter $$\delta $$ in the discrete range $$\{2\cos (\pi /(k+2)):\,k=1,2,\ldots \}\cup \{2\}$$ a certain C*-algebra $${\mathcal {B}}$$ of compact operators. We use the unitary braiding on $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ to equip the category $$\mathrm {Mod}_{{\mathcal {B}}}$$ of (right) Hilbert $${\mathcal {B}}$$ -modules with the structure of a braided C*-tensor category. We show that $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ is equivalent, as a braided C*-tensor category, to the full subcategory $$\mathrm {Mod}_{{\mathcal {B}}}^f$$ of $$\mathrm {Mod}_{{\mathcal {B}}}$$ whose objects are those modules which admit a finite orthonormal basis. Finally, we indicate how these considerations generalize to arbitrary finitely generated rigid braided C*-tensor categories.- 23 May 2020
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 380 (1) , 103-130
Open AccessRealizing the Braided Temperley–Lieb–Jones C*-Tensor Categories as Hilbert C*-Modules
We associate to each Temperley–Lieb–Jones C*-tensor category $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ with parameter $$\delta $$ in the discrete range $$\{2\cos (\pi /(k+2)):\,k=1,2,\ldots \}\cup \{2\}$$ a certain C*-algebra $${\mathcal {B}}$$ of compact operators. We use the unitary braiding on $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ to equip the category $$\mathrm {Mod}_{{\mathcal {B}}}$$ of (right) Hilbert $${\mathcal {B}}$$ -modules with the structure of a braided C*-tensor category. We show that $${\mathcal {T}}{\mathcal {L}}{\mathcal {J}}(\delta )$$ is equivalent, as a braided C*-tensor category, to the full subcategory $$\mathrm {Mod}_{{\mathcal {B}}}^f$$ of $$\mathrm {Mod}_{{\mathcal {B}}}$$ whose objects are those modules which admit a finite orthonormal basis. Finally, we indicate how these considerations generalize to arbitrary finitely generated rigid braided C*-tensor categories. - Open Access
$K$-theory of AF-algebras from braided C*-tensor categories
Renault, Wassermann, Handelman and Rossmann (early 1980s) and Evans and Gould (1994) explicitly described the $K$-theory of certain unital AF-algebras $A$ as (quotients of) polynomial rings. In this paper, we show that in each case the multiplication in the polynomial ring (quotient) is induced by a $*$-homomorphism $A\otimes A\to A$ arising from a unitary braiding on a C*-tensor category and essentially defined by Erlijman and Wenzl (2007). We also present some new explicit calculations based on the work of Gepner, Fuchs and others. Specifically, we perform computations for the rank two compact Lie groups SU(3), Sp(4) and G$_2$ that are analogous to the Evans-Gould computation for the rank one compact Lie group SU(2). The Verlinde rings are the fusion rings of Wess-Zumino-Witten models in conformal field theory or, equivalently, of certain related C*-tensor categories. Freed, Hopkins and Teleman (early 2000s) realized these rings via twisted equivariant $K$-theory. Inspired by this, our long-term goal is to realize these rings in a simpler $K$-theoretical manner, avoiding the technicalities of loop group analysis. As a step in this direction, we note that the Verlinde rings can be recovered as above in certain special cases.Open Access$K$-theory of AF-algebras from braided C*-tensor categories
Renault, Wassermann, Handelman and Rossmann (early 1980s) and Evans and Gould (1994) explicitly described the $K$-theory of certain unital AF-algebras $A$ as (quotients of) polynomial rings. In this paper, we show that in each case the multiplication in the polynomial ring (quotient) is induced by a $*$-homomorphism $A\otimes A\to A$ arising from a unitary braiding on a C*-tensor category and essentially defined by Erlijman and Wenzl (2007). We also present some new explicit calculations based on the work of Gepner, Fuchs and others. Specifically, we perform computations for the rank two compact Lie groups SU(3), Sp(4) and G$_2$ that are analogous to the Evans-Gould computation for the rank one compact Lie group SU(2). The Verlinde rings are the fusion rings of Wess-Zumino-Witten models in conformal field theory or, equivalently, of certain related C*-tensor categories. Freed, Hopkins and Teleman (early 2000s) realized these rings via twisted equivariant $K$-theory. Inspired by this, our long-term goal is to realize these rings in a simpler $K$-theoretical manner, avoiding the technicalities of loop group analysis. As a step in this direction, we note that the Verlinde rings can be recovered as above in certain special cases. - 22 March 2016
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 343 (3) , 811-850
Spectral Measures Associated to Rank two Lie Groups and Finite Subgroups of ${GL(2,\mathbb{Z})}$ G L ( 2 , Z )- 22 March 2016
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 343 (3) , 811-850
Spectral Measures Associated to Rank two Lie Groups and Finite Subgroups of ${GL(2,\mathbb{Z})}$ G L ( 2 , Z )