Email address: bxliu AT math.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 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 (35 pages, to appear at The Michigan Math. Journal),

__arXiv:2109.09156__.On full asymptotics of analytic torsions for compact locally symmetric orbifolds (61 pages, to appear at Analysis & PDE),

__arXiv:2005.02055__.Hypoelliptic Laplacian and twisted trace formula (77 pages, to appear at Annales de l'Institut Fourier),

__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 Mathematique, Volume 357, Issue 1, 2019, Pages 74-83, ISSN 1631-073X,__https://doi.org/10.1016/j.crma.2018.11.010__.

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

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

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.__Workshop on Dirac operators (Opérateur de Dirac)__organized by Prof. Jean-Michel Bismut in Unversité Paris Sud (Orsay), since October 2014.Conference "Index theory, Duality and Related Fields" at the Chern Institute, June 17th - 20th 2019, Tianjin.

Analyse Complexe, Géométrie Complexe et Applications, Colloque en mémoire de G. Henkin, Dec 11th - 12th 2017, UPMC-Paris 6, Jussieu, Paris.

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

Summer Program: Recent Advances in Complex Differential Geometry (Institut de Mathématiques de Toulouse), June 13th - 22nd 2016, Toulouse, France.

Conference on Topology and Geometry ( Hausdorff Research Institute for Mathematics, Universität Bonn), August 17th - 21st 2015, Bonn, Germany.