Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
Modules | Credits | TAF | SSD |
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One course chosen from the following
One course chosen from the following
2° Year activated in the A.Y. 2013/2014
Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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One course chosen from the following
One course chosen from the following
Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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One course chosen from the following
One course chosen from those that will be activated from the following
Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Differential geometry and topology (2012/2013)
Teaching code
4S001100
Credits
12
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/03 - GEOMETRY
The teaching is organized as follows:
Modulo 1
Modulo 2
Learning outcomes
Module: 1
Learning objectives:
The course provides an introduction to differentiable manifolds
and Riemannian geometry; it will possess a quite concrete character and will be based
on examples emerging from other areas of mathematics as well.
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Program
Module: 1
Syllabus:
Multilinear algebra.
Differentiable manifolds.
Lie groups.
Tensor calculus. Lie group actions on manifolds and their orbit spaces.
Riemannian manifolds.
Levi-Civita connection.
Curvature tensors (Riemann, sectional, Ricci, scalar).
Geodesics and their variational aspects.
Exponential map.
Riemannian geometry of Lie groups.
Module: 2
First Part:
0) Integration on manifolds and Stokes Theorem
1) Riemannian Geometry: connections, parallel transport, curvature
tensors, Levi-Civita connection, geodesics and applications (Chap. 1 and 2
of Chavel's Book "Riemannian Geometry, a modern Introduction" (2nd
Edition, Cambridge University Ppress, 2006).
2) Morse theory: Morse lemma and applications ( J. Milnor "Morse Theory" ,
Annals of Mathematics Studies, Princeton University Press).
3) De Rham cohomology and applications (Chap.1 of Bott, Tu "Differential
Forms in Algebraic Topology" , Graduate Texts in Mathematics, 82).
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Examination Methods
Exam methods (1st module): written test, immediately followed by an oral exam. The final grade will be assigned after completion of the second module.
Teaching materials e documents
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diffgeotopo-19-2-13 (it, 150 KB, 2/19/13)
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diffgeotopo-I (it, 281 KB, 10/31/12)
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diffgeotopo-II (it, 3914 KB, 11/3/12)
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diffgeotopo-III (it, 2598 KB, 11/3/12)
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diffgeotopo-IV (it, 221 KB, 11/6/12)
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diffgeotopo-IX (it, 390 KB, 11/16/12)
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diffgeotopo-V (it, 225 KB, 11/9/12)
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diffgeotopo-VI (it, 257 KB, 11/9/12)
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diffgeotopo-VII (it, 347 KB, 11/12/12)
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diffgeotopo-VIII (it, 188 KB, 11/16/12)
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diffgeotopo-X-1-bad (it, 1350 KB, 11/19/12)
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diffgeotopo-X-2-bad (it, 649 KB, 11/19/12)
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diffgeotopo-XI (en, 294 KB, 11/23/12)
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diffgeotopo-XII (en, 550 KB, 11/26/12)
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diffgeotopo-XIII (en, 285 KB, 12/17/12)
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diffgeotopo-XIII-corrections (it, 93 KB, 4/11/13)
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diffgeotopo-XII-p.15 (it, 43 KB, 11/30/12)
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diffgeotopo-XIV (en, 559 KB, 12/17/12)
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diffgeotopo-XIX (en, 304 KB, 12/14/12)
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diffgeotopo-XV (en, 491 KB, 11/30/12)
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diffgeotopo-XVI (en, 200 KB, 12/3/12)
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diffgeotopo-XVII (en, 493 KB, 12/7/12)
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diffgeotopo-XVIII-1 (en, 323 KB, 12/10/12)
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diffgeotopo-XVIII-2 (en, 181 KB, 12/10/12)
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diffgeotopo-XX (en, 545 KB, 12/21/12)
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diffgeotopo-XX-addendum (it, 30 KB, 5/28/13)
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diffgeotopo-XX-addendum2 (it, 30 KB, 5/28/13)
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official-programme-1st module 12/13 (en, 37 KB, 12/20/12)