Schedule

Invited Talks:

• Xiao-Qi Lu (University of Glasgow) - Hilbert transforms on graph products of finite von Neumann algebras
  
  Abstract:
  The boundedness of Fourier multipliers on non-commutative $L_p$-spaces ($1 < p < \infty$) is a fundamental problem in non-commutative analysis. Building on the non-commutative Cotlar identity introduced by Mei and Ricard (2017), which yields $L_p$-boundedness ($1 < p < \infty$) of Hilbert transforms on amalgamated free products of finite von Neumann algebras, their approach relies heavily on freeness in the underlying free product structure.
  
  In this talk, we introduce a new strategy that overcomes this limitation. Our approach combines a generalized Cotlar identity, which holds on suitable subspaces and captures non-freeness information, with the property of Rapid Decay to control the remaining components. From this framework, we establish the $L_p$-boundedness ($1 < p < \infty$) of Rademacher-type Hilbert transforms on graph products of finite von Neumann algebras. This unified framework extends earlier results for free products of finite von Neumann algebras and for graph products of groups acting on right-angled buildings. This is a joint work with Runlian Xia.

Contributed Talks:

• Ujan Chakraborty (University of Glasgow) - Ergodic Average Dominance for Unimodular Amenable Groups
  
  Abstract:
  We show that the ergodic averages of the action of any unimodular amenable group along certain Følner sequences can be dominated by the Cesàro means of a suitably constructed Markov operator, that is, the ergodic averages of an integer action. Moreover, the restriction on these Følner sequences are mild enough so that every two-sided Følner sequence has a subsequence satisfying these conditions. As a consequence of this inequality, we obtain the maximal and pointwise (individual) ergodic theorems for actions of unimodular amenable groups directly from the corresponding ergodic theorems for integer actions. This allows us to deal with the commutative and noncommutative ergodic theorems on an equal footing. This is based on joint work with Joachim Zacharias and Runlian Xia.