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Seminar
Master class

Master class matematik

Symbolsk dynamik og operatoralgebraer
Unge danske og norske matematikere mødes

Informasjon:
22. juli 2015 - 6. august 2015

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Denne master class vil introducere kandidat- og ph.d.-studerende til samspillet mellem symbolsk dynamik og operatoralgebraer. De to felter har de sidste 35 år haft et frugtbart samarbejde, ikke mindst på grund af danske og norske matematikere. Master classen vil bestå af to dele: i den første del vil de studerende blive introduceret til symbolsk dynamik af Douglas Lind, og i den anden del vil de studerende arbejde med operatoralgebraer knyttet til dynamiske systemer under vejledning af Mark Tomforde.

Emne & formål

Symbolsk dynamik er studiet af den diskrete tidsudvikling af systemer med endeligt mange tilstande. Det anvendes blandt andet til at studere mere generelle systemers tidsudvikling og til at lagre data effektivt i computere. Studiet af operatoralgebraer startede som en matematisk formalisering af kvantemekanik. Det har siden udviklet sig til en selvstændig disciplin der dog ofte søger kontakten med fysik og andre grene af matematikken. Danske og norske matematikere har længe studeret sammenspillet mellem symbolsk dynamik og operatoralgebraer. Det er et aktivt forskningsemne på universiteterne i København, Odense, Oslo, Thorshavn og Trondheim, og på postdoc-niveau og op er der tradition for samarbejde (bl.a. ved konferencer på Lysebu og Schæffergården). Vi forventer at emnet forbliver stærkt i både Danmark og Norge og ønsker at sikre at de fremtidige generationer også samarbejder på tværs af Kattegat. Vores formål er således at vække de studerendes interesse for emnet og sikre at de tidligt skaber et dansk-norsk netværk.

Datoer

Første del: 22.–26. juli på Schæffergården. Anden del: 2.–6. august på Lysebu.

Struktur

Master classens to dele vil begge strække sig over fem dage, og de vil have den samme overordnede struktur. Der vil blive lagt vægt på projektarbejde frem for forelæsning for at de studerende kan interagere direkte med masteren. Projekterne vil bestå af mindre resultater med bevis, konsekvenser og belysende eksempler. Før hvert af de to ophold, vil de studerende blive tildelt relevant læsning med tilhørende opgaver. Udover at fungere som introduktion til de basale begreber vil dette giver masteren mulighed for på dag 1 at danne sig et indtryk af de studerendes faglige niveau, udfordringer og interesser.

Masterne

Douglas Lind fra University of Washington har indvilliget i at være master for første del. Lind har været en konstant bidragyder til mange områder af dynamik. Han er måske bedst kendt som en af forfatterne til “An Introduction to Symbolic Dynamics and Coding”, en af de mest brugte lærebøger til introduktionskurser i symbolsk dynamik, samt en fremragende reference for forskere (den er blevet citeret mere end 620 gange ifølge MathSciNet).

Mark Tomforde fra University of Houston har indvilliget i at være master for anden del. Tomforde er en førende forsker inden for grafalgebraer, en klasse af operatoralgebraer der er forbundet med symbolsk dynamik. Han har også stor interesse for formidling af matematik og har bl.a. startet outreach-programmet CHAMP der bringer unge fra belastede områder i Houston i forbindelse med universitetet gennem ugentlige matematiktimer.

De har begge udtrykt begejstring for og stort engagement i den foreslåede master class. De agter at samarbejde tæt så første og anden del knyttes godt sammen, og sørgede derfor for at blive præsenteret for hinanden ved AMS’ JMM15 og gik allerede da i gang med planlægningen.

Programansvarlige:

Sara Esther Arklint, Postdoc (50%) & center administrator (50%) at Centre for Symmetry and Deformation, University of Copenhagen.
Adam Peder Wie Sørensen, Postdoktor ved University of Oslo 

Deltakere

Petter Kjeverud Nyland, NTNU
Nicholas Gauguin Houghton-Larsen, KU
Thomas Gotfredsen, SDU
Ulrik Enstad, NTNU
Lars Mølgaard, AU
Benjamin Randeris Johannesen, AU
Thomas Schmidt, AU
Matthew Aadne, UiO
Marius Lie Winger, NTNU
Helene Svane, AU
Peter Madsen, AU
Lars Andreas Van Woensel Kooy Tveiten, UiO
Siver K. Volle, UiO
Adam Sørensen, UiO
Mark Tomforde, Houston
Doug Lind, Seattle
Sara Arklint, KU

Schæffergården Denmark
Wednesday, July 22nd 2015

12:30 – 13:00

Arrival and registration

 

13:00 – 14:00

Lunch in Restaurant Wohlert

 

14:15 - 14:45

Welcome and introduction to Fondet for dansk-norsk samarbejde

 

 

 

Anne Mette Eckholdt, Fondet for dansk-norsk samarbejde

 

14.45 – 16.30

Dynamical systems, what are they good for? An overview of dynamical systems and their many applications

 

 

Douglas Lind

 

16:30 -17.00

Check in to rooms. Coffee and cake.

 

17:00 – 18:30

Plenum discussion of pre-master class reading.

 

 

Douglas Lind

 

19:00 – 21:00

Dinner in Restaurant Wohlert

 

21:00 -

Casual dessert in the cafe. The bar is open.

 

Schæffergården Denmark
Thursday, July 23rd 2015

07:00 – 09:00

Breakfast in Restaurant Wohlert

 

09:15 – 12.00

Introduction to Dynamical Systems. A thorough introduction to the core concepts of dynamical systems.

 

 

Douglas Lind

 

12.00 – 13:00

Lunch in Restaurant Wohlert

 

13:00 – 14.00

Presentation of the projects students can work on.

 

14.00 – 18.00

Spread out across the conference center and work in small groups on the projects. Coffee and cake available from the cafe.

 

18:00 – 20:00

Dinner in Restaurant Wohlert

 

20:00 -

Social Night

 

Schæffergården Denmark
Friday, July 24th 2015

07:00 – 09:00

Breakfast I Restaurant Wohlert

09:15 – 11:00

Other topics in Dynamical Systems.

 

Douglas Lind

11.00 – 14.00

We will ride bikes to the beach and have our lunch there.

14:00 – 18:00

Spread out across the conference center and work in small groups on the projects. Coffee and cake available from the cafe.

18:00 – 20:00

Dinner in Restaurant Wohlert

20:00 -

Casual dessert in the cafe. The bar is open.

Schæffergården Denmark
Saturday, July 25th 2015

08:00 – 10:00

Breakfast in Restaurant Wohlert

10:15 – 12:00

Students present their work I.

12:00 – 13.00

Lunch in Restaurant Wohlert

13:15 – 14:00

Students present their work II.

14.00 – 15:00

Coffee break in the cafe

15:00 – 16:00

Prepare a surprise for the dinner under the guidance of chefs

18:00 – 20:00

Dinner in Restaurant Wohlert

20:00 -

Coffee in the cafe. The bar is open.

Schæffergården Denmark
Sunday, July 26th 2015

08:00 – 10:00

Breakfast in Restaurant Wohlert

10:00 – 10:30

Check out from rooms

10:30 – 11:15

Open problems in Dynamical Systems.

 

Douglas Lind

11:15 – 11:30

Coffee break

11:30 – 12.00

Evaluation of the master class in plenum.

 

Sara Esther Arklint and Adam Peder Wie Sørensen

12:00 – 13:00

Lunch in Restaurant Wohlert

Lysebu Norway
Sunday, August 2nd 2015

12:30 -13:00

Arrival and registration

13:00 – 14.00

Lunch in Restaurant

14:15 - 14:45

Welcome to Lysebu

 

Per Ivar Vaagland, Fondet for dansk-norsk samarbejde

14.45 – 16.30

Operator algebras, algebras, and dynamical systems, how are they connected? An overview of the plentiful connections between operator algebras and dynamical systems

 

 

Mark Tomforde

16.30 – 17:00

Check in to rooms. Coffee and cake.

17.00 – 18.30

Plenum discussion of pre-master class reading.

 

Mark Tomforde

19:00 – 21:00

Dinner in the Restaurant

21:00 -

Coffee in Giljestuen. The bar is open.

Lysebu Norway
Monday, August 3rd 2015

07:00 – 09:00

Breakfast in Restaurant

09:15 – 12:00

Classification of simple graph C*-algebras, and simple Leavitt path algebras.

 

Mark Tomforde

12:00 – 13:00

Lunch in Restaurant

13:00 – 14:00

Presentation of projects students can work on.

14:00 – 18:00

Spread out across the conference center and work in small groups on the projects. Coffee and cake available in the conference room.

18:00 – 20:00

Dinner in Restaurant

20:00 -

Coffee in Giljestuen. The bar is open.

Lysebu Norway
Tuesday. August 4th 2015

07:00 – 09:00

Breakfast in Restaurant

09:15 – 10:00

Classification when the Graph is Not Finite

 

Mark Tomforde

11:00 – 13.00

Walk  to Øvresetertjern/Tryvann. We will meet our guide Reidun and have lunch in the lavvo.

14:00 – 18:00

Spread out across the conference center and work in small groups on the projects. Coffee and cake available in conference room.

18:00 – 20:00

Dinner in Restaurant

20:00 -

Coffee in Giljestuen. The bar is open.

Lysebu Norway
Wednesday, August 5th 2015

07:00 – 09:00

Breakfast in Restaurant

09:15 – 12:00

Students present their work I

12:00 – 13:00

Lunch in Restaurant
13:00 - 14:00 Students present their work II
14:00 - 14:30 Bus transportation from Lysebu to Holmenkollen

14:30 – 16:00

Visit to the Ski Museum, go up in the ski jump Holmenkollen and maybee some of us wants to try the ski simulator? Bus pick-up and return to Lysebu at 16:00 hours

18.00 -

Closing Dinner in Skogstuen

Lysebu Norway
Thursday, August 6th 2015

07:00 – 09:00

Breakfast in Restaurant

09:00 - 10:00

Check Out from Rooms

10:30 – 11:15

Further interactions with Dynamics and Open problems

 

Mark Tomforde

11:15 – 11.30

Coffee Break

11:30 – 12:00

Evaluation of the master class in plenum.

 

Sara Esther Arklint and Adam Peder Wie Sørensen

12:00 – 13:00

Lunch in Restaurant and Goodbye

Medvirkende

  • Douglas Lind

    Education:
    University of Virginia, 1964–68; B.A. (with Highest Distinction) in Mathematics.
    Cambridge University, 1968–69; Mathematical Tripos, Part III.
    Stanford University, 1969–73; M.A. in Mathematics, 1971; Ph.D. in Mathematics,
    1973. Ph.D. advisor: Donald Ornstein; Dissertation title: Locally Compact
    Measure-Preserving Flows.
    Employment:
    University ofWashington, Assistant Professor, Department of Mathematics, 1976–
    78; Associate Professor, 1978–83; Professor, 1983–present; Department Chair,
    1993–98.
    Research Member, MSRI Program on Ergodic Theory and Additive Combinatorics,
    Autumn Semester, 2008.
    Visiting Professor, Department of Mathematics, Yale University, 2001–02, 2005–
    06, and 2009–2010.
    Professeur Invit´e, Universit´e Aix-Marseilles, June, 1993.
    Member, Mathematical Sciences Research Institute, Berkeley, California, Fall
    semester, 1992, Program on Symbolic Dynamics.
    Consultant to Heath Tecna Aerospace Company, Kent, Washington, June, 1989–
    December, 1990. Provided mathematical analysis for the manufacture of jet
    intake ducts by carbon filament winding using geodesics, and used this to
    develop FORTRAN software to drive filament winding machine.
    Visiting Faculty, IBM Watson Research Center, Yorktown Heights, New York,
    September-December, 1984.
    Member, Mathematical Sciences Research Institute, Berkeley, California, 1983–
    1984, Program on Ergodic Theory.
    Fellow, Institute for Advanced Studies, Hebrew University, Jerusalem, Israel,
    1975–76.
    Miller Research Fellow, University of California, Berkeley, California, 1973–75.

  • Mark Tomforde

    Positions Held
    Associate Professor, University of Houston, Houston, TX 2012{present
    Assistant Professor, University of Houston, Houston, TX 2006{2012
    Visiting Assistant Professor, College of William & Mary, Williamsburg, VA 2005{2006
    NSF Postdoctoral Fellow, University of Iowa, Iowa City, IA 2002{2005
    Instructor of Mathematics, Dartmouth College, Hanover, NH 1999{2002
    Education
    Ph.D. in Mathematics, Dartmouth College, Hanover, NH June 2002
    Advisor: Dana P. Williams
    Thesis: Extensions of graph C-algebras
    M.A. in Mathematics, Dartmouth College, Hanover, NH June 1999
    B.A. in Mathematics, Gustavus Adolphus College, St. Peter, MN June 1997
    graduated Summa Cum Laude and with departmental honors in Mathematics

  • Sara Arklint

    Programansvarlig

    Postdoc, Københavns Universitet.

    Arklint fik sin ph.d. i 2012. Hendes forskning omhandler struktur og K-teoretisk klassifikation af de dynamisk inspirerede Cuntz–Krieger-algebraer.

  • Adam Sørensen

    Programansvarlig

    Postdoc, Universitetet i Oslo.

    Sørensen fik sin ph.d. i 2013. Han arbejder blandt andet med at klassificere grafalgebraer ved hjælp af teknikker fra symbolsk dynamik.

  • Anne Mette Eckholdt

    Koordinator og værtinde for Masterclassen på Schæffergården

    Anne Mette Eckholdt arbejder som fondssekretær for Fondet for dansk-norsk samarbejde på Lysebu

  • Aja Bugge

    Koordinator og værtinde for Masterclassen på Lysebu

    Aja Bugge arbejder som rådgiver i Fondet for dansk-norsk samarbejde på Schæffergården

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