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

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 2021University 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 WorkshopThe feasible region for consecutive patterns of permutations is a cycle polytope.

30/07/2019

Random Trees and Graphs Summer SchoolCIRM, 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 UniversityCalifornia (USA), Probability seminar, Permutons and patterns.

23/03/2022

ETH ZürichZürich (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

TBD,  Montreal (Toronto), CRM-PIMS Summer School in Probability.

01-12/04/2024

TBD, The Fields Institute for Research in Mathematical Sciences, Toronto (Canada), Thematic Program on Randomness and Geometry.

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), Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes.

30/10/2019

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

02/05/2019

Graduate seminar of probabilityETH 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

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 …

Meanders and Meandric SystemsRead More »

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) …

Permutations in Random GeometryRead 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: a new universal limit for random constrained permutations and its connections with Liouville quantum gravityRead More »

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, …

The skew Brownian permutonRead 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 …

Random permutations: A geometric point of viewRead More »

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 …

Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processesRead More »

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 …

Phase transition for almost square permutationsRead More »

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 …

An approach through random walks to local limits of permutations encoded by generating treesRead More »

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 …

Square permutations are typically rectangularRead More »

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, …

What is… a permuton?Read More »

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 …

Local convergence for random permutations: the case of uniform pattern-avoiding permutations.Read More »