Vitali Retšnoi "Vector fields and Lie group representations" | University of Tartu

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Contacts of UT units

Faculty of Arts and Humanities
Faculty phone: 
+372 737 5341
Faculty address: 
Jakobi 2, rooms 116–121, 51005 Tartu
  • Dean's Office
    Faculty phone: 
    + 372 737 5341
    Faculty address: 
    Jakobi 2, rooms 116–121, 51005 Tartu
  • Institute of History and Archaeology
    Faculty phone: 
    +372 737 5651
    Faculty address: 
    Jakobi 2, 51005 Tartu
  • Institute of Estonian and General Linguistics
    Faculty phone: 
    +372 737 5221
    Faculty address: 
    Jakobi 2, 51005 Tartu
  • Institute of Philosophy and Semiotics
    Faculty phone: 
    +372 737 5314
    Faculty address: 
    Jakobi 2, rooms 309–352, 51005 Tartu
  • Institute of Cultural Research
    Faculty phone: 
    (+372) 737 5223
    Faculty address: 
    Ülikooli 16, 51003 Tartu
  • School of Theology and Religious Studies
    Faculty phone: 
    +372 737 5301
    Faculty address: 
    Ülikooli 18–310, 50090 Tartu
  • College of Foreign Languages and Cultures
    Faculty address: 
    J. Liivi 4, 50409, Tartu
  • Viljandi Culture Academy
    Faculty phone: 
    +372 435 5232
    Faculty address: 
    Posti 1, 71004 Viljandi
Faculty of Social Sciences
Faculty phone: 
+372 737 5957
Faculty address: 
Lossi 36, 51003 Tartu
  • Dean's Office
    Faculty phone: 
    + 372 737 5900
    Faculty address: 
    Lossi 36, 51003 Tartu
  • Institute of Education
    Faculty phone: 
    +372 737 6440
    Faculty address: 
    Salme 1a–29, 50103 Tartu
  • Johan Skytte Institute of Political Studies
    Faculty phone: 
    +372 737 5582
    Faculty address: 
    Lossi 36–301, 51003 Tartu
  • School of Economics and Business Administration
    Faculty phone: 
    +372 737 6310
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Institute of Psychology
    Faculty phone: 
    +372 737 5902
    Faculty address: 
    Näituse 2, 50409 Tartu
  • School of Law
    Faculty phone: 
    +372 737 5390
    Faculty address: 
    Näituse 20–324, 50409 Tartu
  • Institute of Social Studies
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    +372 737 5188
    Faculty address: 
    Lossi 36, 51003 Tartu
  • Narva College
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    Raekoja plats 2, 20307 Narva
  • Pärnu College
    Faculty phone: 
    +372 445 0520
    Faculty address: 
    Ringi 35, 80012 Pärnu
Faculty of Medicine
Faculty phone: 
+372 737 5326
Faculty address: 
Ravila 19, 50411 Tartu
  • Dean's Office
    Faculty phone: 
    +372 737 5326
    Faculty address: 
    Ravila 19, 50411 Tartu
  • Institute of Biomedicine and Translational Medicine
    Faculty phone: 
    +372 737 4210
    Faculty address: 
    Biomeedikum, Ravila 19, 50411 Tartu
  • Institute of Pharmacy
    Faculty phone: 
    +372 737 5286
    Faculty address: 
    Nooruse 1, 50411 Tartu
  • Institute of Dentistry
    Faculty phone: 
    +372 731 9856
    Faculty address: 
    Raekoja plats 6, 51003 Tartu
  • Institute of Clinical Medicine
    Faculty phone: 
    +372 737 5323
    Faculty address: 
    L. Puusepa 8, 50406 Tartu
  • Institute of Family Medicine and Public Health
    Faculty phone: 
    +372 737 4190
    Faculty address: 
    Ravila 19, 50411 Tartu
  • Institute of Sport Sciences and Physiotherapy
    Faculty phone: 
    +372 737 5360
    Faculty address: 
    Jakobi 5–205, 51005 Tartu
Faculty of Science and Technology
Faculty phone: 
+372 737 5820
Faculty address: 
Vanemuise 46–208, 51014 Tartu
  • Dean's Office
    Faculty phone: 
    +372 737 5820
    Faculty address: 
    Vanemuise 46–208, 51003 Tartu
  • Institute of Computer Science
    Faculty phone: 
    +372 737 5445
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Estonian Marine Institute
    Faculty phone: 
    +372 671 8902
    Faculty address: 
    Mäealuse 14, 12618 Tallinn
  • Institute of Physics
    Faculty address: 
    W. Ostwaldi 1, 50411 Tartu
  • Institute of Chemistry
    Faculty phone: 
    +372 737 5261
    Faculty address: 
    Ravila 14a, 50411 Tartu
  • Institute of Mathematics and Statistics
    Faculty phone: 
    +372 737 5860
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Institute of Molecular and Cell Biology
    Faculty phone: 
    +372 737 5027
    Faculty address: 
    Riia 23, 23b–134, 51010 Tartu
  • Tartu Observatory
    Faculty phone: 
    +372 737 4510
    Faculty address: 
    Observatooriumi 1, Tõravere, 61602 Tartumaa
  • Institute of Technology
    Faculty phone: 
    +372 737 4800
    Faculty address: 
    Nooruse 1, 50411 Tartu
  • Institute of Ecology and Earth Sciences
    Faculty phone: 
    +372 737 5835
    Faculty address: 
    Vanemuise 46, 51003 Tartu
Institutions
  • Library
    Faculty phone: 
    +372 737 5702
    Faculty address: 
    W. Struve 1, 50091 Tartu
  • Youth Academy
    Faculty phone: 
    +372 737 5581
    Faculty address: 
    Uppsala 10, 51003 Tartu
  • Institute of Genomics
    Faculty phone: 
    +372 737 4000
    Faculty address: 
    Riia 23b, 51010 Tartu
  • Museum
    Faculty phone: 
    +372 737 5674
    Faculty address: 
    Lossi 25, 51003 Tartu
  • University of Tartu Natural History Museum and Botanical Garden
    Faculty phone: 
    +372 737 6076
    Faculty address: 
    Vanemuise 46, 51003 Tartu
Support Units
  • Administrative Office
    Faculty phone: 
    +372 737 5606
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Centre for Entrepreneurship and Innovation
    Faculty phone: 
    +372 737 4809
    Faculty address: 
    Narva mnt 18, 51009, Tartu
  • University Office in Tallinn
    Faculty phone: 
    +372 737 6600
    Faculty address: 
    Teatri väljak 3, 10143 Tallinn
  • Estates Office
    Faculty phone: 
    +372 737 5137
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Finance Office
    Faculty phone: 
    +372 737 5125
    Faculty address: 
    Jakobi 4, 51005 Tartu
  • Grant Office
    Faculty phone: 
    +372 737 6215
    Faculty address: 
    Raekoja plats 9, 51004 Tartu
  • Information Technology Office
    Faculty phone: 
    +372 737 6000, IT-help: +372 737 5500
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Human Resources Office
    Faculty phone: 
    +372 737 5145
    Faculty address: 
    Ülikooli 18, rooms 302 and 304, 50090 Tartu
  • Internal Audit Office
    Faculty address: 
    Ülikooli 18-244, 51005 Tartu
  • Marketing and Communication Office
    Faculty phone: 
    +372 737 5687
    Faculty address: 
    Ülikooli 18, rooms 102, 104, 209, 210, 50090 Tartu
  • Office of Academic Affairs
    Faculty phone: 
    +372 737 5620
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • Procurement Office
    Faculty phone: 
    +372 737 6632
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Rector's Strategy Office
    Faculty phone: 
    +372 737 5600
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • Student Council
    Faculty address: 
    Ülikooli 18b, 51005 Tartu
  • University of Tartu Press
    Faculty phone: 
    +372 737 5945
    Faculty address: 
    W. Struve 1, 50091 Tartu
Other Units
  • University of Tartu Academic Sports Club
    Faculty phone: 
    +372 737 5371
    Faculty address: 
    Ujula 4, 51008 Tartu
  • Tartu Student Village
    Faculty phone: 
    +372 740 9959
    Faculty address: 
    Narva mnt 25, 51013 Tartu
  • Tartu Students’ Club
    Faculty phone: 
    +372 730 2400
    Faculty address: 
    Kalevi 24, 51010 Tartu
  • Tartu University Hospital
    Faculty address: 
    L. Puusepa 1a, 50406 Tartu
  • University of Tartu Foundation
    Faculty phone: 
    +372 737 5852
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • View all other units

Vitali Retšnoi "Vector fields and Lie group representations"

Date: 
16.11.2012 - 14:15 to 16:15

Supervisor: Maido Rahula, emeriitprofessor, TÜ matemaatika instituut
Opponents:
Vladimir Balan, professor, Bukaresti Polütehniline Ülikool, Rumeenia
Kaarin Riives-Kaagjärv, füüs.-mat.kand., Eesti Maaülikool, Eesti

Summary:
One of the most significant tools in differential geometry and global analysis, in continuous environment mechanics and dynamical systems is the notion of vector field. In the current thesis the vector field is considered as follows. First, the vector field can be interpreted as a differential operator and as a stop-frame of a movement. Second, a manifold can be projected by vector field onto the space of invariants, and this involves classification of singularities. Third, the vector field itself can be projectable, which allows to obtain the necessary symmetries and invariants from other structures (for instance, from the jet space). The central notion of this thesis is the Lie derivatives of tensor fields. The Lie differentiation technique is developed in nonholonomic (noncoordinate) basis, where an important role is played by derivation formulas together with the nonholonomy object. There is introduced an integration of tensor fields as a reverse process to the Lie differentiation. This definition generalizes the notion of integral of an ordinary function. A few geometrical examples included in the text clarify the topic being discussed. The Lie derivatives are infinitesimal versions of representation of a diffeomorphism group on tensor fields. In this regard, the structure of a tangent group of a Lie group is studied, and is shown how general linear group GL(n,R) acts on itself by left and right translations, and by interior automorphisms (adjoint representation). In this thesis the structure of the space of infinite jets is studied. In particular, analogously to the process, when a smooth map induces an infinite jet, the composition of smooth maps induces a composition of jets. The problem is how to define the jet composition in such a way that the definition does not depend on a choice of maps. The problem leads to another question: how the corresponding total differentiation operators and Cartan forms are related under the jet composition. The answers are given in the form of convenient recurrence formulas.

Organizer: 
Location: 
J. Liivi Street 2, room 403
Event category: