## Integrable probability

My research interests lie in **probability theory**, mainly in discrete probabilistic models that arise from **statistical physics**, e.g. random polymers, stochastic growth models, and interacting particle systems. I am especially interested in those models that disclose fertile connections with other areas of mathematics such as **algebraic combinatorics**, **random matrices**, and **representation theory**.

Here and here, Nikos Zygouras and I studied some KPZ integrable models on the 2D integer lattice (**log-gamma polymer** and exponential **last passage percolation**) with various point-to-(half-)line geometries of directed lattice paths. We found novel connections with special functions from algebraic combinatorics and representation theory, such as **orthogonal Whittaker functions** and **symplectic Schur functions**.

In another paper with Nikos Zygouras, we established numerous formulas for **last passage percolation** models with various symmetries in terms of all the **irreducible characters** of the classical groups and, more generally, in terms of certain classes of** interpolating symmetric polynomials**. At the level of KPZ asymptotic analysis, our formulas yielded new routes to universal **random matrix limiting distributions** and provided a structural explanation of the duality between their Pfaffian and determinant formulations.

In a joint work with Fabio Deelan Cunden, Shane Gibbons, and Dan Romik (see extended abstract and full version), we studied some connections between the **oriented swap process**, the **corner growth model**, and the** last passage percolation** model. We also conjectured a distributional identity between these models that implies an asymptotic result for the absorbing time of the oriented swap process. This conjecture is equivalent to a purely combinatorial identity that involves **sorting networks** and **staircase shape Young tableaux** and is connected to the celebrated **Edelman-Greene bijection**.

In this paper with Neil O’Connell and Nikos Zygouras, we constructed a **geometric lifting** of the **Burge correspondence** (a modification of the Robinson-Schensted-Knuth algorithm) as a composition of local birational maps. We applied our construction to a model of two polymer paths of given length constrained to have the same endpoint, known as **polymer replica**: we found that the distribution of the polymer replica partition function in a log-gamma random environment is a certain **Whittaker measure**.

In a paper with Jonas Arista and Neil O’Connell, we established analogues of the** Matsumoto-Yor **theorem and of the **Dufresne identity** for a multiplicative **random walk on positive definite matrices**. In another paper, we studied certain systems of **matrix-valued interacting random walks**; these can be viewed as high-dimensional analogues of **log-gamma polymer** partition functions and exhibit **matrix Whittaker measures**.

In a joint work with Yuchen Liao, Axel Saenz and Nikos Zygouras, we considered a discrete-time Totally Asymmetric Simple Exclusion Process, where each particle jumps according to Bernoulli random variables with particle-dependent and time-inhomogeneous parameters. Using the RSK algorithm, intertwining relations and non-intersecting path constructions, we obtained a representation for the correlation kernel of the particle positions in terms of random walk hitting probabilities, à la Matetski-Quastel-Remenik.

## Applied cryptography

In 2014 I worked as a research intern at STMicroelectronics, Agrate Brianza (Italy), in the Advanced System Technology security group. I collaborated with Guido Bertoni, Eleonora Cagli, Filippo Melzani, and Ruggero Susella.

I worked on the security of **symmetric-key cryptographic algorithms** such as AES, with special attention to **high order Boolean masking schemes** designed to thwart side channel attacks (e.g. Correlation Power Analysis). These attacks exploit vulnerable leakage combinations, i.e. sets of data physically leaked during the execution of a cryptographic implementation (for example in the form of power consumption), that statistically depend on sensitive data and involve a part of the secret key. My research focused on studying equivalent and easy-to-verify conditions for the **vulnerability of leakage combinations**, useful to validate the protection order guaranteed by a given cryptographic implementation. I used Matlab and C. I was a referee for ASYACRYPT 2014.

After further elaboration of this research with Filippo Melzani and Vittorio Zaccaria, in 2016 we wrote this article.