Prof. Dr. Boris Vertman

E-mail: vertman(at)
Institute: Mathematical Institute
Bonn International Graduate School - BIGS

Academic Career

2001 - 2006

Diploma in Mathematics (M.Sc.), “Dirac Operators and the weak unique continuation property” under the auspices of Prof. Matthias Lesch, Preliminary Diploma (Vordiplom) in Physics and Mathematics

2004 - 2005

Masters in Mathematics (Part III of Mathematical Tripos), Masters Essay under the auspices of A.G. Kovalev, Distinction, University of Cambridge, England, UK

2006 - 2008

PhD in Mathematics, “Analytic Torsion on Manifolds with Boundary and Conical Singularities” under the auspices of Prof. Matthias Lesch, Scholar of “Graduate School of Cologne” University of Bonn

2008 - 2009

Postdoc (Scientific Assistant), Department of Mathematics, University of Bonn

2009 - 2010

Postdoctoral Fellow in Mathematics, under the auspices of Prof. Rafe Mazzeo, Scholarship of German Research Foundation, Stanford University, CA, USA


Academic Long Term Visit, research with Prof. Rafe Mazzeo and Prof. Bismut, March, Paris, France


Academic Long Term Visit, cooperation with Prof. Reshetikhin, June - August, University of California, Berkeley, CA, USA

Since 2010

Postdoc (Akademischer Rat), Department of Mathematics,

WS 2012/2013 and SS 2014: Substitute Lecturer (Lehrauftrag), University of Bonn

Research Profile

My research expertise lies in the field of partial differential equations on spaces with singular geometry. In particular I currently work on topics in spectral geometry, parabolic Schauder theory with applications to non-linear geometric evolution equations, in the setup of singular spaces. One fundamental aspect of my research is the microlocal approach to the elliptic theory of edge degenerate differential operators. The analysis of regular-singular Sturm-Liouville operators also takes a central place within my research interests. One other activity area results from the ansatz to define the quantum field theoretical path integral als the regularized limit of its discrete realisation, using tools from discrete geometry and approximation theory.

• Spectral geometry on singular spaces, spectral invariants
• Boundary value problems for degenerate elliptic operators
• Geometric flows, Ricci and Yamabe problems, fourth order equations
• Regular singular Sturm Liouville operators, zeta determinants
• Topological quantum field theory, discrete geometry

My research results are specifically concerned with the following topics

• Analytic Torsion on Singular Manifolds
• Refined Analytic Torsion on Manifolds with Boundary
• Parabolic Schauder Theory, Geometric Flows
• Edge Degenerate Boundary Value Problems
• Regular Singular Sturm-Liouville Operators
• Discrete Quantum Field Theory

Selected Publications

[1] Matthias Lesch, Boris Vertman
Regularizing infinite sums of zeta-determinants
Math. Ann. , 361: (3-4): 835--862
DOI: 10.1007/s00208-014-1078-7
[2] Boris Vertman
Heat-trace asymptotics for edge Laplacians with algebraic boundary conditions
J. Anal. Math. , 125: : 285--318
DOI: 10.1007/s11854-015-0009-1
[3] Nicolai Reshetikhin, Boris Vertman
Combinatorial quantum field theory and gluing formula for determinants
Lett. Math. Phys. , 105: (3): 309--340
DOI: 10.1007/s11005-015-0744-3
[4] Rafe Mazzeo, Boris Vertman
Elliptic theory of differential edge operators, II: Boundary value problems
Indiana Univ. Math. J. , 63: (6): 1911--1955
DOI: 10.1512/iumj.2014.63.5435
[5] Werner Müller, Boris Vertman
The metric anomaly of analytic torsion on manifolds with conical singularities
Comm. Partial Differential Equations , 39: (1): 146--191
DOI: 10.1080/03605302.2013.851212
[6] Eric Bahuaud, Boris Vertman
Yamabe flow on manifolds with edges
Math. Nachr. , 287: (2-3): 127--159
DOI: 10.1002/mana.201200210
[7] Rafe Mazzeo, Boris Vertman
Analytic torsion on manifolds with edges
Adv. Math. , 231: (2): 1000--1040
DOI: 10.1016/j.aim.2012.05.008
[8] Matthias Lesch, Boris Vertman
Regular singular Sturm-Liouville operators and their zeta-determinants
J. Funct. Anal. , 261: (2): 408--450
DOI: 10.1016/j.jfa.2011.03.011
[9] Boris Vertman
Analytic torsion of a bounded generalized cone
Comm. Math. Phys. , 290: (3): 813--860
DOI: 10.1007/s00220-009-0862-9
[10] Boris Vertman
Refined analytic torsion on manifolds with boundary
Geom. Topol. , 13: (4): 1989--2027
DOI: 10.2140/gt.2009.13.1989

Publication List


2001 - 2005

German National Merit Foundation (Studienstiftung) for academic studies at University of Cologne and Cambridge, England, UK

2004 - 2005

DAAD Excellence Programme Cambridge for the Mathematical Tripos Part III at University of Cambridge, England, UK


Scholar of the Downing College at Cambridge, in recognition of Certificate of Advanced Studies in Mathematics (Masters) with Distinction, June

2006 - 2008

Scholarship of the “Graduiertenkolleg Köln” for Doctoral Research at University of Cologne, University of Bonn

2009 - 2010

DFG Research Scholarship for Postdoctoral Research at Stanford University, CA, USA


Feodor Lynen Postdoctoral Scholarship was also offered for Postdoctoral Research at Stanford University, CA, USA

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