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!DOCTYPE HTML>!--	Dimension by HTML5 UP	html5up.net | @ajlkn	Free for personal and commercial use under the CCA 3.0 license (html5up.net/license)-->html langen>	head>		title>H.Z.Munthe-Kaas Homepage/title>		meta charsetutf-8 />		meta nameviewport contentwidthdevice-width, initial-scale1, user-scalableno />		link relstylesheet hrefassets/css/main.css />        script srcassets/js/jquery.min.js>/script>        script srcassets/js/typed.js>/script>		noscript>link relstylesheet hrefassets/css/noscript.css />/noscript>        style>            p.ex1 {            font-size: 20px;            }            p.ex2 {            font-size: 30px;            }        /style>	/head>	body classis-preload>        		!-- Wrapper -->			div idwrapper>                div idtyped-strings>                    p>                         Professor of Mathematics/p> p>at/p>                    p>University of Bergen                                            /p>                    p>                        Birdwatcher and Nature Photographer                    /p>                    p>Maze-maker/p>                   !-- p>Professor of Mathematics                                                     /p>                    -->                /div>				!-- Header -->					header idheader>						!-- div classlogo>							span classicon fa-gem>/span>						/div> -->						div classcontent>							div classinner>								h1>Hans Z. Munthe-Kaas/h1>                                    span idtyped>/span>                                    script>                                        $(document).ready(function(){                                            var typed  new Typed(#typed,{                                                stringsElement: #typed-strings,                                                backSpeed: 30,                                                 typeSpeed: 40,                                                loop: true                                            });                                        });                                    /script>    					    /div>						/div>						nav>							ul>								                                li>a href#about>About/a>/li>								li>a href#research>Research/a>/li>								li>a href#teach>Teaching/a>/li>								li>a href#outreach>Outreach/a>/li>								li>a href#photo>Photo/a>/li>                                li>a href#personal>Personal/a>/li>							/ul>						/nav>                        p classex1>NEWS: a hrefhttps://uit.no/research/lsc>Lie-Størmer Center!/a>/p>					/header>				!-- Main -->					div idmain>                            article idabout>								h2 classmajor>Hans Z. Munthe-Kaas/h2>                                 !-- span classimage main>img srcimages/HMunthe-Kaas.jpg alt />small>a hrefhttps://steidl.de/Artists/Peter-Badge-0029405255.html>Photo: Peter Badge/a>/small>/span>                                -->	                           span classimage main>img srcimages/HMunthe-Kaas.jpg alt />small>a hrefhttps://www.melanieburford.com>Photo: Melanie Burford/a>/small>/span>								p>                                ul>                                li>a href#contact>CONTACT/a>/li>                                li> Professor: a hrefhttps://www.uib.no/en>University of Bergen/a>/li>                                !-- li> Adjunct Professor: a hrefhttps://en.uit.no/startsida>UiT The Arctic University of Norway/a>/li>                                -->                                li> Chair: a hrefhttps://abelprize.no>Abel Prize Committee/a>/li>                                li> Editor-in-Chief: a hrefhttps://www.springer.com/journal/10208>Foundations of Computational Mathematics/a>                                /li>                                li> President: a hrefhttps://web.matematikkforeningen.no>Norwegian Mathematical Society/a>/li>                                li> Scientific advisory committee: a hrefhttps://mohnfoundation.no/?langen>Trond Mohn Foundation/a>/li>                                li>Project leader: RCN-Fripro project: a hrefhttps://sites.google.com/view/codysmageoproco/codysma>                                    CODYSMA/a>/li>                                li> Project leader: a hrefhttps://uit.no/research/lsc>Lie--Størmer Center/a>/li>                                /ul>                                /p>							/article>                                                !-- Contact -->							article idcontact>								h2 classmajor>Contact Hans Munthe-Kaas:/h2>                                ul>                                li>Email: a hrefmailto:hans.munthe-kaas@uib.no>hans.munthe-kaas@uib.no/a>/li>                                li>Homepage: a hrefhttp://hans.munthe-kaas.no>http://hans.munthe-kaas.no/a>/li>                                li> Phone office: +47 55584179/li>                                li> Cell phone: +47 45238987 /li>                                li> Office: Realfagbygget, Allégaten 41, Room 4A7d/li>                                li> Office mail address: br>                                     p styleborder:1px; border-style:solid; border-color:#999999; padding: 1em;>University of Bergenbr>                                    Department of Mathematicsbr>                                    Postbox 7803br>                                    NO-5020 BERGENbr> NORWAY/p>/li>                                li> Private address:                                    p styleborder:1px; border-style:solid; border-color:#999999; padding: 1em;>Mølleveien 4br>                                    NO-5067 BERGENbr> NORWAY/p>                                /li>                                 /ul>                                								ul classicons>									li>a hrefhttps://facebook.com/hanszmk classicon brands fa-facebook-f>span classlabel>Facebook/span>/a>/li>									li>a hrefhttps://instagram.com/hanszmk classicon brands fa-instagram>span classlabel>Instagram/span>/a>/li>								/ul>							/article>						!-- Research -->							article idresearch>								h2 classmajor>Research/h2>                                ul>                                li>a href#res_overview>OVERVIEW/a>/li>                                li>  a href#publications>Publications, reverse chronologic order/a>/li>                                li> a hrefhttps://scholar.google.com/citations?user-oWmMI8AAAAJ>Publications, by citation/a>/li>                                li>a href#projects>Projects and software/a>/li>                                /ul>                            !-- A2Cheby picture -->                                span classimage main>img srcimages/A2Cheby.jpg alt/>a hrefhttp://hans.munthe-kaas.no/publ/munthe2012groups.pdf>Multivariate Chebyshev polynomials./a> Domain of A2-family./span>                       !-- A3Cheby picture -->                                span classimage main>img srcimages/Cheby_A3.jpg alt/>a hrefhttp://hans.munthe-kaas.no/publ/munthe2012groups.pdf>Multivariate Chebyshev polynomials./a> Domain of A3-family/span>                         !-- MKW picture -->                                span classimage main>img srcimages/mkw_coprod.jpg alt/>Coproduct of the a href>MKW Hopf algebra/a>/span>                         !-- Størmer pictrure -->								span classimage main>img srcimages/nordlys.jpg alt />a hrefhttp://hans.munthe-kaas.no/publ/iserles00lgm.pdf>Lie group integration/a> of Størmers problem/span>                               							/article>                 !-- Research Overview -->							article idres_overview>								h2 classmajor>Research overview/h2>                                 h3>Overview/h3>                                p>My research is in the borderland between pure- and applied mathematics and computer science. A recurring theme is the role of mathematical abstractions in computational science, both as a tool for constructing efficient algorithms and as an organizing principle for computational software. Thus, as an overall label, most of my work is within Foundations of Computational Mathematics./p>                                p>I am interested in applications of differential geometric techniques, geometric integration and structure preserving algorithms for solution of differential equations. Lie group integrators are numerical integration methods for differential equations built from coordinate independent operations such as Lie group actions on a manifold. Lie group integrators have been developed in tight cooperation between the research groups in Bergen, DAMTP Cambridge and mathematics NTNU./p>p>Analysis of numerical Lie group integrators lead us to the study of new types of formal power series for flows on manifolds. Lie-Butcher theory combines classical B-series for integration schemes with Lie series. This research activity has connections to many areas of mathematical research such as control theory, stochastic differential equations, renormalization, combinatorial Hopf algebra theory and non-commutative symmetric functions./p>p>In my PhD (1989) I, among other things, investigated FFTs for functions possessing crystallographic symmetries. After 2004, I have again found interest in this topic, due to connections between this theory and multivariate versions of Chebyshev polynomials. This is applied in the construction of spectral element methods based on triangular and simplicial subdivisions of the domain. A related topic is applications of Fourier transforms on groups, with applications in numerical linear algebra and image processing./p>p>My PhD work, for which I was awarded the Esso prize in 1999, was on numerical linear algebra and parallel algorithms. I was interested in applications of group theory in the construction of fast elliptic solvers, as well as an organizing principle for massively parallel computations. In the early 1990s I was writing software and developing algorithms for massively parallel computers, in particular FFTs and various algebraic techniques for routing permutations on massively parallel computers. I was also interested in construction of permutation networks, in particular I studied some generalized shuffle-exchange networks. These are based on interesting connections between permutation networks and the theory of linear shift registers./p>p>Object oriented program design is founded on the distinction between specification and implementation, or ‘what’ and ‘how’. This is a well established principle in core computer science.  In computational mathematics, however, software has traditionally been organized around coordinate based formulations and discrete representations. In the SOPHUS project, initiated around 1991, we investigated coordinate free formulations for numerical algorithm design and for numerical software. In particular we developed coordinate free formulations of tensor computations and this was also an initial motivation for the study of Lie group integrators. The DiffMan Matlab toolbox for solving differential equations on manifolds is based on the ideas of the SOPHUS C++ library./p>							/article>                                						!-- Work -->							article idteach>								h2 classmajor>Teaching/h2>								span classimage main>img srcimages/matsirk.jpg alt />small>Teaching em>‘Mattesirkelen’/em> for high school students/small>/span>								p>Munthe-Kaas has over more than three decades been lecturing courses in applied mathematcs, pure mathematics, and computer science at all university levels, from advanced seminars to introductory courses. Internationally he has given advanced courses at AIMS South Africa, at a CIMPA school in Brazil, at Morningside Centre in Beijng, Uppsala University Sweden, and he has given lecture series various research semesters./p>                                                                p>Teaching autumn 2021: Mat101 (precalculus)./p>                                                                p>Students who want master thesis projects: Please take contact./p>							/article>						!-- Outreach -->							article idoutreach>								h2 classmajor>Outreach/h2>								span classimage main>img srcimages/pic03.jpg alt />/span>								p>Lorem ipsum dolor sit amet, consectetur et adipiscing elit. Praesent eleifend dignissim arcu, at eleifend sapien imperdiet ac. Aliquam erat volutpat. Praesent urna nisi, fringila lorem et vehicula lacinia quam. Integer sollicitudin mauris nec lorem luctus ultrices. Aliquam libero et malesuada fames ac ante ipsum primis in faucibus. Cras viverra ligula sit amet ex mollis mattis lorem ipsum dolor sit amet.                                                                Lorem ipsum dolor sit amet, consectetur et adipiscing elit. Praesent eleifend dignissim arcu, at eleifend sapien imperdiet ac. Aliquam erat volutpat. Praesent urna nisi, fringila lorem et vehicula lacinia quam. Integer sollicitudin mauris nec lorem luctus ultrices. Aliquam libero et malesuada fames ac ante ipsum primis in faucibus. Cras viverra ligula sit amet ex mollis mattis lorem ipsum dolor sit amet.                                Lorem ipsum dolor sit amet, consectetur et adipiscing elit. Praesent eleifend dignissim arcu, at eleifend sapien imperdiet ac. Aliquam erat volutpat. Praesent urna nisi, fringila lorem et vehicula lacinia quam. Integer sollicitudin mauris nec lorem luctus ultrices. Aliquam libero et malesuada fames ac ante ipsum primis in faucibus. 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classmajor>Publications/h2>                                Reverse chronologic order:!-- INCLUDE PUBLICATIONS TABLE (fix: should be included as external file) ------------------->table>tr valigntop>td alignright classbibtexnumber>a namemunthe2020invariant>1/a>/td>td classbibtexitem>Hans Z Munthe-Kaas, Ari Stern, and Olivier Verdier. Invariant connections, Lie algebra actions, and foundations of  numerical integration on manifolds. em>SIAM Journal on Applied Algebra and Geometry/em>, 4(1):49-68,  2020. a hrefhzmunthekaas_bib.html#munthe2020invariant>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/munthe2020invariant.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namecurry2020planarly>2/a>/td>td classbibtexitem>Charles Curry, Kurusch Ebrahimi-Fard, Dominique Manchon, and Hans Z  Munthe-Kaas. Planarly branched rough paths and rough differential equations on  homogeneous spaces. em>Journal of Differential Equations/em>, 269(11):9740-9782, 2020. a hrefhzmunthekaas_bib.html#curry2020planarly>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/curry2020planarly.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namemunthe2019correction>3/a>/td>td classbibtexitem>Hans Z Munthe-Kaas and Alexander Lundervold. Correction to: On post-Lie algebras, Lie-Butcher series and  moving frames. em>Foundations of Computational Mathematics/em>, 19(1):241-241, 2019. a hrefhzmunthekaas_bib.html#munthe2019correction>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/munthe2019correction.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namefloystad2019universal>4/a>/td>td classbibtexitem>Gunnar Fløystad, Dominique Manchon, and Hans Z Munthe-Kaas. The universal pre-lie-rinehart algebras of aromatic trees. In em>International conference on Geometric and Harmonic Analysis  on homogeneous spaces and Applications in Honor of Professor Takaaki Nomura/em>,  pages 137-159. Springer, 2019. a hrefhzmunthekaas_bib.html#floystad2019universal>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/floystad2019universal.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namemunthe2018lie>5/a>/td>td classbibtexitem>Hans Z Munthe-Kaas and Kristoffer K Føllesdal. Lie-butcher series, geometry, algebra and computation. In em>Discrete Mechanics, Geometric Integration and Lie-Butcher  Series/em>, pages 71-113. Springer, 2018. a hrefhzmunthekaas_bib.html#munthe2018lie>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/munthe2018lie.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namecelledoni2018computation>6/a>/td>td classbibtexitem>E. Celledoni, G. Di Nunno, K. Ebrahimi-Fard, and H.Z. Munthe-Kaas, editors. em>Computation and Combinatorics in Dynamics, Stochastics and  Control/em>. Abel Symposia. Springer, 2018. a hrefhzmunthekaas_bib.html#celledoni2018computation>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/celledoni2018computation.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a nameebrahimi2017post>7/a>/td>td classbibtexitem>Kurusch Ebrahimi-Fard, Igor Mencattini, and Hans Munthe-Kaas. Post-Lie algebras and factorization theorems. em>Journal of Geometry and Physics/em>, 119:19-33, 2017. a hrefhzmunthekaas_bib.html#ebrahimi2017post>bib/a> | a hrefhttp://hans.munthe-kaas.no/ebrahimi2017post.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namemaclachlan2017butcher>8/a>/td>td classbibtexitem>Robert I McLachlan, Klas Modin, Hans Munthe-Kaas, and Oliver Verdier. Butcher series - A story of rooted trees and numerical methods  for evolution equations. em>Asia Pacific Mathematics Newsletter/em>, 7(1):1-11, 2017. a hrefhzmunthekaas_bib.html#maclachlan2017butcher>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/maclachlan2017butcher.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namecurry2017post>9/a>/td>td classbibtexitem>Charles Curry, Kurusch Ebrahimi-Fard, and Hans Munthe-Kaas. What is a post-Lie algebra and why is it useful in geometric  integration. In em>European Conference on Numerical Mathematics and Advanced  Applications/em>, pages 429-437. Springer, 2017. a hrefhzmunthekaas_bib.html#curry2017post>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/curry2017post.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namemunthe2016groups>10/a>/td>td classbibtexitem>Hans Z Munthe-Kaas. Groups and symmetries in numerical linear algebra. In em>Exploiting Hidden Structure in Matrix Computations:  Algorithms and Applications/em>, pages 319-406. Springer, 2016. a hrefhzmunthekaas_bib.html#munthe2016groups>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/munthe2016groups.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namemunthe2016aromatic>11/a>/td>td classbibtexitem>Hans Munthe-Kaas and Olivier Verdier. Aromatic Butcher series. em>Foundations of Computational Mathematics/em>, 16(1):183-215, 2016. a hrefhzmunthekaas_bib.html#munthe2016aromatic>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/munthe2016aromatic.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namemclachlan2016b>12/a>/td>td classbibtexitem>Robert I McLachlan, Klas Modin, Hans Munthe-Kaas, and Olivier Verdier. B-series methods are exactly the affine equivariant methods. em>Numerische Mathematik/em>, 133(3):599-622, 2016. a hrefhzmunthekaas_bib.html#mclachlan2016b>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/mclachlan2016b.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namemunthe2016integrators>13/a>/td>td classbibtexitem>Hans Munthe-Kaas and Olivier Verdier. Integrators on homogeneous spaces: isotropy choice and connections. em>Foundations of Computational Mathematics/em>, 16(4):899-939, 2016. a hrefhzmunthekaas_bib.html#munthe2016integrators>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/munthe2016integrators.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namefloystad2016pre>14/a>/td>td classbibtexitem>Gunnar Fløystad and Hans Munthe-Kaas. Pre-and post-lie algebras: The algebro-geometric view. In em>The Abel Symposium/em>, pages 321-367. Springer, 2016. a hrefhzmunthekaas_bib.html#floystad2016pre>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/floystad2016pre.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a nameebrahimi2015lie>15/a>/td>td classbibtexitem>Kurusch Ebrahimi-Fard, Alexander Lundervold, and Hans Z Munthe-Kaas. On the lie enveloping algebra of a post-lie algebra. em>Journal of Lie Theory/em>, 25(4):1139-1165, 2015. a hrefhzmunthekaas_bib.html#ebrahimi2015lie>bib/a> | a hrefhttps://arxiv.org/abs/1410.6350>http/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namelundervold2015algebraic>16/a>/td>td classbibtexitem>Alexander Lundervold and Hans Z Munthe-Kaas. On algebraic structures of numerical integration on vector spaces and  manifolds. em>Faà di Bruno Hopf Algebras, Dyson-Schwinger Equations, and  Lie-Butcher Series/em>, pages 219-263, 2015. a hrefhzmunthekaas_bib.html#lundervold2015algebraic>bib/a> | a hrefhttps://arxiv.org/abs/1112.4465>http/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a nameebrahimi2015post>17/a>/td>td classbibtexitem>Kurusch Ebrahimi-Fard, Alexander Lundervold, Igor Mencattini, Hans Z  Munthe-Kaas, et al. Post-Lie algebras and isospectral flows. em>SIGMA. Symmetry, Integrability and Geometry: Methods and  Applications/em>, 11:093, 2015. a hrefhzmunthekaas_bib.html#ebrahimi2015post>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/ebrahimi2015post.pdf>.pdf/a> /td>/tr>tr valigntop>td alignright classbibtexnumber>a namemunthe2014symmetric>18/a>/td>td classbibtexitem>Hans Z Munthe-Kaas, Gilles Reinout W Quispel, and Antonella Zanna. Symmetric spaces and Lie triple systems in numerical analysis of  differential equations. em>BIT Numerical Mathematics/em>, 54(1):257-282, 2014. a hrefhzmunthekaas_bib.html#munthe2014symmetric>bib/a> | a hrefhttp://hans.munthe-kaas.no/publ/munthe2014symmetric.pdf>.pdf/a> /td>/tr>/table>!-- END INCLUDE PUBLICATIONS TABLE ----------------------------------------------------------->                                p>a hrefhttp://hans.munthe-kaas.no/work/Papers.html>h3>Earlier publications/h3>/a>/p>                                hr>p>em>This file was generated by                                a hrefhttp://www.lri.fr/~filliatr/bibtex2html/>bibtex2html/a> 1.96./em>/p>                                                                  							/article>                            !-- End publications -->					/div>          				!-- Footer -->					footer idfooter>						p classcopyright>© HZMK   Design: a hrefhttps://html5up.net>HTML5 UP/a>./p>					/footer>			/div>		!-- BG -->			div idbg>/div>		!-- Scripts -->			script srcassets/js/jquery.min.js>/script>			script srcassets/js/browser.min.js>/script>			script srcassets/js/breakpoints.min.js>/script>			script srcassets/js/util.js>/script>			script srcassets/js/main.js>/script>			script srcassets/js/typed.js>/script>	/body>/html>

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