Professor, dr.phil. et h.c.Department of Mathematical Sciences
Phone: (+45) 35320743
Fax: (+45) 35320704
Home address: Duevej 26, 6. sal, 2000 Frederiksberg, Denmark.
Current research areas:
Pseudodifferential calculi, for manifolds with boundary and with spectral parameters. Geometric analysis. Asymptotic trace expansions of parameter-dependent operators, the geometric interpretation of the coefficients. The logarithmic and nonlocal terms. The noncommutative residue and the canonical trace. The zeta coefficients. Spectral boundary conditions in Brane theory. Applications of pseudodifferential methods to Navier-Stokes problems. Extension theory and boundary problems for elliptic operators. Krein resolvent formulas. Nonsmooth boundary value problems. Krein-like extensions (without regularity). Spectral asymptotics for problems with jumps. Fractional Laplacians, heat kernels, regularity properties on a domain.
Recent publications and preprints: publications.htm
List of earlier works: publist.pdf
Pictures (by Peter Gilkey) from the meeting "Spectral Theory and Partial Differential Equations" November 19-21 2008: nov08
Basic courses in Mathematical Analysis. Basic and advanced courses in Ordinary and Partial Differential Equations, Functional Analysis, Pseudodifferential operators. Calculus of Variations and Optimal Control Theory. Wavelets. Distribution theory.
Fall 1999: Applications of the Fourier transform. (Based on X. Saint Raymond: Elementary introduction to the theory of pseudodifferential operators.)
Spring 2000: Solution of PDE. (Same book.)
Fall 2000: Introduction to Partial Differential Equations. (Based on L. C. Evans: Partial Differential Equations, AMS 1999.) Kursushjemmeside
Spring 2001: 1) Distribution Theory. 2) Continuation of PDE course. Hjemmeside for evolutionskursus
Fall 2001: 1) Mat 3GT. Hjemmeside for Mat 3GT 2) Wavelets. Hjemmeside for Wavelets 3) Seminar: Analysis on manifolds. Hjemmeside for Manifolds
Fall 2002: Grundkursus i partielle differentialligninger Hjemmeside for PDL02
Spring 2003: Modern Analysis - Distributions and Operators. Hjemmeside for distributionskursus.
Fall 2003 / Spring 2004: Reel analyse og lineær algebra, Mat H1 (Copenhagen Business School). Hjemmeside for Mat H1 efterår 03
Fall 2004: Reel analyse og lineær algebra, Mat H1 (Copenhagen Business School). Hjemmeside for Mat H1 efterår 04
Spring 2005: PDL - Elliptiske problemer Hjemmeside: pdlep, Lectures in Noncommutative Geometry Seminar ncg05.pdf
Fall 2005: SDL - Sædvanlige Differential Ligninger http://www.math.ku.dk/kurser/2005-06/blok1/sdl/
Spring 2006: ModAn - Distributions and Operators. Hjemmeside.
Fall 2006: Introduktion til PDL Hjemmeside for PDL06
Spring 2007: ModAn - Distributioner og Operatorer, Blok 3. ModAn2 - Anvendelser af Distributionsteori, Blok 4
Fall 2007: Ordinary Differential Equations, SDL.
Spring 2008: Applied Analysis - Parabolic Differential Equations, Anvendt Analyse - Parabolske Differentialligninger.
Fall 2008: Introduction to PDE, Introduktion til PDL, consultant, lectures given by Uuye Otgonbayar.
Simons professor at MSRI September 2008, lectures Intro to Index Theory New Residue Definitions
Spring 2009: ModAn - Distributions and Operators. Uses a book with this name, Graduate Texts in Mathematics 252, Springer-Verlag, New York 2009.
Lecture at Banach Center Bedlewo May 2009 Resolvents on nonsmooth domains
Fall 2009: Ordinary Differential Equations SDL09 sdl09.htm
Fall 2010: Differential Operators and Function Spaces, DifFun10 Course description.htm
Lecture in Analysis and Geometry Seminar Copenhagen University February 2011 Extension theory for nonsmooth boundary problems
Lecture Sept. 2011 at Imperial College, London Resolvent differences and their spectral estimates
Fall 2011: Differential Operators and Function Spaces, DifFun11 DifFun11.html
Lecture in Spectral Theory meeting at Cardiff University May 2012 Spectral asymptotics for resolvent differences with rough coefficients
Lecture August 2012 at Spectral Theory - Differential Operators meeting at Graz University Eigenvalue asymptotics for nonsmooth singular Green operators
Exaugural lecture at IMF November 2012 Encounters with Spectral Theory
Some pictures from the occasion (unfortunately the organized cameras didn’t work, so most of the reception was not covered) nov12
Memorial lecture at the 26th Nordic and 1st Nordic-European Congress June 2013 Boundary Problems
Lecture September 2013 in Elliptic-Parabolic Workshop at Hannover University Heat kernels.pdf
Lecture April 2014 in Spectral Theory Workshop at University of Kent Fractional.pdf
Lecture June 20, 2014, in the Geometry and Analysis Seminar at Copenhagen University cph14k.pdf
Pictures from reception and dinner at the workshop Boundary Problems and Spectral Theory August 2014 pict0814
Latest update: August 27, 2014