Tobias Diez Photo

About Me

I am an Assistant Professor at the Shanghai Jiao Tong University. Before this, I was a post­doctoral fellow in the Analysis Group at Delft University of Technology, working with Bas Janssens.
In 2019, I completed my PhD at the University of Leipzig and the Max Planck Institute for Mathematics in the Sciences under the supervision of Gerd Rudolph.

If you want to get in touch with me, write me an email to research@tobiasdiez.de.

My Research

I am interested in the mathematical aspects of classical and quantum field theories. Symmetries and their fascinating occurrence throughout physics are the prevalent theme of my research.
This translates into a broad spectrum of research interest:

  • Infinite-dimensional symplectic manifolds with symmetries
  • Moduli spaces of geometric structures
  • Geometric quantization
  • Representation theory of infinite-dimensional Lie groups
  • Dynamics of infinite-dimensional Hamiltonian systems, especially in hydrodynamics and gauge theory

Publications

  • [1]

    Expectation values of polynomials and moments on general compact Lie groups

    T. Diez, L. Miaskiwskyi

    Mar 2022


  • [2]

    Normal form of equivariant maps in infinite dimensions

    T. Diez, G. Rudolph

    Oct 2021


  • [3]

    Singular symplectic cotangent bundle reduction of gauge field theory

    T. Diez, G. Rudolph

    Sep 2020


  • [4]

    Induced differential characters on nonlinear Graßmannians

    T. Diez, B. Janssens, K.-H. Neeb, C. Vizman

    Sep 2020

    Submitted abstract

  • [5]

    Central Extensions of Lie Groups Preserving a Differential Form

    T. Diez, B. Janssens, K.-H. Neeb, C. Vizman

    Jun 2020

    Int. Math. Res. Not. 2021 no. 5 (pp. 3794-3821) abstract

  • [6]

    Group-valued momentum maps for actions of automorphism groups

    T. Diez, T. Ratiu

    Feb 2020

    Submitted abstract

  • [7]

    Realizing the Teichmüller space as a symplectic quotient

    T. Diez, T.S. Ratiu

    Dec 2019


  • [8]

    Clebsch-Lagrange variational principle and geometric constraint analysis of relativistic field theories

    T. Diez, G. Rudolph

    Aug 2019

    J. Math. Phys. 60 no. 8 (pp. 082903) abstract

  • [9]

    Slice theorem and orbit type stratification in infinite dimensions

    T. Diez, G. Rudolph

    Aug 2019


  • [10]

    Analyzing the Importance of JabRef Features from the User Perspective

    M.K. Simon, L.W. Dietz, T. Diez, O. Kopp

    Feb 2019


  • [11]

    Yang-Mills moduli spaces over an orientable closed surface via Fréchet reduction

    T. Diez, J. Huebschmann

    Oct 2018

    J. Geom. Phys. 132 (pp. 393-414) abstract

Theses

  • [1]

    Normal Form of Equivariant Maps and Singular Symplectic Reduction in Infinite Dimensions with Applications to Gauge Field Theory

    T. Diez

    Jul 2019

    PhD Thesis Universität Leipzig abstract

  • [2]

    Slice theorem for Fréchet group actions and covariant symplectic field theory

    T. Diez

    Oct 2013

    Master Thesis Universität Leipzig abstract

Talks

  • [1]

    Normal Form of Equivariant Maps in Finite and Infinite Dimensions

    T. Diez

    Jul 2021


  • [2]

    Group-valued momentum maps for diffeomorphism groups

    T. Diez

    Mar 2021

    Global Poisson Webinar abstract

  • [3]

    Normal Form of Equivariant Maps in Infinite Dimensions

    T. Diez

    Dec 2020

    2020 Winter Young Mathematician Forum abstract

  • [4]

    Group-valued momentum maps for diffeomorphism groups

    T. Diez

    Sep 2020

    Junior Global Poisson Workshop abstract

  • [5]

    Group-valued momentum maps for diffeomorphism groups and generalized Clebsch variables

    T. Diez

    Feb 2020

    Analysis Seminar Delft abstract

  • [6]

    Normal Form of Equivariant Maps in Infinite Dimensions

    T. Diez

    Feb 2020


  • [7]

    Group-valued momentum maps for automorphism groups

    T. Diez

    Jan 2020

    Utrecht Geometry Center Seminar abstract

  • [8]

    Singular symplectic cotangent bundle reduction in infinite dimensions

    T. Diez

    Nov 2019


  • [9]

    Smooth Path Groupoids and the Smoothness of the Holonomy Map

    T. Diez

    Nov 2019


  • [10]

    Normal form of equivariant maps in infinite dimensions

    T. Diez

    Nov 2018


  • [11]

    Central extensions using holonomy preserving diffeomorphisms in infinite dimensions

    T. Diez

    Nov 2017

    Shanghai abstract

  • [12]

    On the universality of the incompressible Euler equation

    T. Diez

    Nov 2017

    Shanghai abstract

  • [13]

    Smoothness of the holonomy map

    T. Diez

    Aug 2017


  • [14]

    Normal form of momentum maps in infinite dimensions

    T. Diez

    Jun 2017

    Workshop Geometry and PDEs Timișoara

  • [15]

    Singular symplectic reduction in infinite dimensions using the Nash-Moser theorem

    T. Diez

    Dec 2016


  • [16]

    JabRef and its architecture

    T. Diez, O. Kopp, S. Harrer, J. Lenhard, S. Kolb, M. Geiger, O. Gustafsson, C. Schwentker

    Nov 2016


  • [17]

    Singular symplectic reduction in infinite dimensions using the Nash-Moser theorem

    T. Diez

    Oct 2016

    Shanghai abstract

  • [18]

    Momentum maps for diffeomorphism and gauge groups

    T. Diez

    Jun 2016

    Workshop Geometry and PDEs Timișoara abstract

  • [19]

    Yang-Mills moduli spaces over a surface via Fréchet reduction

    T. Diez

    Mar 2015

    Séminaire Physique Mathématique Lille abstract

  • [20]

    Slice theorem for Fréchet group actions

    T. Diez

    Sep 2014

    Special Geometric Structures Hamburg abstract

  • [21]

    Slice theorem for Fréchet group actions

    T. Diez

    Jun 2014

    Master's Thesis Defence Leipzig

Curriculum Vitae

Assistant Professor
Shanghai Jiao Tong University, China
2021
Postdoctoral fellow
Delft University of Technology, Netherlands
2019-2021
Working with Bas Janssens
Ph.D. student
University of Leipzig & Max Planck Institute for Mathematics in the Sciences, Germany
2014-2019
Thesis: Normal Form of Equivariant Maps and Singular Symplectic Reduction in Infinite Dimensions with Applications to Gauge Field Theory
Supervised by Gerd Rudolph
Visiting Scholar
Université Lille 1, France
2013-2014
Working with Johannes Huebschmann
M.Sc. International Physics Studies Program
University of Leipzig, Germany
2011-2014
Thesis: Slice theorem for Fréchet group actions and covariant symplectic field theory
Supervised by Gerd Rudolph
B.Sc. Physics
University of Leipzig, Germany
2008-2012
Thesis: Geometric quantization and semiclassical approximation
Supervised by Gerd Rudolph