__Department Mathematik/Informatik, Abteilung Mathematik__,

Universität zu Köln,

Weyertal 86 - 90,

D-50931 Köln,

Deutschland

Email address: bingxiao.liu AT uni-koeln.de

I am
currently a research assistant at the Mathematics Institute of the
University of Cologne from October 2020. I work with __Prof.
Drewitz__ and __Prof.
Marinescu__ on the SPP project __Random
polynomials and random Kähler geometry__.

I was a
Postdoctoral Fellow at __Max
Planck Institute for Mathematics__ in Bonn from September 2018
to September 2020. Before Bonn, I was a Ph.D. student in Université
Paris-Sud (Orsay, France).

During the university year 2017/2018, I was also in ATER in Université Paris-Sud(Orsay), with a teaching load of 192 hours for undergraduates in Université Paris-Sud and Polytech Paris-Sud.

My Ph.D.
supervisor: __Professor
Jean-Michel Bismut__ (Université Paris-Sud, Orsay).

My thesis
title: __Hypoelliptic
Laplacian and twisted trace formula.__

Research interests:

Local index theory, analytic torsion, and microlocal analysis;

Complex and Kähler geometry, random holomorphic sections;

Symmetric spaces, semisimple Lie groups, and their representations;

Loop spaces and mathematical physics;

with Dominik Zielinski, Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros (45 pages).

__arXiv:2407.15106__.with Alexander Drewitz and George Marinescu, Toeplitz operators and zeros of square-integrable random holomorphic sections (66 pages).

__arXiv:2404.15983__.with Hisatoshi Kodani (Kyushu University, Japan), Integral invariants for framed 3-manifolds associated to trivalent graphs possibly with self-loops (52 pages).

__arXiv:2311.02682__.with Alexander Drewitz and George Marinescu, Gaussian holomorphic sections on noncompact complex manifolds (47 pages).

__arXiv:2302.08426__.with Alexander Drewitz and George Marinescu,

__Large deviations for zeros of holomorphic sections on punctured Riemann surfaces__, Michigan Math. J. Advance Publication 1-41 (2023). DOI: 10.1307/mmj/20226253.__arXiv:2109.09156__.__On full asymptotics of analytic torsions for compact locally symmetric orbifolds__. Anal. PDE, 17(4):1261–1329, 2024.__arXiv:2005.02055__.__Hypoelliptic Laplacian and twisted trace formula__. Annales de l'Institut Fourier, Tome 73 (2023) no. 5, pp. 1909-1985.__arXiv:1910.11382__.__Asymptotic equivariant real analytic torsions for compact locally symmetric spaces__. J. Funct. Anal., 281(7):Paper No. 109117, 54 pp., 2021.__Hypoelliptic Laplacian and twisted trace formula__, Comptes Rendus Mathématique, Volume 357, Issue 1, 2019, Pages 74-83, ISSN 1631-073X,__https://doi.org/10.1016/j.crma.2018.11.010__.

On-line lectures: Introduction to random zeros of holomorphic sections, 19, 21, 26, 28/03/2024, the lectures will be given on-line in Chinese with English notes, see

__abstracts__.

__Lecture Note 1____Lecture Note 2____Lecture Note 3____Lecture Note 4__Latexified notes with more details and references still under construction.Teaching assistant for the lecture Random Kähler Geometry, Winter semester 2023/2024, Universität zu Köln.

__Seminar semiklassische Analysis und Darstellungstheorie__, Universität zu Köln.__AG Random Geometry__, Universität zu Köln.

__Conference Geometric and topological properties of random algebraic varieties__, 4th - 6th Oct. 2023, Universität zu Köln.

July 12th, 2024, Toeplitz-Fubini-Study forms and lowest eigenvalues of Toeplitz operators.

__Joint Seminar on Complex Algebraic Geometry and Complex Analysis (Bochum - Essen - Köln - Münster - Wuppertal).__Ruhr-Universität Bochum, Bochum, Germany.April 29th, 2024,

__Toeplitz Operators and Zeros of Square-integrable Gaussian Holomorphic Sections.__Probability Seminar Series, NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, NYU Shanghai, Shanghai, China.April 4th, 2024, Opérateur de Toeplitz et zéros de sections holomorphes gaussiennes de carré intégrable. Séminaire d'algèbre, topologie et géométrie, Laboratoire J.A. Dieudonné, Université Côte d'Azur, Nice, France.

Oct 26th, 2023, Random holomorphic sections on noncompact complex manifolds.

__Workshop on Pluripotential Theory and Holomorphic foliations__, Oct 25th - 27th 2023, Université Polytechnique Hauts-de-France, Valenciennes, France.July 26th, 2023, Random holomorphic sections on noncompact complex manifolds.

__Conference: Quantization in Geometry__, July 24th - 28th 2023, Universität zu Köln, Köln, Germany.__slides__May 25th, 2023, Hypoelliptic Laplacian of Bismut on symmetric spaces.

__Oberwolfach Workshop: Hypoelliptic Operators in Geometry (Workshop ID 2321)__, May 21st - 26th 2023, MFO, Oberwolfach, Germany.__MFO Report (Reporter: Bingxiao Liu)__Apr 28th, 2023, Hypoelliptic Laplacian of Bismut on symmetric spaces and applications. ECNU Differential Geometry Seminar, East China Normal University, Shanghai.

Mar 27th, 2023, Random polynomials and random Kähler geometry.

__2nd Annual Conference of Random Geometric Systems (SPP2265)__, Mar 27th - 30th 2023, DLR site in Cologne-Porz.Mar 7th, 2023,

__Zeros of random holomorphic sections on complex manifolds.__Session: Limit theorems, large deviations and extremes, German Probability and Statistics Days (GPSD 2023), Mar 7th - 10th 2023, Essen.Jan 17th, 2023,

__Zeros of random holomorphic sections on noncompact complex manifolds.__Séminaire Analyse Harmonique, Orsay, Université Paris-Saclay.Dec 15th, 2022,

__Zeros of random holomorphic sections on noncompact complex manifolds.__ECNU Differential Geometry Seminar, East China Normal University, Shanghai.Oct 15th, 2022, Zeros of random holomorphic sections on noncompact complex manifolds.

__Workshop Cologne-Nice Complex and CR Geometries, Dynamics__, Nov 14th - 15th 2022, Nice.Mar 8th, 2022, Large deviation estimates for zeros of random holomorphic sections on punctured Riemann surfaces. Séminaire d'Analyse et Géométrie, Jussieu, Paris.

Nov 17th, 24th, and 26th, 2021, Introduction to Hypoelliptic Laplacian of Bismut on Symmetric Spaces, on-line mini-lecture, School of Mathematical Sciences, Tongji University, Shanghai.

Oct 26th, 2021, Large deviation estimates for zeros of random holomorphic sections for punctured Riemann surfaces, in Conference ACQUA: Quantitative Aspects in Complex analysis, Geometry and Dynamics, Lille.

July 13th, 2021, Asymptotic real analytic torsions for compact locally symmetric orbifold (on-line), in Seminar semiklassische Analysis und Darstellungstheorie, University of Cologne.

Feb 2nd, 2021, joint talk with Prof. Drewitz, Random polynomials and random Kähler geometry (on-line), in Probability / SPP 2265 Research Seminar Ruhr.

May 15th, 2020, Asymptotic analytic torsion for compact locally symmetric orbifold, Online Seminar on the

__Hypoelliptic Laplacian and Noncommutative Geometry__.July 29th - Aug 2nd, 2019, Mini-course 'An introduction to symmetric spaces', in Workshop on Global Analysis on Manifolds, USTC, Hefei.

July 15th, 2019, Asymptotics of equivariant analytic torsion on compact locally symmetric spaces, Conference '

__Quantization in symplectic geometry__', July 15th - 19th, 2019, Cologne.__International Micro-Workshop on the Hypoelliptic Laplacian__, May 7th - 10th, 2019, Department of Mathematics, Penn State University, State College.Apr 30th, 2019, Hypoelliptic Laplacians on symmetric spaces and twisted orbital integrals, Noncommutative Geometry Festival 2019, Apr 29th - May 3rd, 2019, Washington University in St. Louis.

Apr 12th, 2019, Hypoelliptic Laplacians on symmetric spaces and twisted trace formula, mini-workshop '

__Recent Progress in Path Integration on Graphs and Manifolds__', Apr 7th - 13th 2019, MFO, Oberwolfach, Germany.__MFO Report__Dec 18th, 2018, Introductions to hypoelliptic Laplacian on symmetric spaces, in Oberseminar Global Analysis and Operator Algebras, University of Bonn.

Nov 11th, 2018, Asymptotics of equivariant analytic torsion on compact locally symmetric spaces, in Seminar semiklassische Analysis und Darstellungstheorie, University of Cologne.

Oct 9th, 2018, Selberg's twisted trace formula and asymptotics of equivariant analytic torsion, in International Workshop on Geometric Quantization and Applications, Oct 8th - 12th, 2018, at Luminy - CIRM.

__slides__Aug 1st, 2018, Hypoelliptic Laplacian and twisted orbital integrals, in Workshop on Global Analysis on Manifolds, USTC, Hefei.

Jun 30th, 2018, Hypoelliptic Laplacian and semisimple orbital integrals, in

__Séminaire Mathjeunes__, Université Paris-Sud, Orsay.May 5th, 2018, Semisimple orbital integrals associated with real reductive groups, in

__Séminaire Mathjeunes__, Université Paris-Sud, Orsay.

__The 2021 Shaw Prize in Mathematical Sciences__for Prof. Jean-Michel Bismut.__An overview of Bismut's work (in French)__by__Prof. Xiaonan Ma__.Results of the dissertation of my Bachelor degree (2013) at USTC are cited in the survey articles (

__English__,__Chinese__) of Prof. Xiao Zhang (AMSS, CAS), he was my supervisor of Bachelor thesis.__Some videos of talks__given by Prof. Jean-Michel Bismut.Conference "Index theory, Duality and Related Fields" at the Chern Institute, June 17th - 20th 2019, Tianjin.

Workshop in Chern Institute of Mathematics (Tianjin): Loop spaces, Supersymmetry and Index theory, July 17th - 21st 2017.