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November 3, 2015 phi 0

PeiPC – Mathématiques 1

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Je vais succeder au Prof. Santharoubane comme chargée du cours de Maths en PeiPC, module d'Algèbre/Géométrie, qui va se dérouler à partir du 3 Novembre 2015.

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Un programme provisionnel inclut :

  • Droites, plans, equations cartésiennes et forme paramétrique
  • Produit scalaire et produit vectoriel
  • Nombre complexes : trigonométrie, exponentielle complexe, le plan d'Argand-Gauss
  • Espaces vectoriels et affines, sous-espaces : indépendance linéaire, bases, formule de Grassmann
  • Applications linéaires et matrices, théorème du rang, changement de bases

Après une introduction à la géométrie en \mathbb{R}^2 et \mathbb{R}^3 et aux nombres complexes, on va traiter les thèmes du poly de PeiP1 S2, que vous pouvez utiliser comme référence.

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The scaling limit of random outerplanar maps

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Third take on a talk about outerplanar maps, and perhaps the most complete account I ever gave of this paper; the slides are the same those of the Journée YSP, with an extra section that describes the core algorithm. Sorry about the annoying video format; an incredibly heavy pdf file is available here.

A planar map is outerplanar if all of its vertices belong to a single (outer)face. The scaling limit for various classes of large planar maps has been shown to be the so-called “Brownian Map”; under certain conditions, however, different asymptotic behaviours may emerge, and some classes of planar maps with a macroscopic face admit Aldous’ CRT, or a scalar multiple thereof, as the scaling limit. We shall see that this is the case for outerplanar maps as well: using a bijection by Bonichon, Gavoille and Hanusse one can show that uniform outerplanar maps with n vertices, suitably rescaled by a factor 1/\sqrt{n}, converge to 7\sqrt{2}/9 times the CRT.

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  • Date: 1-7 settembre 2014
  • Istruttori: Tanti!
  • Luogo: Dipartimento di Matematica – Pisa

Stage Senior 2014

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Come sempre, qui i video prodotti al senior di quest'anno.

Per quanto mi riguarda, mi sono toccate A2 e A3 basic (disuguaglianze/funzionali), per le quali ho prodotto (unicamente grazie al tampinamento di Sam) un file di prerequisiti (specialmente su somme cicliche e simmetriche). A C2 medium abbiamo parlato di Combinatorial Nullstellensatz.

Art&Stuff

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This section of the website is under construction since about 2015. Sorry!

My PhD-student self was adamant that a personal website needed a space to share non-mathematical projects with the world. Perhaps she was right? Expect some samples of my graphic design work and crafting projects at some point in the future... maybe?

Publications

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Papers
Growing uniform planar maps face by face, with A. Stauffer, to appear in Random Structures and Algorithms.
Bijections for Ranked Tree-Child Networks, with M. Fuchs, G.-R. Yu, Discrete Mathematics, Volume 345, Issue 9 (2022). https://doi.org/10.1016/j.disc.2022.112944
A polynomial upper bound for the mixing time of edge rotations on planar maps, Electron. J. Probab. 25: 1-30 (2020). https://doi.org/10.1214/20-EJP519Probab
Polynomial mixing time of edge flips on quadrangulations, with A. Stauffer, Probab. Theory Relat. Fields (2019). https://doi.org/10.1007/s00440-019-00913-5
Self-avoiding walks on the UIPQ, with N. Curien, In: Sidoravicius V. (eds) Sojourns in Probability Theory and Statistical Physics - III. Springer Proceedings in Mathematics & Statistics, vol 300 (2019). Springer, Singapore. https://doi.org/10.1007/978-981-15-0302-3_5.
Geometry of the Uniform Infinite Half-Planar Quadrangulation, with N. Curien, Random Struct Alg. (2018); 52: 454– 494. doi:10.1002/rsa.20746
The Scaling Limit of Outerplanar Maps, Ann. Inst. H. Poincaré Probab. Statist., Volume 52, Number 4 (2016), 1667-1686. doi:10.1214/15-AIHP694

PhD Thesis
The geometry of large outerplanar and half-planar maps (written under the supervision of Prof. Nicolas Curien and Prof. Franco Flandoli).

See here for a lighter version, missing abstracts and larger illustrations.

Master's Thesis
Lagrangians of Hypergraphs (written under the supervision of Prof. Imre Leader and Prof. Roberto Dvornicich).

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