Newcastle University

Research Interests

Analysis and geometry of higher rank groups.
Spaces of nonpositive curvature and euclidean buildings.
K-theory of operator algebras.

Current Work

My present research interests lie in the general area of Analysis and Geometry on Groups, but I often cross the boundaries of other areas of mathematics. I am particularly interested in the analysis of higher rank groups, and their actions on spaces of nonpositive curvature. There are close connections with ergodic theory, geometric group theory, algebraic topology and C*-algebraic K-theory.

MAS1241/MAS2241 Number Systems  http://www.mas.ncl.ac.uk/~nagr1/teaching/mas1241.html

MAS2216/MAS3216   Enumeration and Combinatorics http://www.mas.ncl.ac.uk/~nagr1/teaching/mas2216.html

MAS3209  Topology  http://www.mas.ncl.ac.uk/~nagr1/teaching/mas3209.html

• Robertson G. Harmonic cochains and K-theory for A_2 groups. Groups, Geometry and Dynamics 2013. In Press.
• King O, Robertson G. On the K-theory of boundary C*-algebras of Ã2 groups. Journal of K-theory 2012, 9(3), 521-536.
• Robertson G. Centralizers in Ã2 groups. Journal of Group Theory 2011, 14(6), 881-890.
• Robertson G. Invariant distributions on projective spaces over local fields. Proceedings of the American Mathematical Society 2011, 139(8), 2705-2711.
• Robertson G, Steger T. Malnormal subgroups of lattices and the Pukánszky invariant in group factors. Journal of Functional Analysis 2010, 258(8), 2708-2713.
• Robertson G. Boundary C* -algebras for acylindrical groups. Proceedings of the American Mathematical Society 2008, 136(11), 3851-3860.
• Robertson G. Invariant boundary distributions for finite graphs. Journal of Combinatorial Theory. Series A 2008, 115(7), 1272-1278.
• Robertson G. Abelian subalgebras of von Neumann algebras from flat tori in locally symmetric spaces. Journal of Functional Analysis 2006, 230(2), 419-431.
• Rattaggi D, Robertson AG. Abelian subgroup structure of square complex groups and arithmetic of quaternions. Journal of Algebra 2005, 286(1), 57-68.
• Robertson G. Boundary operator algebras for free uniform tree Lattices. Houston Journal of Mathematics 2005, 31(3), 913-935.
• Robertson G. Tiling systems and homology of lattices in tree products. New York Journal of Mathematics 2005, 11, 635-647.
• Robertson G. Torsion in boundary coinvariants and K-theory for Affine buildings. K-Theory 2004, 33(4), 347-369.
• MacLaurin C, Robertson AG. Euler characteristic in odd dimensions. Australian Mathematical Society Gazette 2003, 30, 195-199.
• Robertson G, Steger T. Irreducible subshifts associated with A2 buildings. Journal of Combinatorial Theory, Series A 2003, 103(1), 91-104.
• Robertson G. Singular masas of von Neumann algebras: examples from the geometry of spaces of nonpositive curvature. Trav. Math 2003, 14, 153-165.
• Robertson G, Sinclair A, Smith R. Strong singularity for subalgebras of finite factors. International Journal of Mathematics 2003, 14(3), 235-258.
• Cutting P, Robertson AG. Type III actions on boundaries of An buildings. Journal of Operator Theory 2003, 49, 25-44.
• Kimberley JS, Robertson G. Groups acting on products of trees, tiling systems and analytic K-theory. New York J. Math 2002, 8, 111-131.
• Robertson G. Torsion in K-Theory for Boundary Actions on Affine Buildings of Type An. K-Theory 2001, 22(3), 251-269.
• Jacqui Ramagge, Guyan Robertson and Tim Steger. A Haagerup inequality for A1xA1 and A2 buildings. Geometric and Funct. Anal 1998, 8(702-731).
• Guyan Robertson. Crofton formulae and geodesic distance in hyperbolic spaces. J. Lie Theory 1998, 441, 163-172.
• G Robertson and T Steger. Negative definite functions and a dynamical characterization of property (T) for countable groups. Ergodic Th. and Dynam. Sys 1998, 18, 247-253.