Asymptotics of Operator Semigroups

Lead Research Organisation: University of Oxford
Department Name: Mathematical Institute

Abstract

Many physical, biological and economic systems which are evolving in time can be modelled by differential equations whose solutions can be studied via operator semigroups. Typical examples include models of diffusion of heat in a body, wave motions of many kinds and populations of biological systems.

Such equations usually cannot be solved explicitly. Nevertheless one can often find some information about the solutions, such as their long-time behaviour. For example, one may be able to show that the quantity under examination decays (or grows, or oscillates) by analysis of the equations, and to estimate the rate of decay (or growth). In recent years there has been much research into the rates of decay of the energy of damped waves, and operator semigroups have been used to give precise estimates in that case.

This research will build on the previous work in this area. It is hoped to be able to provide general results determining more precisely when decay occurs and to improve the estimates for the rates of decay when quantities other than energy are being examined. Moreover we hope to gain a better understanding of mixed systems where the question whether the solutions decay or grow depends on the initial data.

Planned Impact

The planned research may have direct impacts in operator theory, complex analysis, partial differential equations, control theory, dynamical systems and differential geometry, which may benefit researchers in those areas. The applications to partial differential equations and control theory may provide indirect benefit to physicists, biologists and engineers. One of the most important results on stability semigroups (the ABLV theorem) has been applied in numerous such ways. Moreover results on rates of decay (of energy of waves, for example) have clear relevance to many physical problems. It is not possible to say what impacts the research may have on society in general as any such effects are unlikely to emerge for many years.

The PI, VR and RA will each alert mathematicians to this work by circulating and posting preprints, and by giving talks in seminars and conferences in the UK and around the world. The PI and VR have already given several such talks on the research on stabilty and quasi-hyperbolicity that has already been carried out. We have organised workshops on Asymptotics of Operator Semigroups in Oxford in 2009 and Luminy, France in 2011. We expect to have opportunities to explain our research to specialists in evolution equations and partial differential equations, and to discuss potential applications, at similar events during and after the work on the project.

The PI and the VR have worked together intermittently on various occasions in the last 10 years, and both have many contacts in operator theory already. The PI has already collaborated with a specialist in wave equations and PDEs (T. Duyckaerts) in work on energy decay, and we expect to expand our contacts to include others in that field. The VR has already collaborated with a specialist in complex analysis (A. Borichev). One part of the project related will require expertise in differential geometry, which we will initially seek in Oxford but the contact is likely to expand to
other geometers.

Publications

10 25 50
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Paunonen L (2017) Asymptotics for Infinite Systems of Differential Equations in SIAM Journal on Control and Optimization

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Rozendaal J (2019) Optimal rates of decay for operator semigroups on Hilbert spaces in Advances in Mathematics

 
Description We have obtained very precise results about the rate of decay of solutions of classes of evolution equations, assuming that one has quantified the properties of the system driving the evolution. Arising from this we have obtained more information about functional calculus of unbounded operators, and its relevance for finding rates of decay.

In addition we have solved complex systems of differential equations, such as those that model wave propagation through rough interfaces with corners and edges, and constructed the solutions explicitly from boundary data by the method of layer potentials.
Exploitation Route The results on rates of decay may be applied to estimate or predict the rate of decay of damped waves of various forms, or to various types of dynamical systems. The resutls on functional calculus will assist future work on rates of decay.

The results for complex systems might be used to improve models of wave behaviour, such as that of light, sound or electricity, through rough materials in real world applications.
Sectors Aerospace, Defence and Marine,Agriculture, Food and Drink,Construction,Electronics,Energy,Environment,Transport,Other

 
Description Results on functional calculus and the product rule are currently being used to advance the theory of subordinate semigroups such as arise in probability theory. Methods used to obtain sharp for decays of decay are being used to obtain similar results in other situations. The results for complex systems have been used to solve systems of differential equations that model wave propagation through inhomogeneous media. A recent advance has considerably extended the scope of the results, and applications of it have been identified.
First Year Of Impact 2013
Sector Energy,Other
Impact Types Societal

 
Description Borichev 
Organisation Aix-Marseille University
Country France 
Sector Academic/University 
PI Contribution Collaborative research within the scope of the project
Collaborator Contribution One individual collaborated with our research
Impact A paper has been published
Start Year 2012
 
Description Gomilko 
Organisation Nicolaus Copernicus University in Torun
Country Poland 
Sector Academic/University 
PI Contribution Yuri Tomilov and I collaborated with Alexander Gomilko on research within the scope of the grant.
Collaborator Contribution Alexander Gomilko collaborated with Yuri Tomilov and me on research within the scope of the grant
Impact One paper has been published, and one paper has been submitted
Start Year 2012
 
Description Paunonen 
Organisation Tampere University of Technology
Department Department of Mathematics
Country Finland 
Sector Academic/University 
PI Contribution Collaborative research on rates of decay of certain systems
Collaborator Contribution Collaborative research on rates of decay of certain systems
Impact jOint paper by Batty, Paunonen, Seifert within the EPSRC grant; several papers by Paunonen and Seifert
Start Year 2014
 
Description Analysis Seminar (Cardiff) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Several members of the audience asked questions about the underlying research and possible applications

The audience showed interest in the connections between Tauberian theory, operator semigroups, and applications to dampe wave equations and dynamical systems
Year(s) Of Engagement Activity 2014
 
Description Analysis Seminar (Glasgow) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Lecture in University of Glasgow Analysis Seminar.

Various connections with other research came to light
Year(s) Of Engagement Activity 2013
 
Description Analysis Seminar (Reading) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Lecture in Analysis Seminar, University of Reading.

Several people suggested connections with therir research
Year(s) Of Engagement Activity 2014
 
Description Analysis Seminar (University of Gothenburg) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Approximately 5 researchers in analysis, ranging from graduate students to professors, attended my scientific presentation. There were questions and discussions on my research afterwards. Several meetings were held with colleagues to collaborate on research.

Results were obtained for publication.
Year(s) Of Engagement Activity 2014
URL http://www.chalmers.se/en/departments/math/Pages/default.aspx
 
Description Analysis Seminar (University of New South Wales) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Approximately 15 researchers in analysis, ranging from graduate students to professors, attended my scientific presentation. There were questions and discussions on my research afterwards.


A colleague expressed interest in the research approach presented.
Year(s) Of Engagement Activity 2014
URL https://www.maths.unsw.edu.au/seminars
 
Description Analysis Seminar (Unversity of Edinburgh) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Approximately 30 researchers in analysis, ranging from graduate students to professors, attended my scientific presentation. There were questions and discussions on my research afterwards. A colleague discussed connections with their research.

Information was obtained on related research developments. A colleague suggested future possible collaboration.
Year(s) Of Engagement Activity 2014
URL http://www.maths.ed.ac.uk/events
 
Description Analysis Seminar Edinburgh 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Andrew Morris presented research in which he had participated during the grant
Year(s) Of Engagement Activity 2017
 
Description Bad Herrenalb 2019 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Passing on knowledge to researchers in evolution equations
Year(s) Of Engagement Activity 2019
 
Description Colloquium Queen's Belfast 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Charles Batty presented research carried out during and after the grant
Year(s) Of Engagement Activity 2017
 
Description Complex and Functional Analysis: Bedlewo 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Charles Batty presented research carried out during and after the grant
Year(s) Of Engagement Activity 2017
 
Description European Congress 2016 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Special session on Operator Semigroups. Talks by Charles Batty "Holomorphic functions which preserve holomorphic semigroups" and David Seifert "Ingham's theorem and rates of decay for operator semigroups"
Year(s) Of Engagement Activity 2016
 
Description Functional Analysis Seminar (University of Oxford) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Approximately 10 researchers in analysis, ranging from graduate students to professors, attended my scientific presentation. There were questions and discussions on my research afterwards.

A colleague expressed interest in the research approach presented.
Year(s) Of Engagement Activity 2013
URL https://www.maths.ox.ac.uk/events/past/639/
 
Description Functional Analysis Seminar (University of Oxford) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Approximately 10 researchers in analysis, ranging from graduate students to professors, attended my scientific presentation. There were questions and discussions on my research afterwards.

A colleague expressed interest in the research approach presented.
Year(s) Of Engagement Activity 2014
URL https://www.maths.ox.ac.uk/events/past/639/
 
Description Functional calculus and Harmonic analysis of semigroups; workshop, Besancon, France 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact My talk generated a number of questions, discussions and requests for further information

The talk helped to establish several collaboration links
Year(s) Of Engagement Activity 2014
URL http://trimestres-lmb.univ-fcomte.fr/Semigroups-workshop.html?lang=fr
 
Description Geometry and Analysis Seminar: Queen Mary 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Andrew Morris presented research in which he had been involved during the grant
Year(s) Of Engagement Activity 2017
 
Description Harmonic Analysis Conference Canberra 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Andrew Morris presented work in which he contributed during the grant
Year(s) Of Engagement Activity 2018
 
Description IWOTA Conference Chemniitz 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Charles Batty presented research carried out with Gomilko ad Tomilov during and after the grant
Year(s) Of Engagement Activity 2017
 
Description LMS Regional Meetitng (Sept 2016) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact One of three talks in London Mathematical Soicety Regional Meeting in Birmingham: Subject: Holomorphic functions which preserve holomorphic semigroups
Year(s) Of Engagement Activity 2016
 
Description Lille Seminar (March 2016) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk by David Seifert on "Quantified versions of Ingham's theorem"
Year(s) Of Engagement Activity 2016
 
Description London-Paris Analysis Seminar 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact lecture in Paris-London Analysis Seminar on rates of decay in Tauberian theorems

The audience suggested some applications
Year(s) Of Engagement Activity 2013
 
Description NBFAS meeting 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact David Seifert presented a recent extension of results obtained during the grant, by himsoelf and his collaborators, fo an audience from universities whihc are members fo the North British Functional Analysis Seminar
Year(s) Of Engagement Activity 2018
 
Description One of the organizers of the conference Operator Semigroups meet Harmonic Analysis, Complex Analysis and Mathematical Physics; in honour of Charles J. K. Batty 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The conference fixed the staate of the art in operator semigroups and established links between semigroup theory and related domains of Analysis
with the emphasis on outstanding contrubitions of Prof Batty

The conference raised interest of analysts in semigroup theory and its problems requring synergies and interplay of several parts of analysis.
A discussion of the impact of Prof Batty's research on the field was very helpful and showed a number of perspectives and challenges for a future development,
Year(s) Of Engagement Activity 2013
URL http://www.math.tu-dresden.de/herrnhut2013/
 
Description Research visit (Bordeaux University, France) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact My talk sparked questions and remarks from audience and interesting and useful discussions afterwards

After my talk, I've got several requests of my papers related to its subject
Year(s) Of Engagement Activity 2013
URL http://www.math.u-bordeaux1.fr/imb/article47.html
 
Description Semigroups Conference Delhi 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact In a sereid of lectures Ralph Chill presented results arising from the work carridd out by him, Batty and Tomilov during the grant, and some subsequent developments
Year(s) Of Engagement Activity 2017
 
Description Semigroups in Analysis (Bedlewo) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Charles Batty presented research carried out with Gomilko and Tomilov during and after the grant
Year(s) Of Engagement Activity 2017
 
Description Seminar (Bedlewo) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Type Of Presentation keynote/invited speaker
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited lecture at a conference Semigroups of Operators: theory and Applciations,.

Applications to chaotic behaviour
Year(s) Of Engagement Activity 2013
 
Description Seminar (Bedlewo) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Type Of Presentation paper presentation
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk at seminar on: Semigroups of Operators: Theory and Applications.

Several members of the audience saw connections between quasi-hyperbolic semigroups and their research
Year(s) Of Engagement Activity 2013
 
Description Seminar (Birmingham) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact David Seifert gave a one-hour research presntation on work carried out within the scope of the grant.
Year(s) Of Engagement Activity 2016
 
Description Seminar (Gotehnburg) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Presnetation by Andrew Morris of his research to researchers with similar interests
Year(s) Of Engagement Activity 2014
 
Description Seminar (Kent) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact I spoke about research carried out within the scope of the grant
Year(s) Of Engagement Activity 2015
 
Description Seminar (York) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact I spoke about research carried out within the scope of the grant
Year(s) Of Engagement Activity 2015
 
Description Seminar Presentation (University of Birmingham) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Approximately 15 researchers in analysis, ranging from graduate students to professors, attended my scientific presentation. There we questions and discussions on my research afterwards.

A professor suggested the possibility of a connection with my research and their recent results. The same professor commented that the presentation made the topic quite accessible to the audience and as a result he had gained a new appreciation and understanding of the topic.
Year(s) Of Engagement Activity 2013
URL http://talks.bham.ac.uk/talk/index/1200
 
Description Small Workshop in Operator Theory (Cracow, Poland) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I've got a number of pertinent questions and comments after the talk

The talk helped to establish a collaborative link and produced several requests for my publications
Year(s) Of Engagement Activity 2014
URL http://www.kzm.ur.krakow.pl/swot14/index.php
 
Description Sz. Nagy Centennial Conference (Szeged, Hungary) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact My talk generated a number of questions, comments and further discussions afterwads

The talk increased an interest of audience in subject of the talk and helped to establish several collaboration links
Year(s) Of Engagement Activity 2013
URL http://www.math.u-szeged.hu/SzNagy100/
 
Description TULKA Seminar (Karlsruhe, Germany) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The talk showed a genuine interest of audience in the presented results and received many interesting questions and remarks

My talk has helped to start a collaboration with two mathematicians and describe the start of the art in my research domain for PhD students and postdocs
Year(s) Of Engagement Activity 2014
URL http://www.math.kit.edu/iana3/seite/mi1w-tulka/de
 
Description The international workshop in operator theory and its applications (IWOTA), Amsterdam 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I have two talks at the meeting which generated a number of questions, comments and further discussions

After the talk, I've got several requests for my publications related to its subject
Year(s) Of Engagement Activity 2014
URL http://www.math.vu.nl/~ran/iwota2014/
 
Description Three cities Seminar, Dresden, Germany 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact The talk sparked a number of questions and comments

I've got several requests for a further information (slides of talk, related publications)
Year(s) Of Engagement Activity 2014
 
Description Workshop (Besancon) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Type Of Presentation keynote/invited speaker
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact About 45 researchers attended this 50-minute lecture at a conference on Harmonic Analysis and Functional Calculus of Semigroups in Besancon

The audience suggested that there would be implications for research into damped wave equations
Year(s) Of Engagement Activity 2014
URL http://trimestres-lmb.univ-fcomte.fr/Semigroups-workshop.html?lang=en
 
Description Workshop (ICMS Edinburgh) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Type Of Presentation keynote/invited speaker
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact About 30 researchers attrended this 25-minute talk

The audience suggested that there might be applications to dynamical systems
Year(s) Of Engagement Activity 2014
 
Description Workshop (IMPAN< Warsaw) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Charles Batty and David Seifert each gave two-one hour talka about research carried out within the scope of the grant
Year(s) Of Engagement Activity 2015
 
Description Workshop (IWOTA, Amsterdam) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Type Of Presentation paper presentation
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact About 60 researchers attended this 30-minute talk in a large international workshop

The audience suggested there might be applciations in operator theory
Year(s) Of Engagement Activity 2014
URL http://www.math.vu.nl/~ran/iwota2014/
 
Description Workshop (Lille) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Charels Batty and David Seifert gave separate talks about differnt parts of the research carried out within the scope of the grant
Year(s) Of Engagement Activity 2015
 
Description Workshop (Luminy) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I spoke about research carried out within the scope of the grant
Year(s) Of Engagement Activity 2015
 
Description Workshop (Luminy) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Research presentation and discussions by Andrew Morris with other researchers
Year(s) Of Engagement Activity 2014
 
Description Workshop at CIRM Luminy 2019 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Pass on knowledge to researchers interested in evolution equations
Year(s) Of Engagement Activity 2019
 
Description Workshop in Bedlewo Poland (April 2016) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Presentation on "Rates of convergence obtained from resolvent estimates for semigroup generators"
Year(s) Of Engagement Activity 2016
 
Description Workshop in Harmonic Analysis and Geometry (Australian National University) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Approximately 10 researchers in analysis, ranging from graduate students to professors, attended my scientific presentation. There were questions and discussions on my research afterwards.

A colleague suggested the applicability of my results to magnetic Schrodinger operators; we also discussed the possibility of combining my research and their recent results in a new collaboration. An audience member suggested the extension of my results to include coefficients in weak Lebesgue spaces.
Year(s) Of Engagement Activity 2015
URL http://maths.anu.edu.au/events/quadratic-estimates-additive-perturbations-first-order-systems
 
Description Workshop in harmonic analysis and geometry (ANU) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Talk by Andrew Morris on Quadratic estimates for additive perturbations of first-order systems
Year(s) Of Engagement Activity 2015
 
Description Workshop on Noncommutative Harmonic Analysis and Probability (KCL) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Other academic audiences (collaborators, peers etc.)
Results and Impact Lecture in the workshop on the subject of fine scales of rates of decay of operator semigroups.

The audience indicvated that there might be applications
Year(s) Of Engagement Activity 2013
 
Description Workshop on functional calculus (Besancon) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Research discussions between Andrew Morris and other researchers in harmonica analysis
Year(s) Of Engagement Activity 2014
 
Description Workshop operator semigroups (Herrnhut) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Type Of Presentation keynote/invited speaker
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Workshop talk.

This was a workshop on Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematicial Physics

There was a high level of interest in this talk
Year(s) Of Engagement Activity 2013
 
Description conference Function Spaces and Harmonic Analysis, Luminy, CIRM, France 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact My talk was met by audience with great interest and generated a number of discussions

I established two new collaboration links
Year(s) Of Engagement Activity 2014
URL http://feichtingertorresani.weebly.com/main-conference.html