In your lifetime you won't encounter neither right choices nor bad choices,
but whenever you have to make one, you'll have to fight so that it becomes the best decision you could have ever taken.
Jacopo Borga
Szegő Assistant Professor in Mathematics
Hi! I am a Szegő Assistant Professor in the Mathematics Department of Stanford University.
Before coming to Stanford, I was a Ph.D. student at the Institut für Mathematik of the Universität Zürich. My supervisors were Valentin Féray and Mathilde Bouvel.
I am mainly interested in probability theory and its connections to combinatorics and mathematical physics. I am studying several random combinatorial structures and their continuous limits, such as random permutons, multi-dimensional constrained Brownian motions, Schramm-Loewner evolutions and Liouville quantum gravity.
ALERT: I have neither internships nor RA/PhD positions for anyone other than Stanford mathematics or statistics (incoming) PhDs.
My recent articles
[14] Permutons, meanders, and SLE-decorated Liouville quantum gravity (with Ewain Gwynne and Xin Sun)
We study a class of random permutons which can be constructed from a pair of space-filling Schramm-Loewner evolution (SLE) curves on a Liouville quantum gravity (LQG) surface. This class includes…
[13] Large deviation principle for random permutations (with Sayan Das, Sumit Mukherjee, Peter Winkler)
We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called μ-random permutations. We also introduce and study…
[12] Baxter permuton and Liouville quantum gravity (with Nina Holden, Xin Sun, and Pu Yu)
The Baxter permuton is a random probability measure on the unit square which describes the scaling limit of uniform Baxter permutations. We find an explict formula for the expectation of…
[11] The skew Brownian permuton: a new universality class for random constrained permutations
We construct a new family of random permutons, called skew Brownian permuton, which describes the limits of various models of random constrained permutations. This family is parametrized by two real…
[10] The permuton limit of strong-Baxter and semi-Baxter permutations is the skew Brownian permuton
We recently introduced a new universal family of permutons, depending on two parameters, called skew Brownian permuton. For some specific choices of the parameters, the skew Brownian permuton coincides with some…
[9] The feasible regions for consecutive patterns of pattern-avoiding permutations (with Raul Penaguiao)
We study the feasible region for consecutive patterns of pattern-avoiding permutations. More precisely, given a family of permutations avoiding a fixed set of patterns, we study the limit of proportions…