Marcelo Laca

Functional Analysis, Operator Algebras, Noncommutative Geometry, Dynamical Systems

Interests

• C*-algebras
• C*-dynamical systems
• KMS states
• phase transition
• Bost Connes systems
• graph algebras
• equilibrium states

Courses

• Fall 2024: MATH 311: Linear Algebra  MATH 435: Real Analysis II 
• Spring 2025:
• Summer 2025:

Current Projects

Selected Publications

• M. Laca and S. Neshveyev, KMS states of quasi-free dynamics on Pimsner algebras, J. Funct. Anal. 211 (2004), 457-482.
• M. Laca and M. van Frankenhuijsen, Phase transitions on Hecke C*-algebras and classfield theory over Q, J. reine angew. Math. (Crelle) 595 (2006), 25-53.
• J. Crisp and M. Laca, Boundary quotients of Toeplitz algebras of right-angled Artin groups, J. Funct. Anal. 242 (2007), 125-156.
• M. Laca, N.S. Larsen, and S. Neshveyev, Phase transition in the Connes Marcolli GL2-system, J. Noncommut. Geom. 1 (2007), 397-430.
• M. Laca, N.S. Larsen, and S. Neshveyev, On Bost-Connes type systems for number fields, J. Number Theory 129, (2009), 325-338.
• M. Laca and I. Raeburn, Phase transition on the Toeplitz algebra of the affine semigroup over the natural numbers, Adv. Math. 225 (2010), 643-688.
• M. Laca, S. Neshveyev and M. Trifkovic, Bost-Connes systems, Hecke algebras, and induction, J. Noncommut. Geom. 7 (2013), 525-546.
• J. Cuntz, C. Deninger, and M. Laca, C*-algebras of Toeplitz type associated with algebraic number fields, Math. Ann. 355 (2013), 138-1423.
• M. Laca, I. Raeburn, J. Ramagge, and M. Whittaker, Equilibrium states on the Cuntz-Pimsner algebras of self similar actions, J. Funct. Anal. 266 (2014), 6619-6661.
• A. an Huef, M. Laca, I. Raeburn, and A. Sims, KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space, J. Funct. Anal. 268 (2015), 1840-1875.
• M. Laca, N. S. Larsen, S. Neshveyev, A. Sims, and S.B.G. Webster, Von Neumann algebras of strongly connected higher-rank graphs, Math. Ann. 363 (2015), 657-688.