Professor, dr.phil. et h.c.

Department of Mathematical SciencesUniversity of Copenhagen

Universitetsparken 5

DK-2100 København Ø

Denmark

Phone: (+45) 35320743

Fax: (+45) 35320704

E-mail: grubb@math.ku.dk

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

Pictures from a visit to
Japan February 2014 japan14

Teaching:

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.

Advanced courses:

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 26^{th}
Nordic and 1^{st} 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 Spectral Theory and Boundary Problems August 2014 pict0814

Colloquium
November 19, 2014, at Lund University mu-transmission.pdf

Lecture January 2015 at Oberwolfach Workshop
“Spectral Theory and Weyl Functions” MixedFrac15.pdf

Lecture
September 2015 in the Geometry Seminar at Stanford University Integration-by-partsFrac.pdf

Minicourse
at Magdeburg University March 2016 magde16k.pdf

Lecture
May 2016 at doctors-promotion Lund University dokt16k.pdf

Lecture October 2016 at birthday conference
for Elmar Schrohe, Hannover
University hanno16k.pdf

Latest update: April 29,
2016