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Personal Profile of Dr. Wang Yilin

Dr. Wang Yilin

Massachusetts Institute of Technology

Department of Mathematics

Home Page: https://yilwang.weebly.com/

ORCID: https://orcid.org/0000-0002-8994-1717

MSRI Program:: The Analysis and Geometry of Random Spaces
Visit Dates:: January 18, 2022 - May 27, 2022

Talks

May 10, 2022 (11:00 AM PDT - 12:00 PM PDT)
Seminar Career Development Panel: Grant Writing Pt II
April 05, 2022 (03:30 PM PDT - 05:00 PM PDT)
Seminar AGRS The Ubiquitous Diff(S^1) Learning Seminar Series: Weil-Petersson Metric and Kahler Structure of Kirillov's Space

March 28, 2022 - April 01, 2022

Workshop The Analysis and Geometry of Random Spaces

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Apr 01, 2022
Friday

03:30 PM - 04:30 PM		Jordan Curves with the Piecewise Geodesic Property Wang Yilin (Massachusetts Institute of Technology)
Location MSRI: Simons Auditorium, Online/Virtual Video Abstract We consider Jordan curves passing through a given set of n points with the property such that each edge is the hyperbolic geodesic in the complement of the rest of the curve. Those curves are related to the minimizers of the Loewner energy and give a specific complex projective structure on the n-punctured sphere with real and parabolic holonomy around the punctures. Similar to a result of Takhtajan-Zograf, we also obtain a new type of accessory parameters and show that they can be expressed as differentials of the Loewner energy. This is based on the joint work with Don Marshall and Steffen Rohde. Supplements -- Show Detail

March 22, 2022 (03:30 PM PDT - 05:00 PM PDT)
Seminar AGRS The Ubiquitous Diff(S^1) Learning Seminar Series: Weil-Petersson Metric, Unitary Representations and Unitarizing Measures
March 15, 2022 (03:30 PM PDT - 05:00 PM PDT)
Seminar AGRS The Ubiquitous Diff(S^1) Learning Seminar: Kirillov's Space and Kirillov's Action, Weil-Petersson Metric, and Unitary Representations

January 24, 2022 - January 28, 2022

Workshop [HYBRID WORKSHOP] Introductory Workshop: The Analysis and Geometry of Random Spaces

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Jan 24, 2022
Monday

10:20 AM - 11:10 AM		Loewner Energy, SLE and Weil-Petersson Quasicircles Wang Yilin (Massachusetts Institute of Technology)
Location MSRI: Simons Auditorium, Online/Virtual Video Abstract This is an introductory lecture on the Loewner energy and its links to Schramm-Loewner evolutions and Weil-Petersson quasicircles, a class of Jordan curves arising from the Kahler geometry on the universal Teichmuller space. This class of curves is also of interest in geometric function theory and has many drastically different but equivalent definitions. These links show that the Loewner energy sits at the crossroad of random conformal geometry and analysis. After explaining the basic definitions and the main connections, I will focus on the related open questions. Supplements -- Show Detail

July 19, 2021 - July 30, 2021

Summer Graduate School Random Conformal Geometry (Virtual School)

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Jul 28, 2021
Wednesday

07:30 AM - 08:30 AM		Around the Loewner energy: Lecture 1 Wang Yilin (Massachusetts Institute of Technology)
Location -- Video Abstract The Loewner energy is a conformally invariant quantity that measures the roundness of a Jordan curve, introduced recently, from the study of large deviations of Schramm-Loewner evolutions with vanishing parameter. This perspective naturally connects Loewner energy to determinants of Laplacians and Brownian loop measures. More surprisingly, we show that a curve has finite Loewner energy if and only if it is a Weil-Petersson quasicircle, a class of Jordan curves studied since the eighties, that has more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, and string theory (now we add to the list random conformal geometry for the link to SLE). In these lectures, I will overview the connection of Loewner energy to these probabilistic and analytic concepts. Main references: Yilin Wang: Large deviations of Schramm-Loewner evolutions: A survey. ArXiv:2102.07032 Yilin Wang: Equivalent Descriptions of the Loewner Energy. Invent. Math., Vol. 218. 2, 573-621 (2019) Leon A. Takhtajan and Lee-Peng Teo: Weil-Petersson metric on the universal Teichmüller space. Mem. Amer. Math. Soc., 183(861):viii+119 (2006) Supplements -- Show Detail

Jul 29, 2021
Thursday

07:30 AM - 08:30 AM		Around the Loewner energy: Lecture 2 Wang Yilin (Massachusetts Institute of Technology)
Location -- Video Abstract The Loewner energy is a conformally invariant quantity that measures the roundness of a Jordan curve, introduced recently, from the study of large deviations of Schramm-Loewner evolutions with vanishing parameter. This perspective naturally connects Loewner energy to determinants of Laplacians and Brownian loop measures. More surprisingly, we show that a curve has finite Loewner energy if and only if it is a Weil-Petersson quasicircle, a class of Jordan curves studied since the eighties, that has more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, and string theory (now we add to the list random conformal geometry for the link to SLE). In these lectures, I will overview the connection of Loewner energy to these probabilistic and analytic concepts. Main references: Yilin Wang: Large deviations of Schramm-Loewner evolutions: A survey. ArXiv:2102.07032 Yilin Wang: Equivalent Descriptions of the Loewner Energy. Invent. Math., Vol. 218. 2, 573-621 (2019) Leon A. Takhtajan and Lee-Peng Teo: Weil-Petersson metric on the universal Teichmüller space. Mem. Amer. Math. Soc., 183(861):viii+119 (2006) Supplements -- Show Detail

Jul 30, 2021
Friday

07:30 AM - 08:30 AM		Around the Loewner energy: Lecture 3 Wang Yilin (Massachusetts Institute of Technology)
Location -- Video Abstract The Loewner energy is a conformally invariant quantity that measures the roundness of a Jordan curve, introduced recently, from the study of large deviations of Schramm-Loewner evolutions with vanishing parameter. This perspective naturally connects Loewner energy to determinants of Laplacians and Brownian loop measures. More surprisingly, we show that a curve has finite Loewner energy if and only if it is a Weil-Petersson quasicircle, a class of Jordan curves studied since the eighties, that has more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, and string theory (now we add to the list random conformal geometry for the link to SLE). In these lectures, I will overview the connection of Loewner energy to these probabilistic and analytic concepts. Main references: Yilin Wang: Large deviations of Schramm-Loewner evolutions: A survey. ArXiv:2102.07032 Yilin Wang: Equivalent Descriptions of the Loewner Energy. Invent. Math., Vol. 218. 2, 573-621 (2019) Leon A. Takhtajan and Lee-Peng Teo: Weil-Petersson metric on the universal Teichmüller space. Mem. Amer. Math. Soc., 183(861):viii+119 (2006) Supplements -- Show Detail