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  Yilin Wang (IHES)

Publications

​​Preprints and ​Publications

The list is in reverse chronological order of the first submission to arXiv.

23. [arXiv] 
Epstein curves and holography of the Schwarzian action
Joint with Franco Vargas Pallete and Catherine Wolfram

22. [arXiv] Piecewise geodesic Jordan curves II: Loewner energy, projective structures, and accessory parameters
​Joint with Mario Bonk, Janne Junnila, Steffen Rohde 

21. [arXiv] [pdf]  Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra
​Joint with Maria Gordina and​ Wei Qian
J. Math. Pures Appl., vol. 195 (2025)

20. [arXiv] [pdf] The Brownian loop measure on Riemann surfaces and applications to length spectra
Joint with Yuhao Xue
Comm. Pure Appl. Math., to appear

19. [arXiv] [pdf] Commutation relations for two-sided radial SLE
Joint with ​Ellen Krusell and Hao Wu

18. ​ [arXiv] [pdf] Two optimization problems for the Loewner energy
J. Math. Phys. vol. 66, 023502 (2025) Special issue XXI International Congress on Mathematical Physics 2024

17.  [arXiv] [pdf] Universal Liouville action as a renormalized volume and its gradient flow
Joint with  Martin Bridgeman, Kenneth Bromberg, and Franco Vargas Pallete 
Duke Math. J. to appear

16.  [arXiv] [pdf] Onsager-Machlup functional for SLE loop measures
Joint with Marco Carfagnini 
Comm. Math. Phys. Vol. 405, art. 258 (2024)​

15.  [arXiv] [pdf] Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy
Joint with Jinwoo Sung 
Math. Ann. Vol. 390, p. 4789–4812 (2024)

14.  [arXiv] [pdf] Circle homeomorphisms with square summable diamond shears
Joint with Dragomir Saric and​ Catherine Wolfram 
Int. Math. Res. Not. (IMRN) Vol. 2024, 17 (2024)
​
13.  [arXiv] [pdf] Piecewise geodesic Jordan curves I: weldings, explicit computations, and Schwarzian derivatives
Joint with Don Marshall and Steffen Rohde 
​
12.  [arXiv] The Loewner Energy via the Renormalised Energy of Moving Frames​
Joint with Alexis Michelat 
Arch. Ration. Mech. Anal. (ARMA) Vol. 248, 15 (2024)
​
11.  [arXiv] [pdf] The Loewner-Kufarev energy and foliations by Weil-Petersson quasicircles
Joint with Fredrik Viklund 
Proc. Lond. Math. Soc. (PLMS) Vol. 128, 2 (2024)

10.  [arXiv] [pdf] Large deviations of multichordal SLE0+, real rational functions, and zeta-regularized determinants of Laplacians
​Joint with Eveliina Peltola
J. Eur. Math. Soc. (JEMS) 26 (2024), no. 2, pp. 469–535
​ 
​9.  [arXiv] [pdf] Large deviations of radial SLE infinity
​​Joint with Morris Ang and Minjae Park
Electron. J. Probab. (EJP), Vol. 25, paper no. 102, 1-13 (2020)​​

8.  [arXiv] [pdf] Interplay between Loewner and Dirichlet energies via conformal welding and flow-lines
Joint with Fredrik Viklund
Geom. Funct. Anal. (GAFA), Vol. 30. 1, 289-321 (2020)​
​
7.  [arXiv] [pdf] A note on Loewner energy, conformal restriction and Werner's measure on self-avoiding loops
​Ann. Inst. Fourier, Volume 71 (2021) no. 4, pp. 1791-1805
​
6.  [arXiv] [pdf] Equivalent Descriptions of the Loewner Energy
​Invent. Math. Vol. 218. 2, 573-621 (2019)

5.  [arXiv] The Loewner energy of loops and regularity of driving functions
Joint with Steffen Rohde
Int. Math. Res. Not. (IMRN) Vol. 2021. 10, 7433–7469 (2021)

4.  [arXiv] Remarks on Loewner chains driven by finite variation functions
​Joint with Atul Shekhar and Huy Tran
Ann. Acad. Sci. Fenn. Math. Vol. 44, 311-327 (2019)​
​
3.  [arXiv] [pdf] The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE0+
J. Eur. Math. Soc. (JEMS) Vol. 21. 7, 1915-1941 (2019)

Expository articles

2. [arXiv] [pdf] From the random geometry of conformally invariant systems to the Kähler geometry of universal Teichmüller space
Notices of the AMS (June/July 2024)
​
1.  [arXiv] [pdf] Large deviations of Schramm-Loewner evolutions: A survey
Probability Surveys, vol. 19: 351-403 (2022)​

Thesis

  • 05.2019  «On the Loewner energy of simple planar curves»   
    Doctoral dissertation  supervised by Wendelin Werner, ETH.
    ​
  • 09.2015  «On the Schramm Loewner Evolution with small parameter»  
    Master thesis supervised by Wendelin Werner.

  • 06.2014  «Notions de base en géométrie tropicale et droites contenues dans une surface quartique» 
    Master thesis supervised by Ilia Itenberg.

  • 06.2012 «Amortissement de Landau, stabilité des solutions d’équation de Poisson-Vlasov» 
    Joint with Zihui Zhao.
    Bachelor thesis supervised by Benjamin Texier. 
    ​
  • [pdf] Notes on the 2D Yang-Mills master field and free probability theory
    Lecture notes for reading group at ETH (2018)



Collaborators

Morris Ang
Mario Bonk  
Martin Bridgeman 
Kenneth Bromberg 
Marco Carfagnini 
Maria Gordina  
Janne Junnila 
 
​Ellen Krusell
Greg Lawler  

Donald Marshall  
Alexis Michelat  
Minjae Park  
Eveliina Peltola
 
Wei Qian

Steffen Rohde 
Dragomir Saric
  
Atul Shekhar
Jinwoo Sung
Huy Tran
Franco Vargas-Pallete
Fredrik Viklund
Catherine Wolfram
Hao Wu
Yuhao Xue
​
Zihui Zhao
@ MSRI 
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