## My Curriculum Vitae

Name: Wenjie Fang
Current situation: Postdoc at TU Graz
Contact:

### Education

##### 2017-now
Postdoc at Institute of Discrete Mathematics, TU Graz
##### 2016-2017
Postdoc at ENS Lyon
##### 2013-2016
PhD candidate at LIAFA, University Paris Diderot
##### 2012-2013
Predoctoral internship at LIAFA.
##### 2011-2012
Master 2 of MPRI at ENS. Mention très bien. Ranked 2nd.
##### 2010-2011
Master 1 of MPRI at ENS. Mention très bien.
##### 2009-2010
License 3 of informatique at ENS delivered by Paris 7. Mention très bien.
##### 2007-2009
Class préparatoire MPSI--MP* at Lycée Kléber. Ranked 1 bis in entrance exam (voie INFO) of ENS de Paris. Ranked 4 in entrance exam of Ecole polytechnique.

### Awards

Prix de thèse Gilles Kahn 2017, accessit

### Publications

##### Publications on journals and international conferences
Oliver Cooley, Wenjie Fang, Nicola Del Giudice, Mihyun Kang, Subcritical random hypergraphs, high-order components, and hypertrees. Submitted. arXiv version at 1810.08107. Extended abstract accepted by Analytic Algorithmics and Combinatorics 2019 (ANALCO 2019).

Wenjie Fang, Fighting fish and two-stack sortable permutations. In preparation. rXiv version 1711.05713. Extended abstract accepted by The 30th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2018).

Wenjie Fang, Mihyun Kang, Michael Moßhammer, Philipp Sprüssel, Enumeration of cubic multigraphs on orientable surfaces, Electronic Journal of Combinatorics, Volume 25, Issue 1, 2018, Paper #P1.30. Extended abstract accepted by European Conference on Combinatorics, Graph Theory and Applications 2015 (EuroComb 2015).

Wenjie Fang, Planar triangulations, bridgeless planar maps and Tamari intervals, European Journal of Combinatorics, Volume 70, 2018. arXiv version at 1611.07922.

Wenjie Fang, A trinity of duality: Non-separable planar maps, β-(1,0) trees and synchronized intervals, Advances in Applied Mathematics, Volume 95, 2018. arXiv version at 1703.02774.

Wenjie Fang, Uwe Beckert, Parallel Tree Search in Volunteer Computing: a Case Study, Journal of Grid Computing, 2017. Volume yet to be assigned. Open access.

Wenjie Fang, Louis-François Préville-Ratelle, The enumeration of generalized Tamari intervals, European Journal of Combinatorics, Volume 61, 2017. Extended abstract accepted by The 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), under the title From generalized Tamari intervals to non-separable planar maps (extended abstract).The arXiv version is at 1511.05937.

Guillaume Chapuy, Wenjie Fang, Generating functions of bipartite maps on orientable surfaces, Electronic Journal of Combinatorics, Volume 23, Issue 3, 2016, Paper #P3.31. Extended abstract accepted by The 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), arXiv version at 1502.06239.

Wenjie Fang, Bijective proofs of character evaluations using trace forest of the jeu de taquin, Séminaire Lotharingien de Combinatoire, Volume 72, 2015, Pages B72e, arXiv version at 1403.5679

Wenjie Fang, Roberto Mantaci, A Recursive Structure of Sand Pile Model and Its Applications, Pure Mathematics and Applications, Volume 25, Issue 1, Pages 63-78.

Wenjie Fang, A generalization of the quadrangulation relation to constellations and hypermaps, Journal of Combinatorial Theory, Series A (JCTA), Volume 127, September 2014, Pages 1–21, extended abstract accepted by The 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), arXiv version at 1311.6991.

Wei Chen, Wenjie Fang, Guangda Hu, Michael W. Mahoney, On the Hyperbolicity of Small-World Networks and Tree-Like Graphs, accepted by The 23rd International Symposium on Algorithms and Computation (ISAAC 2012), arXiv version at 1201.1717.

Eric Brier, Wenjie Fang, David Naccache, How to scatter a secret?, Cryptologia, Volume 36 Issue 1, 2012.

##### Manuscripts, informal publications, technical reports
Cesar Ceballos, Wenjie Fang, Henri Mühle, The Steep-Bounce Zeta Map in Parabolic Cataland, in preparation.

Wenjie Fang, A partial order on Motzkin paths, arXiv 1801.04809, 2018.

Wenjie Fang, New Computational Result on Harmonious Trees, arXiv 1106.3490, 2011.

Wenjie Fang, A Computational Approach to the Graceful Tree Conjecture, arXiv 1003.3045, 2010.

### Talks

##### 2018
The Steep-Bounce Zeta Map in Parabolic Cataland at Séminaire Combinatoire of LIX, Palaiseau, 2018/11. Slides

Abstract: As a classical object, the Tamari lattice has many generalizations, including ν-Tamari lattices and parabolic Tamari lattices. In this article, we unify these generalizations in a bijective fashion. We first prove that parabolic Tamari lattices are isomorphic to ν-Tamari lattices for bounce paths ν. We then introduce a new combinatorial object called “left-aligned colored tree”, and show that it provides a bijective bridge between various parabolic Catalan objects and certain nested pairs of Dyck paths. As a consequence, we prove the Steep-Bounce conjecture using a generalization of the famous zeta map in q, t-Catalan combinatorics.

Same topic: Séminaire SPACE of Université de Tour, Tours, 2018/11; AG Diskrete Mathematik in University of Vienna, Vienna, 2018/12

Subcritical random hypergraphs, high-order components, and hypertrees at Workshop ANR-FWF-MOST 2018 in TU Wien, Vienna, 2018/10. Slides

Abstract: The random k-uniform hypergraph H^k(n,p) with vertex set V of size n is constructed by picking subsets of V of size k as hyperedges with probability p. We consider the subcritical phase of the emergence of the giant component on H^k(n,p), under the notion of high-order connectedness. More precisely, for j an integer strictly smaller than k, we say that two hyperedges are j-connected if we can reach one from another through a chain of hyperedges, in which consecutive hyperedges share at least j vertices. We determine precisely the size and the structure of the k-largest components of H^k(n,p) in the subcritical case, closer to the critical window than previous research.

Same topic: Séminaire CALIN, Université Paris Nord, 2018/11.

Fighting fish, two-stack sortable permutations, and so on at AG Diskrete Mathematik in University of Vienna, Vienna, 2018/5. Slides

Abstract: In 2017, Duchi, Guerrini, Rinaldi and Schaeffer proposed a new combinatorial object called "fighting fish", which is counted by the same formula as more classical objects, such as two-stack sortable permutations, non-separable planar maps and $\nu$-Tamari intervals. In this talk, we explore the bijective aspect of fighting fish by establishing a bijection to two-stack sortable permutations, using a new recursive decomposition of these permutations. With our bijection, we give combinatorial explanations of several results of fighting fish previously proved previously with generating functions. We also discuss ideas on extending this bijective connections to other objects.

##### 2017
Cubic graphs and triangulations on an orientable surface at Séminaire Algorithmique of Université de Caen, Caen, 2017/04. Slides

Abstract: Motivated by the study of phase transitions in the models of random graphs with a condition of embeddability, we are interested by the asymptotic enumeration of cubic multigraphs embeddable on a given surface of genus $g$. We obtained the asymptotic number of this family of cubic multigraphs. Our method consists of first reducing the enumeration problem to the 3-connected case, then transfer it to the domain of maps using a well-known theorem about uniqueness of embedding of certain graphs, and finally count the corresponding maps using previous results and bijections. The transfer of enumeration problems from maps to graphs is done with singularity analysis on generating functions. This is a joint work with Mihyun Kang, Michael Moßhammer and Philipp Sprüssel.

Same topic: Journées ALEA, CIRM, 2018/03.

Slice rank of tensors and its applications at One Day Metting in Discrete Structures (Edition 3) in ENS de Lyon, 2017/04. Slides

Abstract: In additive combinatorics, the recent work of Croot, Lev and Pach introduces a powerful and simple method called the polynomial method'', which led to breakthroughs in upper bounds of several problems in additive and extremal combinatorics. In this talk, we present an analysis of the polynomial method by Sawin and Tao, which is centered around a new notion called "slice rank" on tensors. Through two examples, cap set and sunflower-free families, we will see a general scheme of the polynomial method and how it can be applied to various problems. We will also see some limits of this method. This is a presentation of a work of Sawin and Tao, not the work of the presentater.

##### 2015
Bijective link between generalized Tamari intervals and non-separable planar maps at ALEA-Network Workshop, Bordeaux, 2015/11. Slides

Abstract: Let v be an arbitrary path made of north and east steps. The lattice Tam(v), based on all paths weakly above the path v sharing the same endpoints as v, was introduced by Préville-Ratelle and Viennot (2014) and corresponds to the usual Tamari lattice in the case v=(NE)^n. They showed that Tam(v) is isomorphic to the dual of Tam(v'), where v' is the reverse of v with N and E exchanged. Our main contribution is a bijection from intervals in Tam(v) to non-separable planar maps. It follows that the number of intervals in Tam(v) over all v of length n is 2(3n+3)!/(n+2)!/(2n+3)!. This formula was first obtained by Tutte(1963) for non-separable planar maps. We also show that the isomorphism between Tam(v) and the dual of \Tam(v') is equivalent to map duality under our bijection.

Same topic: Journées ALEA, CIRM, 2016/03; Journée cartes, IHES, 2015/04; Séminaire Combinatoire, LIX, 2016/06
Slightly updated version: Séminaire Combinatoire et Théorie des Nombres, UCL - Lyon 1, 2016/09; Séminaire Combinatoire, Marne-la-Vallé, 2017/04.
Further updated version: Workshop "Enumerative Combinatorics", Erwin Schrödinger Institute, Vienna, 2017/10.

Constellations : mise en équation, résolution, rationalité at JCB 2015, Bordeaux, 2015/02. Slides

Abstract : In the study of combinatorial maps, constellations possess a particular position. They are both a special model and a generalization of bipartite maps, and they are also related to factorisations in the symmetric group. Even if planar constellations are well-understood thanks to bijections, their general functional equation remains unsolved. Constellations in higher genera remains mysterious. In this talk, we will see the formulation of a functional equation for constellations, in both planar and higher genera case, the resolution for the planar case, and a result of rationality in higher genera for the bipartite case.

Same topic: Séminaire Combinatoire, LIAFA, 2015/03; Séminaire SpecFun, INRIA Saclay, 2015/05.
##### 2014
Bijective proofs of character evaluations using trace forest of the jeu de taquin at SLC 72, Lyon, 2014/03. Slides

Abstract : Irreducible characters in the symmetric group are of special interest in combinatorics. They can be expressed either combinatorially with ribbon tableaux, or algebraically with contents. In this paper, these two expressions are related in a combinatorial way. We first introduce a fine structure in the famous jeu de taquin called "trace forest", with which we are able to count certain types of ribbon tableaux, leading to a simple bijective proof of a character evaluation formula in terms of contents that dates back to Frobenius (1901). Inspired by this proof, we give an inductive scheme that gives combinatorial proofs to more complicated formulae for characters in terms of contents.

##### 2013
A generalization of the quadrangulation relation to constellations and hypermaps at FPSAC 2013, Paris, 2013/07. Slides

Abstract : Constellations and hypermaps generalize combinatorial maps, i.e. embedding of graphs in a surface, in terms of factorization of permutations. In this paper, we extend a result of Jackson and Visentin (1990) on an enumerative relation between quadrangulations and bipartite quadrangulations. We show a similar relation between hypermaps and constellations by generalizing a result in the original paper on factorization of characters. Using this enumerative relation, we recover a result on the asymptotic behavior of hypermaps of Chapuy (2009).

Same topic: Journée Cartes, LIX, 2013/02; ALEA, CIRM, 2013/03; Workshop "Enumerative Combinatorics", Oberwolfach, 2014/03; Seminar Diskrete Mathematik und Optimierung, TU Graz, 2014/11.

Parallelizing large search in BOINC: a case study at BOINC Workshop 2013, Grenoble, 2013/09. Slides
##### 2012
A Recursive Structure of Sand Pile Model and Its Applications at LIAFA, 2012/07

Abstract : The Sand Pile Model (SPM) and its generalization, the Ice Pile Model (IPM), originate from physics and have various applications as simple discrete dynamical systems. In this talk, we will deal with enumeration and exhaustive generation of accessible configurations of the system. The central ingredient is a unique decomposition theorem for SPM configurations, based on the notion of staircase bases. Based on this theorem, we provide a unified treatment leading to a recursive formula for counting, to a random generation method and to a constant amortized time (CAT) algorithm for the exhaustive generation of all SPM configurations with given weight. The same approach is extended to the Ice Pile Model. Joint work with Roberto Mantaci.

### Experiences

##### March 2011 - July 2012
Generalized RSK algorithm, combinatorial maps and bijective aspect of Young tableaux.
Internship at LIAFA, Paris 7, supervised by Guillaume Chapuy.
Duration: 4.5 months.
Slides (French)
##### March 2010 - August 2011
On hyperbolic geometry structure of complex networks.
Internship at Microsoft Research Asia, supervised by Wei Chen.
Duration: 5 months.
Report (English), Slides (English)
##### June 2009 - August 2010
Parameters of local search algorithms for SAT and its tuning.
Internship at University of Nantes, supervised by Charlotte Truchet and Frédéric Saubion.
Duration: 2.5 months.
Report (French), Slides (French), Homepage of Toolkit sat4sat

### Miscellaneous

I speak English (fluent), French (fluent), Cantonese (native) and Mandarin (native).

I am a member of Science Squirrels Club (Kexue Songshuhui), an association of Chinese science writers all over the world.

End of CV