My research area is probability theory with connections to combinatorics and mathematical physics. I mainly focus on studying various random discrete structures such as random permutations, random walks, random trees, and random planar maps. I am interested in their continuous and discrete limits and look at universality phenomena [1,2,3,5,6,7,10,15,17]. I introduced a new universal family of limiting permutons (limits of permutations), called skew Brownian permutons, and explored its connections with Schramm–Loewner evolutions (random self-avoiding curves) and Liouville quantum gravity surfaces (random metric spaces) [10,11]. I am currently interested in better understanding the relations between permutons, Schramm–Loewner evolutions, and Liouville quantum gravity [12, 14].

The primary focus of my recent endeavors has been directed towards addressing two prominent challenges, namely the meander problem [14,15, and some pictures]  (see also this beautiful survey paper) and the problem of the longest increasing subsequence in skew Brownian permutons [16, and some pictures], which can be also interpreted as a model of last passage percolation on planar maps.

I also studied some limiting surfaces arising from random Young diagrams [17], a large deviation principle for random permutations [13], a central limit theorem for consecutive patterns in permutations [6] and for multiplayer leagues [8], and some polytopes arising from local limits of permutations [4,9].

Here, you can find my Google scholar profile.