Mathav Murugan | PIMS - Pacific Institute for the Mathematical Sciences

University of British Columbia

Prof. Murugan is an Associate Professor, and Canada Research Chair in Probability (Tier 2) in the Department of Mathematics at the University of British Columbia. He received his PhD at Cornell University under the supervision of Laurent Saloff-Coste. He was a PIMS Postdoctoral Fellow in the 2015 competition.

Prof. Murugan was awarded the 2025 PIMS/UBC Mathematical Sciences Early Career Award.

Personal Website: https://personal.math.ubc.ca/~mathav/

The energy image density property arises in two seemingly distinct lines of research. It first appeared in Malliavin’s proof of Hörmander’s hypoellipticity theorem and has since played a central role in the study of regularity properties of...

We affirmatively resolve the energy image density conjecture of Bouleau and Hirsch (1986). This conjecture generalizes a foundational result in Malliavin calculus: the non-degeneracy of the Malliavin matrix of a random variable implies absolute...

Given a strongly local Dirichlet form on a metric measure space that satisfies Gaussian heat kernel bounds, we show that the martingale dimension of the associated diffusion process coincides with Cheeger's analytic dimension of the underlying metric...

Event Organizers Gordon Slade University of British Columbia Omer Angel University of British Columbia Louigi Addario-Berry McGill University Mathav Murugan University of British Columbia Course Descriptions Main course: Tom Hutchcroft Title...

We describe a solution to the inverse problem of constructing diffusions and random walks with prescribed sub-Gaussian heat kernel bounds with given volume growth and escape time profiles.

There is a well-developed theory of Sobolev spaces on metric measure spaces, stemming from the seminal works of Cheeger and Shanmugalingam in the 1990s. However, this notion does not lead to a suitable space for fractals. We develop an alternate...

Spitzer (1958) showed that the trace of reflected Brownian motion on the upper half space on its boundary is a Cauchy process. More generally, every symmetric stable process in n-dimensional Euclidean space can be obtained as a trace process of a...

I report recent progress on heat kernel estimates for reflected diffusion on uniform domains where the underlying space admits sub-Gaussian heat kernel bounds. A key novelty of our work is the use of an extension operator that extends functions from...

The conformal Assouad dimension is the infimum of all possible values of the Assouad dimension after a quasisymmetric change of metric. We show that the conformal Assouad dimension equals a critical exponent associated with the combinatorial modulus...

A metric space is a length space if the distance between two points equals the infimum of the lengths of curves joining them. For a measured length space, we characterize Gaussian estimates for iterated transition kernel for random walks and...