## Heath EmersonAssociate ProfessorDepartment of Mathematics and Statistics University of Victoria Victoria, B.C., Canada David Turpin Building A447 hemerson@uvic.ca |

## Research

My research area, sometimes called Noncommutative Geometry, involves C*-algebras, K-theory, index theory and KK-theory, and their applications and connectionsto topology and dyamical systems. My current work is aimed at extending some of Connes' framework of Noncommutative Geometry to the Type III situation,

especially that of hyperbolic groups acting on their boundaries, using the relatively new concept of twisted spectral triples.

*List of papers*(most recent first)

- Zeta functions and topology of Heisenberg cycles for linear ergodic flows
(with Nathaniel Butler and Tyler Schulz)
arXiv:2008.09701

(*In submission 2022*) - Baum-Connes and the Fourier-Mukai transform (with Dan Hudson)
arXiv:2001.06124 (
*Ill. J. Math., to appear, 2022).* - Transversals, duality, and irrational rotation
(with Anna Duwenig)
arXiv:1906.00079
(
*Trans. Amer. Math. Soc. Ser.B, 2020.*)

- The class of a fibre in Noncommutative Geometry
arxiv:1802.064 (
*J. Geom. Phys. 148, 2020.*) - K-homological finiteness for hyperbolic groups (with
Bogdan Nica)
arXiv:1312.4646
(
*J. Reine. Angew. Math. 745, 2018.)*

- Equivariant correspondences and the Borel-Bott-Weil Theorem
(with Robert Yuncken)
arXiv:1812.4949
(
*Muenster J. Math. 10, no.1, 2017).* - An equivariant Lefschetz fixed-point formula for
correspondences (w. Ralf Meyer and Ivo Dell'Ambrogio) arXiv:1303.4777
(
*Doc. Math. 19, 2014)*. - Localization techniques in circle-equivariant KK-theory
arXiv:1004.2970
(
*Muenster J. Math. 2013).*

- Structure and K-theory of crossed-products by proper actions
(with Siegfried Echterhoff)
arXiv:1012.5214

(*Expo. Math. 29, no. 3, 2011).* - Equivariant embedding theorems and topological index maps
(with Ralf Meyer)
arXiv:0908.1465
(
*Adv. Math. 225, 2010.)* - Bivariant K-theory via correspondences
(with Ralf Meyer)
arXiv:0812.4949
(
*Adv. Math. 225, 2010.)* - Duality, correspondences, and the Lefschetz map in equivariant KK:a survey
arXiv:0904.4744
(
*Fields Inst. Commun., Perspectives in Noncommutative Geometry, 2011.)* - Lefschetz numbers for C*-algebras.
arXiv:0708.4278
(
*Can. Math. Bull. 54, no.1, 2010.)* - Dualities in equivariant Kasparov theory
(with Ralf Meyer)
arXiv:0711.0025
(
*New York J. Math. 16, 2010.)* - Equivariant Lefschetz maps for simplicial complexes and smooth manifolds
(with Ralf Meyer)
arXiv:0711.0027
(
*Math. Ann. 345, 2009.)* - Equivariant representable K-theory
(with Ralf Meyer)
arXiv:0710.1410
(
*J. Topology, no. 2, 2009.)* - A Lefschetz fixed-point formula for certain orbifold C*-algebras
(with Siegfried Echterhoff and Hyun-Jeong Kim)
arXiv:0708.4279
(
*J. Noncomm. Geom. 4, no.1, 2010.)* - KK-duality for proper twisted actions (with Siegfried Echterhoff and Hyun-Jeong Kim). PDF (
*Math. Ann. 340, no.4, 2008.)* - Coarse and equivariant co-assembly maps
(with Ralf Meyer) PDF
(
*Conference proceedings from `K-theory and Noncommutative Geometry,' Aug.-Sept. 2006, Valladolid, Spain, 2006)* - A descent method for the Dirac-dual-Dirac method (with Ralf Meyer)
*(Topology 46, no.2, 2007)*. - Dualizing the coarse assembly map (with Ralf Meyer),
*(J. Inst. Math. Jussieu 5, 2006).* - Euler characteristics and Gysin sequences for group actions on boundaries (with Ralf Meyer)
PDF (
*Math. Ann. Math. 344, no. 4, 2006.)* - The Baum-Connes Conjecture, Noncommutative Poincare
duality, and the boundary of the free group
PDF (
*Int. J. Math. Sci. 38, 2003.)* - Noncommutative Poincare duality for boundary actions of hyperbolic groups
PDF (
*J. Reine. Angew. Math. 564, 2003).*

*An introduction to C*-algebras and Noncommutative Geometry*This book is designed to teach advanced undergraduates or graduate students the basic ideas of C*-algebras, K-theory,

Index Theory and Noncommutative Geometry. The book is a draft.