Meeting times: MWF 3:30 - 4:30 PM online using Zoom. The Zoom link is: Math 603 Fall 2020 Zoom Meeting Link
Prof. Feingold's Office: WH-115, Office Phone: 777-2465. Send me an email to get my cell phone number. Office Hours: Online by appointment using Zoom. To schedule an appointment, please send me an email at least 2 hours ahead of time.
Here I will post links to pdf files of my lecture notes and to Panopto recordings of my lectures.
August 26: Lecture Notes pages 1-10 and Panopto recording of August 26 Lecture.
August 28: Lecture Notes pages 11-26 and Panopto recording of August 28 Lecture.
August 31: Lecture Notes pages 27-36 and Panopto recording of August 31 Lecture.
September 2: Lecture Notes pages 37-50 and Panopto recording of September 2 Lecture.
September 4: Lecture Notes pages 51-59 and Panopto recording of September 4 Lecture.
September 7: Lecture Notes pages 60-71 and Panopto recording of September 7 Lecture.
September 9: The lecture on Sept. 9 covered pages 65-73 of my notes, so those were already posted above except for 72-73, and Panopto recording of September 9 Lecture.
September 11: Lecture Notes pages 72-81 and Panopto recording of September 11 Lecture.
September 14: Lecture Notes pages 82-95 and Panopto recording of September 14 Lecture.
September 16: Lecture Notes pages 95-102 and Panopto recording of September 16 Lecture.
September 18: Lecture Notes pages 103-109 and Panopto recording of September 18 Lecture.
September 21: Lecture Notes pages 110-117 and Panopto recording of September 21 Lecture.
September 23: Lecture Notes pages 118-126 and Panopto recording of September 23 Lecture.
September 25: Lecture Notes pages 127-134 and Panopto recording of September 25 Lecture.
September 28: Lecture Notes pages 135-141 and Panopto recording of September 28 Lecture.
September 30: Lecture Notes pages 142-145 and Panopto recording of September 30 Lecture.
October 2: Lecture Notes pages 146-154 and Panopto recording of October 2 Lecture.
October 5: Lecture Notes pages 155-161 and Panopto recording of October 5 Lecture.
October 7: Lecture Notes pages 162-167 and Panopto recording of October 7 Lecture.
October 9: Lecture Notes pages 168-174 and Panopto recording of October 9 Lecture.
October 12: Lecture Notes pages 175-181 and Panopto recording of October 12 Lecture.
October 14: Lecture Notes pages 182-188 and Panopto recording of October 14 Lecture.
October 16: Lecture Notes pages 189-194 and Panopto recording of October 16 Lecture.
October 19: Lecture Notes pages 195-200 and Panopto recording of October 19 Lecture.
October 21: Lecture Notes pages 201-207 and Panopto recording of October 21 Lecture.
October 23: Lecture Notes pages 208-213 and Panopto recording of October 23 Lecture.
October 26: Lecture Notes pages 214-225 and Panopto recording of October 26 Lecture.
October 28: Lecture Notes pages 226-234 and Panopto recording of October 28 Lecture.
October 30: Lecture Notes pages 235-245 and Panopto recording of October 30 Lecture.
November 2: Lecture Notes pages 246-253 and Panopto recording of November 2 Lecture.
November 4: Lecture Notes pages 254-262 and Panopto recording of November 4 Lecture.
November 6: Lecture Notes pages 263-268 and Panopto recording of November 6 Lecture.
November 9: Lecture Notes pages 269-273 and Panopto recording of November 9 Lecture.
November 11: Lecture Notes pages 274-281 and Panopto recording of November 11 Lecture.
November 13: Lecture Notes pages 282-287 and Panopto recording of November 13 Lecture.
November 16: Lecture Notes pages 287-298 and Panopto recording of November 16 Lecture.
November 18: Lecture Notes pages 299-312 and Panopto recording of November 18 Lecture.
November 20: Here is an article about the Rogers-Ramanujan identities and two pdf files showing aspects of the root system of the rank 2 hyperbolic Kac-Moody Lie algebra I call ``Fib": Rogers-Ramanujan identities article, Rank2_Fib_Hyperbolic_RootSystem, Rank2_Fib_Hyperbolic_Positive_Roots. and Panopto recording of November 20 Lecture.
November 30: Lecture Notes pages 313-322 and Panopto recording of November 30 Lecture.
December 2: Lecture Notes pages 323-331 and Panopto recording of December 2 Lecture.
December 4: Lecture Notes pages 332-339 and Panopto recording of December 4 Lecture.
December 7: Panopto recording of December 7 Lecture.
Introduction to Lie Algebras and Representation Theory by James E. Humphreys, Springer-Verlag, Graduate Texts in Mathematics 9, 1972. ISBN-13: 978-0387900537, ISBN-10: 0387900535. Available in various formats from Amazon.com and other used book online shops.
Introduction to Lie Algebras (Springer Undergraduate Mathematics Series) by K. Erdmann and Mark J. Wildon, 2007. ISBN-13: 978-1846280405, ISBN-10: 1846280400. Available in various formats from Amazon.com and other used book online shops.
We will cover various parts of the textbooks and additional material as time allows.
As a topics course at the 600 level, this course involves sophisticated material which will require your serious attention in class, as well as effort to do problems from the textbooks. Various problems will be assigned or suggested during lectures, and written solutions should be submitted as pdf files within a reasonable amount of time. Class participation would be welcome, including questions, comments, and presentations of new material as described below.
Homework Problems (Humphreys):
Pages 5-6: Problems 4, 6, 11, 12.
Page 10: Problems 5, 11.
Page 14: Problems 4, 6.
Page 21: Problem 5.
Page 24: Problems 1, 2, 4.
Pages 30-31: Problems 2, 3, 6.
Page 35: Problems 6, 7.
Page 40: Problem 5.
Pages 46-47: Problems 3, 6, 10.
Page 54: Problems 6, 7, 9, 10.
Page 63: Problem 3.
Page 67: Problems 4, 6.
Pages 71-72: Problems 2, 5, 6, 7, 12, 13 (challenging!).
The course grade will be determined by the quality of presentations given and of homeworks completed. Although homeworks will not be precisely graded, the number of homeworks attempted and the quality of the attempts will be considered as a factor in determining your course grade. Collaboration among students on homeworks is reasonable and encouraged, but the solutions turned in should be written in your own words. As in professional collaborations, if the key ideas of a proof were worked out by more than one person, then the paper turned in should state clearly that the results were obtained in collaboration, and those involved should be named to give credit.
CLASS ATTENDANCE IS ABSOLUTELY ESSENTIAL. I hope that I can stimulate your interest and participation in the classroom, so that I am not the only one talking. If you are prepared to talk about some of the material, you may take the floor and do the lecturing. There is no better way of learning material than to teach it yourself to others. This can be done individually or in teams, but it takes some planning to be ready ahead of time. I cannot force you to do this, but if you have any serious interest in an academic career, I strongly recommend this preparation. The theoretical material is rather abstract, and it is necessary to understand the theory in order to do sensible calculations and interpret them correctly. Problems will be a combination of theory questions (proofs) and calculations appropriate for a course of this level. Lectures can be interrupted at any time for questions or comments. At the start of each class be ready to ask questions about homework problems or about the previous lecture.
My classes are presented online, attendance is still absolutely essential, but Panopto recordings of my lectures will be made and links posted on this webpage, along with pdf files of my written lecture notes. Classroom participation is still possible using Zoom, but student presentations would require a method of showing your writing and hearing your voice. An oral interview component during the final exam period may be substituted for a presentation.
File last modified on 12-7-2020.