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MAST90068 |
Semester II 2012 |
Lecturer: Arun Ram, 174 Richard Berry, phone: 8344 6953, email: aram@unimelb.edu.au
Time and Location:
Lecture ????????Tuesday 9:00 - 10:00 Richard Berry 215
Lecture ??????????Friday 9:00-10:00 Richard Berry 215
Lecture/Practical ???????????Monday 12:00-1:00 Richard Berry 215
Announcements
- No books, notes, calculators, ipods, ipads, phones, etc at the exam.
- Tips to avoid freaking out:
- The assignments are designed to take "an average of 7 hours per week. This is an average.
- Tips for time management:
- It is much easier (and safer) to run 45 min per day to attain 12 hours in 4 weeks, than to run for 12 hours solid every fourth week on Sunday.
- To actually run 45 min, it takes me at least 15 min to psyche myself up and convince myself that it is actually not raining and so therefore I should go running, and after a 45 min run I always walk for 5 min and I always go home and have a glass of milk and tell my wife (at length) how cool I am for running 45 min per day. All in all, I waste a good 40 min when I go running for 45 min. If I were more efficient (and every so often, but rarely, I am) then it would only takes me 50 min.
- Measurement of time is a tricky thing and requires real discipline. Teaching and research faculty at University of Melbourne recently had to complete a survey on distribution of their time on the various activities of the job: Do I count the 6 times I had to go check my email and the weather and my iPhone in the time that I spend preparing my Commutative and Multilinear algebra lecture?
- Tips for exam preparation:
- The time that a 100m olympic runner (who wins a medal) is actually competing at the olympics is say (5 heats, 7sec each) 40 seconds. Successful performance during these 40 sec is impossible without adequate preparation.
- The time that a Representation Theory student spends on the final exam is 3 hours. Successful performance during these 3hours is .....
- Consultation hours are by appointment. Talk to me before or after class to make an appointment.
- Prof. Ram reads email but generally does not respond.
- The start of semester pack includes: Plagiarism (pdf file), Plagiarism declaration (pdf file), Academic Misconduct (pdf file), SSLC (pdf file), SSLC responsibilities (pdf file), SSLC timelines (pdf file), Beyond third year (pdf file), Vacation scholarships (pdf file), Local third ann (pdf file).
- It is University Policy that:
“a further component of assessment, oral, written or practical, may be administered by the examiners in any subject at short notice and before the publication of results. Students must therefore ensure that they are able to be in Melbourne at short notice, at any time before the publication of results” (Source: Student Diary).
Students who make arrangements that make them unavailable for examination or further assessment, as outlined above, are therefore not entitled to an alternative opportunity to present for the assessment concerned (i.e. a ‘make-up’ examination). - Printing arrangements from computer Lab G70: Students must use their Unicards to print documents. Locations for Unicard uploaders can be found at: http://www.studentit.unimelb.edu.au/images/facilities/autoloaders.gif
Subject Outline
The handbook entry for this course is at https://handbook.unimelb.edu.au/view/2011/MAST90068. The objective of the course listed there are:
- The geometry of Lie groups, and important examples coming from linear groups,
- Lie algebras, the exponential map, and the relation with Lie groups,
- Free groups, presentations, free products (with amalgamation),
- Basic category theory: categories, functors, natural transformations, adjoints. (Co)products, universal objects, (co)limits, especially pushouts and pullbacks,
- Homological algebra: (pro/in)jective objects, resolutions, chain complexes, homotopy, the snake lemma. Applications: Ext, Tor, group homology,
- Noncommutative algebra: semisimple rings, modules, Wedderburn theorem.
- prove results about Lie groups and algebras,
- give presentations of groups and algebras,
- construct and compute derived functors.
Main Topics
- (1) ???Categories
- (2) ???Modules
- (3) ???Algebras
- (4) ???Lie groups and Lie algebras
- (5) ???Enveloping algebras and quantum groups
- (6) ???Roots and weight and Weyl's theorem
- (7) ???Flag varieties and the Borel-Weil theorem
- (8) ???Affine Hecke algebras
- (9) ???Quiver Hecke algebras
- (10) ???Cohomology of flag varieties
- (11) ???Representations of symmetric groups
- (12) ???Loop groups and affine Grassmannians
Assessment
Assessment will be based on up to 60 pages of written assignments (75%: three assignments worth 25% each, due early, mid and late in semester), a and a two-hour written examination (25%, in the examination period).
The plagiarism declaration is available here FIX THIS LINK. The homework assignments are as follows:
- Assignment 1: Due 26 March 2012: ????
- Assignment 2: Due 30 April 2012: ???
- Assignment 3: Due 28 May 2012: ???
- The final exam will be 2 hours.
Resources part I: recommended Texts
- see http://ms.unimelb.edu.au/~ram/Teaching/RepThy2010/RepThy2010.html
- see http://ms.unimelb.edu.au/~ram/notes.html
- Wikipedia
- ????Atiyah and Macdonald, Introduction to commutative algebra, Addison-Wesley ???
- ????Bourbaki, Algebre, Chapt 1-9, ???
Resources part II: Lectures and lecture notes
- Lecture 1, 23 July 2012: ??? -- handwritten lecture notes (pdf file)
- Math Grammar: Definitions, Theorems and How to do Proofs (pdf file)
- Examples of proofs written in proof machine (pdf file)
- Lecture 2, 25 July 2012: ???? -- handwritten lecture notes (pdf file)
- Lecture 3, 27 July 2012: ??? - handwritten lecture notes (pdf file)
- Lecture 4, 30 July 2012: ???
- Lecture 5, 1 August 2012:
- Lecture 6, 3 August 2012:
- Lecture 7, 6 August 2012:
- Lecture 8, 8 August 2012:
- Lecture 9, 10 August 2012:
- Lecture 10, 13 August 2012:
- Lecture 11, 15 August 2012:
- Lecture 12, 17 August 2012:
- Lecture 13, 20 August 2012:
- Lecture 14, 22 August 2012:
- Lecture 15, 24 August 2012:
- Lecture 16, 27 August 2012:
- Lecture 17, 29 August 2012:
- Lecture 18, 31 August 2012:
- Lecture 19, 3 September 2012:
- Lecture 20, 5 September 2012:
- Lecture 21, 7 September 2012:
- Lecture 22, 10 September 2012:
- Lecture 23, 12 September 2012:
- Lecture 24, 14 September 2012:
- 17-29 September: MID SEMESTER BREAK
- Lecture 25, 1 October 2012:
- Lecture 26, 3 October 2012:
- Lecture 27, 5 October 2012:
- Lecture 28, 8 October 2012:
- Lecture 29, 10 October 2012:
- Lecture 30, 12 October 2012:
- Lecture 31, 15 October 2012:
- Lecture 32, 17 October 2012:
- Lecture 33, 19 October 2012:
- Lecture 34, 22 October 2012:
- Lecture 35, 24 October 2012:
- Lecture 36, 26 October 2012: