# Research

## Preprints

All my preprints on the ArXiv.

Gabor frames and Wannier bases from groupoid Morita equivalences (with C. Bourne), arXiv:2009.13806.

Gauge theory for noncommutative Riemannian principal bundles (with B. Ćaćić), arXiv:1912.04179.

Curvature of differentiable Hilbert modules and Kasparov modules (with A. Rennie and W.D.van Suijlekom), arXiv:1911.05008.

## Journal articles

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.

## Refereed conference proceedings

Toeplitz extensions in noncommutative topology and mathematical physics (with F.Arici), to appear in Trends in Mathematics, Geometric methods in physics XXXVIII (2020), arXiv:1911.0582.

A K-theoretic Selberg trace formula (with M. H. Sengun and H. Wang), to appear in Operator Theory: Advances and Applications 278: Operator theory, operator algebras and their interaction with geometry and topology - Ron Douglas memorial volume (2020), arXiv:1904.04728.

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.

## Editorial

Operator spaces and noncommutative geometry in interaction, Oberwolfach reports 6 (2016).