*NOTE:* Most of the slides of my talks are at the end of the following list of talks.

### List of Talks

##### Selected/Invited talks

25/07/2023

**43rd Conference on Stochastic Processes and their Applications,** Lisbon (Portugal), *Meanders and Meandric systems.*

09/03/2023

**UCLA department colloquium**, UCLA (USA), *Meanders and Meandric systems.*

07/07/2022

**ICM satellite probability conference: Probability and Mathematical physics 2022**, University of Helsinki (Finland), *Permutons, meanders, and SLE-decorated Liouville quantum gravity.*

27/06/2022

**42nd Conference on Stochastic Processes and their Applications**, Wuhan (China), *The skew Brownian permuton.*

20/01/2022

**Workshop “Random Geometry”**, CIRM, Marseille (France), *The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity.*

07/09/2020

**Workshop “Random Polymers and Networks”**, IGESA, Iles de Porquerolles (France), *Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes.*

21/10/2019

**Journées MathSTIC 2019, Université Paris 13**, Paris (France), *Phase transition for almost square permutations.*

##### Contributed talks in conferences

10/07/2024

**Two-Dimensional Random Geometry. **IMSI, Chicago (USA), *Lattice Yang-Mills theory in the large N limit via random surfaces.*

17/06/2024

**4th Italian Meeting on Probability and Mathematical Statistics. **Rome Sapienza, Rome (Italy), *On the geometry of uniform meandric systems.*

22/05/2024

**IPAM Workshop – Vertex Models: Algebraic and Probabilistic Aspects of Universality, **IPAM, UCLA, Los Angeles (USA), *On the geometry of uniform meandric systems.*

15/04/2024

**IPAM Workshop – Integrability and Algebraic Combinatorics****. **IPAM, UCLA, Los Angeles (USA), *Limit shapes for random Young tableaux via determinantal point* processes

06/01/2024

**Joint Mathematics Meetings (JMM) 2024,**** **San Francisco (USA), *On the Brownian separable permuton*.

07/09/2023

**XXII Congresso dell’Unione Matematica Italiana**, Pisa (Italia), *On the geometry of random meanders.*

06/06/2023

**Random Conformal Geometry and Related Fields**, Jeju (Korea), *Meanders and Meandric systems.*

16/06/2022

**Third Italian Meeting on Probability and Mathematical Statistics**, Università di Bologna, Bologna (Italia), *Skew Brownian permuton, Schramm–Loewner evolutions & Liouville Quantum Gravity.*

21/07/2021

**Bernoulli-IMS 10th WORLD CONGRESS in PROBABILITY and STATISTICS**, Seoul National University, Seoul (Korea), online conference, *Universal phenomena for random constrained permutations.*

24/06/2021

**8th European congress of Mathematics****, session Extremal and Probabilistic Combinatorics**, Portoroz (Slovenia), online conference,

*Universal phenomena for random constrained permutations.*

15/06/2021

**Permutation Patterns 2021**, University of Strathclyde, Glasgow (UK), online conference, *A probabilistic approach to generating trees.*

16/03/2021

**ALÉA 2021**, CIRM, Luminy (France), online conference, *Random permutations: A geometric point of view.*

24/08/2020

**Bernoulli-IMS One World Symposium 2020** (online), *Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes.*

01/07/2020

**2020 Permutation Patterns online Workshop**, *The feasible region for consecutive patterns of permutations is a cycle polytope.*

30/07/2019

**Random Trees and Graphs Summer School**, CIRM, Marseille (France), *Square permutations are typically rectangular.*

28/06/2019

**AofA 2019,** CIRM, Marseille (France), Local convergence for permutations: a Markov chain approach via generating trees.

20/06/2019

**Permutation Patterns 2019**, UZH Zurich (Switzerland), *Square permutations are typically rectangular*.

09/07/2018

**Permutation Patterns 2018**, Dartmouth College in Hanover (USA, New Hampshire), *Local convergence for permutations: the case of uniform 231-avoiding permutations.*

##### Seminar talks

10/11/2023

**NYU**, New York (USA), Probability seminar, *Long increasing subsequences in Brownian-type permutations**.*

06/11/2023

MIT, Boston (USA), Probability seminar, *An introduction to universal permutons**.*

31/07/2023

**EPFL**, Lausanne (Switzerland), Probability seminar, *Permutations in Random Geometry**.*

13/04/2023

**Institute for Advanced Study**, Princeton, New Jersey (USA), Probability seminar, *Long increasing subsequences in Brownian-type permutations.*

05/04/2023

The University of British Columbia, British Columbia (Canada), Probability seminar, *Long increasing subsequences in Brownian-type permutations.*

03/04/2023

The University of Washington, Washington state (USA), Probability seminar,* **Long increasing subsequences in Brownian-type permutations.*

06/03/2023

Stanford University, California (USA), Probability seminar,* **Meanders and Meandric Systems.*

01/02/2023

U.C. Davis, California (USA), Probability seminar, *Meanders and Meandric Systems.*

11/02/2022

**U.C. Berkeley,** California (USA), Probability seminar, *Permutations in random geometry***.**

13/09/2022

**University of Vienna,** Vienna (Austria), Probability seminar, *Permutations in random geometry***.**

27/04/2022

**San Francisco State University**, California (USA), Probability seminar, *Permutons and patterns***.**

23/03/2022

**ETH Zürich**, Zürich (Switzerland), Probability seminar, *The skew Brownian permuton***.**

17/02/2022

**Stanford University**, California (USA), Combinatorics seminar, *The skew Brownian permuton***.**

16/02/2022

**U.C. Davis**, California (USA), Probability seminar, *The skew Brownian permuton***.**

09/02/2022

**The University of British** **Columbia**, British Columbia (Canada), Probability seminar, *The skew Brownian permuton.*

16/11/2021

**University of Pennsylvania**, Pennsylvania (USA), Probability seminar, *The skew Brownian permuton.*

11/11/2021

**Dartmouth College in Hanover**, New Hampshire (USA), Combinatorics seminar, *Local limits for permutations and generating trees.*

05/11/2021

**The University of Chicago**, Illinois (USA), Probability seminar, *The skew Brownian permuton.*

14/10/2021

**ENS Lyon**, Lyon (France), Probability seminar, *The skew Brownian permuton.*

20/09/2021

**Stanford University**, California (USA), Probability seminar,* Local limits for permutations and generating trees.*

25/01/2021

**Stanford University**, California (USA), online seminar, *Random permutations: A geometric point of view.*

13/11/2020

**Dartmouth College in Hanover**, New Hampshire (USA), online seminar, *Phase transition for almost square permutations.*

05/10/2020

**MIT**, Boston (USA), online seminar, *Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes*.

28/04/2020

**Bilkent University**, Ankara (Turkey), Analysis online seminar,* Phase transition for almost square permutations.*

31/03/2020

**CUNY**, New York (USA), online seminar, *Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes.*

07/12/2018

**ENS Lyon**, Lyon (France), *Local convergence for permutations: a Markov chain approach via generating trees.*

19/03/2018

**Universität Zürich**, Zürich (Switzerland), Discrete mathematics seminar, *Local convergence for permutations: the case of uniform 321-avoiding permutations.*

20/02/2018

**Università degli Studi di Padova**, Padova (Italy), Probability seminar, *Local convergence for permutations.*

##### Mini courses

08-15/07/2024

**Permutations in random geometry**, Montreal (Toronto), CRM-PIMS Summer School in Probability.

01-12/04/2024

**Meanders & meandric systems**, The Fields Institute for Research in Mathematical Sciences, Toronto (Canada), Thematic Program on Randomness and Geometry (see this webpage for more details).

08-15/10/2020

**The limiting shape of random permutations: an introduction to permuton convergence**, Nancy (France), Gdt.

##### Student seminar talks

03/04/2020

**Graduate seminar of probability** (online), ETH Zürich (Switzerland),

30/10/2019

**Graduate seminar of probability**, ETH Zürich (Switzerland), *Phase transition for almost square permutations,.*

02/05/2019

**Graduate seminar of probability**, ETH Zürich (Switzerland), *Square permutations are typically rectangular.*

26/03/2019

**Zurich Graduate Colloquium, **ETH Zürich (Switzerland), *What is… a permuton?.*

11/10/2018

**Graduate seminar of probability**, ETH Zürich (Switzerland), *A Galton-Watson tree approach to local limits of substitution-closed permutation classes.*

27/06/2018

**Groupe de travail des thésards du LPSM**, Laboratoire de Probabilités, Statistique et Modélisation de Paris (France), *Local convergence for permutations: the case of uniform 321-avoiding permutations.*

##### Other talks

10/05/2019

**Premiazione delle gare di matematica**, Liceo scientifico Leonardo da Vinci, Treviso (Italy), *Studiare matematica, quali prospettive?*.

### Slides

### My Posts

### Lattice Yang-Mills theory in the large N limit via random surfaces

Lattice Yang-Mills theories are important models in particle physics. They are defined on the d-dimensional lattice using a group of matrices of dimension , and Wilson loop expectations are the fundamental observables of these theories. Recently, Cao, Park, and Sheffield showed that Wilson loop expectations can be expressed as sums over certain embedded bipartite maps of any genus. Building on this novel approach, …

Lattice Yang-Mills theory in the large N limit via random surfacesRead More »

### Long increasing subsequences in Brownian-type permutations

What is the behavior of the longest increasing subsequence of a uniformly random permutation? Its length is of order plus Tracy–Widom fluctuations of order . Its scaling limit is the directed geodesic of the directed landscape. This talk discusses how this behavior changes dramatically when one looks at universal Brownian-type permutations, i.e., permutations sampled from the Brownian separable permutons. We show that there are explicit constants such that …

Long increasing subsequences in Brownian-type permutationsRead More »

### Meanders and Meandric Systems

In 1912 Henri Poincaré asked the following simple question: “In how many different ways a simple loop in the plane, called a meander, can cross a line a specified number of times?” Despite many efforts, this question remains very open after more than a century. In this talk, I will present the conjectural scaling limit …

### Permutations in Random Geometry

Random geometry and random permutations have been extremely active fields of research for several years. The former is characterized by the study of large planar maps and their continuum limits, i.e. the Brownian map, Liouville quantum gravity surfaces and Schramm–Loewner evolutions. The latter is characterized by the study of large uniform permutations and (more recently) …

### Permutons, meanders, and SLE-decorated Liouville quantum gravity

In 1912 Henri Poincaré asked the following question: “In how many different ways a simple loop in the plane, called meander, can cross a line a specified number of times?” Despite many efforts, this question remains open after more than a century. In this talk we construct and study the conjectural scaling limit of uniform …

Permutons, meanders, and SLE-decorated Liouville quantum gravityRead More »

### The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity

Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permuton. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these …

### The skew Brownian permuton

Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permutons. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these results, …

### Local limits for permutations and generating trees

For large combinatorial structures, two main notions of convergence can be defined: scaling limits and local limits. In particular, for graphs both notions are well-studied and well-understood. For permutations only a notion of scaling limits, called permutons, has been investigated in the last decade. In the first part of the talk, we introduce a new …

Local limits for permutations and generating treesRead More »

### Random permutations: A geometric point of view

Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question by presenting the notion of permuton convergence. Then we answer the question for different choices of random permutation models. We mainly focus on two examples of permuton convergence, introducing …

### The limiting shape of random permutations: an introduction to permuton convergence.

In this series of two lectures we overview some recent progress in the study of the liming shape of large random (non uniform) permutations. We start by properly introducing the notion of permuton convergence and by exploring its connection with the convergence of proportion of pattern densities, this being a striking feature of the permuton topology. In …

The limiting shape of random permutations: an introduction to permuton convergence.Read More »

### The feasible region for consecutive patterns of permutations is a cycle polytope

We study proportions of consecutive occurrences of permutation patterns of a given size . Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a polytope, more precisely the cycle polytope of a specific graph called overlap graph. The latter is a …

The feasible region for consecutive patterns of permutations is a cycle polytopeRead More »

### Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes

Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant are well-known to be related to each other through several bijections. In order to study their scaling and local limits, we introduce a further new family of discrete objects, called coalescent-walk processes and we relate them with the other previously …

### Phase transition for almost square permutations

A record in a permutation is an entry which is either bigger or smaller than the entries either before or after it (there are four types of records). Entries which are not records are called internal points. We explore scaling limits (called permuton limits) of uniform permutations in the classes Sq(n,k) of almost square permutations of size n+k with exactly k internal points.We …

### An approach through random walks to local limits of permutations encoded by generating trees

We develop a general technique to study local limits of random permutations in families enumerated through generating trees. We propose an algorithm to sample uniform permutations in such families using random walks and we recover the local behavior of permutations studying local properties of the corresponding random walks. The method applies to families of permutations …

### Square permutations are typically rectangular

We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. First we describe the global behavior by showing these permutations have a permuton limit which can be described by a random rectangle. We also explore fluctuations about this random rectangle, which we can describe through coupled Brownian motions. Second, we …

### What is… a permuton?

How does a large random permutation behave? We will try to answer this question for different classical models of random permutations, such as uniform permutations, pattern-avoiding permutations, Mallows permutations and many others. An appropriate framework to describe the asymptotic behaviour of these pemutations is to use a quite recent notion of scaling limits for permutations, …

### Local convergence for random permutations: the case of uniform pattern-avoiding permutations.

For large combinatorial structures, two main notions of convergence can be defined: scaling limits and local limits. In particular for graphs, both notions are well-studied and well-understood. For permutations only a notion of scaling limits, called permutons, has been recently introduced. The convergence for permutons has also been characterized by frequencies of pattern occurrences. We …