Research
- Ideal quantum metrics from fractional Laplacians (with D.M. Gerontogiannis), arXiv:2502.04187.
- Theta correspondence via group C*-algebras (with M.Goffeng and M.H. Sengun), arXiv:2412.07501.
- Adelic C*-correspondences and parabolic induction (with M.Goffeng and M.H. Sengun), arXiv:2412.02379.
- Curvature and Weitzenbock formula for the Podles quantum sphere (with A. Rennie), arXiv:2406.18483.
- Existence and uniqueness of the Levi-Civita connection on noncommutative differential forms (with A. Rennie), Adv.Math.468, 110207, (2025).
- Heat operators and isometry groups of Cuntz-Krieger algebras (with D.M. Gerontogiannis and M. Goffeng), Int. Math. Res. Not. 6, rnaf054 (2025).
- Curvature and Weitzenbock formula for spectral triples (with A. Rennie), Math. Nachr.297 (12),4582-4604 (2024).
- The logarithmic Dirichlet Laplacian on Ahlfors regular spaces (with D.M. Gerontogiannis), Trans. Amer. Math. Soc (2024), in press.
- Equal rank local theta correspondence as a strong Morita equivalence (with M. H. Sengun), Selecta Math. (New Series) 30, article nr 72 (2024).
- Classifying the dynamics of architected materials via groupoid methods (with E. Prodan), J. Geom. Phys., 1196, 105059 (2024)
- The Friedrichs angle and alternating projections in Hilbert C*-modules (with A. Rennie), J. Math. Anal. Appl. 516 (1) 1 (2022) 126474.
- A groupoid approach to interacting fermions (with E. Prodan), Commun. Math. Phys. 394, 143-213 (2022)
- Curvature of differentiable Hilbert modules and Kasparov modules (with A. Rennie and W.D.van Suijlekom), Adv. Math. 402 (2022), 108128.
- Gauge theory on noncommutative Riemannian principal bundles (with B. Ćaćić), Commun. Math. Phys. 388 (2021), 107–198.
- Localised module frames and Wannier bases from groupoid Morita equivalences (with C. Bourne), J. Fourier Anal. Appl. 27 (69) (2021).
- Homotopy equivalence in unbounded KK-theory (with K. van den Dungen), Ann. K-theory 5 (3) (2020), 501--537.
- Hecke operators in KK-theory and the K-homology of Bianchi groups, (with M. H. Sengun), J. Noncommut. Geom. 14 (1) (2020), 125–189.
- Untwisting twisted spectral triples (with M. Goffeng and A. Rennie), Int. J. Math. 30 (14) (2019), 1950076.
- Boundaries, spectral triples and K-homology (with I. Forsyth, M. Goffeng and A. Rennie), J. Noncommut. Geom. 13 (2) (2019), 407–472.
- Index theory and topological phases of aperiodic lattices, (with C. Bourne), Ann. Henri Poincare 20 (6) (2019), 1969--2038.
- Sums of regular self-adjoint operators in Hilbert C*-modules, (with M. Lesch), J. Math. Anal. Appl. 472 (1) (2019), 947--980.
- Hecke modules for arithmetic groups via bivariant K-theory (with M.H. Sengun), Ann. K-theory 3 (4) (2018), 631--656.
- Wieler solenoids, Cuntz-Pimsner algebras and K-theory (with R.J. Deeley, M.Goffeng and M. F. Whittaker), Ergodic Th. Dynam. Sys. 38 (8) (2018), 2942--2988.
- Operator *-correspondences in analysis and geometry (with D. Blecher and J. Kaad), Proc. Lond. Math. Soc.117 (2) (2018), 303--344.
- Shift tail equivalence and an unbounded representative of the Cuntz-Pimsner extension (with M.Goffeng and A. Rennie), Ergodic Th. Dynam. Sys. 38 (4) (2018), 1389--1421.
- The bordism group of unbounded KK-cycles (with R.J. Deeley and M. Goffeng), J. Topol. Anal.10 (2) (2018) 355--400.
- Nonunital spectral triples and metric completeness in unbounded KK-theory (with A. Rennie), J. Funct. An. 271 (9) (2016), 2460--2538.
- Gauge theory for spectral triples and the unbounded Kasparov product (with S. Brain and W.D. van Suijlekom), J. Noncommut. Geom. 10 (2016), 135--206.
- Spectral triples and finite summability for Cuntz-Krieger algebras (with M. Goffeng), Documenta Math. 20 (2015), 89--170.
- Dense domains, symmetric operators and spectral triples (with I. Forsyth and A. Rennie), New York J. Math. 20 (2014), 1001--1020.
- Unbounded bivariant K-theory and correspondences in noncommutative geometry, J. Reine Angew. Math. 69 (2014), 101--172 (published online September 2012).
- Groupoid cocycles and K-theory, Munster J. of Math. 4 (2011), 233--256.
- Toeplitz extensions in noncommutative topology and mathematical physics (with F.Arici), Trends in Mathematics, Geometric methods in physics XXXVIII (2020), 3--29.
- A K-theoretic Selberg trace formula (with M. H. Sengun and H. Wang), Operator Theory: Advances and Applications 278: Operator theory, operator algebras and their interaction with geometry and topology - Ron Douglas memorial volume (2020), 403--424.
- Spectral triples on O_N (with M.Goffeng), 2016 Matrix Annals, "Refining C*-algebraic invariants for dynamics using KK-theory".
- Spectral triples and KK-theory, a survey Clay Math. Proceedings 16, "Topics in Noncommutative Geometry,"(2012), 197--213.
- Operator spaces and noncommutative geometry in interaction, Oberwolfach reports 6 (2016).
Preprints
All my preprints on the ArXiv.