Research

Research Interests

Teichmüller Thurston theory and its generalizations,  differential geometry in higher Teichmüller spaces, and Higgs bundles.

Papers

• Geodesic Coordinates for the Pressure Metric at the Fuchsian Locus. Geometry & Topology. PDF.

• Correlation of the Renormalized Hilbert Length for Convex Projective surfaces, with Giuseppe Martone.  Ergodic Theory Dynam. Systems.  PDF.

• Thurston's  asymmetric metric for Anosov representations,  with  León Carvajales, Beatrice Pozzetti and Anna Wienhard.  Accepted in Groups Geometry Dynamics.  arXiv:2010.05292.

• The covariant metric for the Blaschke locus, with Nikolas Eptaminitakis.  J. Geom. Anal.   PDF.

Expository articles

• Lusztig's Total Positivity, in Proceedings of the Young Researchers Workshop on Positivity in Lie Groups, 2022.

Talks     

• Higgs bundles, character varieties and higher Teichmüller spaces, Madrid, May 22 - May 26, 2023. (Riemannian metrics and Finsler metrics in higher Teichmuller spaces)

• Joint Seminar on Teichmuller theory and Related topics, online zoom seminar, China, March 21, 2023. (Riemannian metrics and Finsler metrics in higher Teichmuller spaces)

• Workshop in symmetric spaces and Labourie's conjecture,  l'Escandille, Autrans, France, August 22 - August 27, 2022. (talks about Labourie's work on cyclic surfaces)

• Geometry structures, compaticifications and group actions, Strasbourg, June 27 - July 1, 2022. (short talk about Thurston's stretch metric on higher Teichmüller spaces.)

• Oberseminar Differentialgeometrie. University of bonn, May 12, 2022. (talk about the correlation theorem)

• Fifth Meeting for Young Women in Mathematics, University of Freiburg, April 6-8, 2022.  (talk about the pressure metric in the space of Riemannian metrics) 

• Seminar&Colloquia, Feb 25, 2022, Shanghai Jiao Tong University, China, zoom talk . (talk about the pressure metric in the space of Riemannian metrics) 

•  Online research seminar: Algebra, Geometry & Physics, Jan 25, 2022, MPIM/HU, Germany. (talk about the pressure metric in the space of Riemannian metrics) 

• Positivity Workshop, Jan 10 - Jan 15, 2021, Heidelberg, Germany. (talk about Lusztig's total positivity)

• Oberwolfach Mini-Workshop Anosov^3, Dec 5- Dec 10, 2021, Oberwolfach, Germany. (talk about the pressure metric in the space of Riemannian metrics)

• Geometry and topology seminar, Oct 14, 2021, Université Côte d'Azur, France. (talk about correlation theorem) 

•  Workshop on Anosov Representations, Aug 29 - Sep 4, 2021 Aussois, France. (talk about pressure metrics)

•   UCR Differential Geometry seminar,  April 2, 2021, zoom talk.  (talk about correlation theorem)

• Connections for Women: Holomorphic Differentials in Mathematics and Physics, Aug 15 -16, 2019, MSRI, CA. (talk about my thesis work)

• Workshop on Geometric aspects of Higgs bundles, May 11-18,  2019, Sunriver, Oregon. (talk about analytic aspects of convex real projective structures)

• The Gradute Student Topology and Geometry Conference,  March 30-31, 2019, UIUC. (talk about my thesis work)

• Gear log cabin workshop for Relative character varieties and parabolic Higgs bundles,  Feb 23-Mar 3, 2018, CA. (talk about cubic differentials and convex projective structures with boundary)

Conference (co-organized)

• the conference 2021 NCNGT  Lie group section.