Email: fei dot qi at yale dot edu

Research Interest: Vertex algebraic structures in Mathematics and Physics, Mathematical Constructions of Quantum Field Theory

Work in progress

• Meromorphic open-string vertex algebras and modules over spheres.
• Second cohomology and the deformations of meromorphic open-string vertex algebras

Publications:

• The first cohomology, derivations and the reductivity of a (meromorphic open-string) vertex algebra, arXiv:1804.07424
• On the cohomology of meromorphic open-string vertex algebras, arXiv:1804.07423
• Representations of meromorphic open-string vertex algebras, arXiv:1801.08638
• Bud Coulson, Shashank Kanade, James Lepowsky, Robert McRae, Fei Qi, Matthew C. Russell, Christopher Sadowski, A motivated proof of the Göllnitz-Gordon-Andrews identities, Ramanujan Journal, September 2015.

• Classification to 2-dimensional Hom-Novikov algebras
• Solutions to associative Yang-Baxter equations up to dimension 5
• Construction of infinite dimensional Lie bialgebras and pre-Lie bialgebras

Current Teaching: Math 755, Vertex algebras and representations

• Lecture 1 (Jan. 23, 2019)
• Lecture 2 (Jan. 28, 2019)
• Lecture 3 (Jan. 30, 2019)
• Lecture 4 (Feb. 4, 2019)
• Lecture 5 (Feb. 6, 2019)
• Lecture 6 (Feb. 11, 2019)
• Lecture 7 (Feb. 13, 2019)
• Lecture 8 (Feb. 18, 2019)
• Lecture 9 (Feb. 20, 2019)
• Lecture 10 (Feb. 25, 2019)
• Lecture 11 (Feb. 27, 2019)
• Lecture 12 (Mar. 4, 2019)
• Lecture 13 (Mar. 6, 2019)
• Lecture 14 (Mar. 25, 2019)
• Lecture 15 (Mar. 27, 2019)
• Lecture 16 (Apr. 1, 2019)
• Lecture 17 (Apr. 3, 2019)
• Lecture 18 (Apr. 8, 2019)
• Lecture 19 (Apr. 10, 2019)
• Lecture 20 (Apr. 15, 2019)
• Lecture 21 (Apr. 17, 2019)
• Lecture 22 (Apr. 22, 2019)
• Lecture 23 (Apr. 24, 2019)
• Lecture 24 - 25 (Apr. 29 - May 1, 2019)

In Fall 2018 I taught Math 115a, Calculus of Functions of One Variable II

• Lecture 1 (Aug. 29, 2018): Syllabus (annotated), Lecture Notes
  Answers to the Practice, First Day Survey (designed by Dr. Smith), Worksheets of finding the area of the unit disk (designed by Dr. Smith)
  Before coming to class on Friday, you should finish reading 5.1 and 5.2. Also, you can watch Ghrist Lecture 25
  Please also make sure that you can receive the announcements sent in Canvas.

• Lecture 2 (Aug. 31, 2018): Lecture Notes, Details of discussion
  In case you are still not confident in playing with the sigma notation, please go over this introduction, then work on Section 2 of this worksheet.
  Before coming to class next Wednesday, you should finish reading 5.3 and 5.4 and finish the corresponding explorations.
  Also, you can watch Ghrist Lecture 26 and Ghrist Lecture 26 - Bonus

• Lecture 3 (Sep. 5, 2018): Lecture Notes, Details of discussion
  In case you need more practice with trigonometry functions, please use this booklet (from Sydney University). Please make sure you are absolutely comfortable with the first three chapters.
  Problem Set 1 is due tonight at 11:59PM. Please let me know if you have any issue uploading your work to Canvas.

• Lecture 4 (Sep. 7, 2018): Lecture Notes. All details are in the textbook. Please read!
  In addition to the book problems, you can also play with Problem 1191 - 1200 of the famous Demidovitch Problem book.
  You are now ready to work on Problem Set 2. You are advised to start working now.

• Lecture 5 (Sep. 10, 2018): Lecture Notes, Details (done in D & I), Details (done with implicit substitution)
  The problems I have done in the lecture are in general trickier than what you will see in the exam. If you are comfortable with these questions, you will have no problem getting a perfect score with integration by parts.
  For Problem 5.3.4.(f), you may use the method introduced in Example 2.8.1 of the textbook

• Lecture 6 (Sep. 12, 2018): Lecture Notes, Details
  Here is a handout from University of Adelaide recording the usual trig. identities.
  The sum and difference formulas at the end of Section 7.2 is not required for tests and exams. Still, it doesn't hurt to know more.

• Lecture 7 (Sep. 14, 2018): Lecture Notes, Details
  I have been using implicit substitutions in class, which is based on the knowledge of linear approximation and differentials. Here is a scan of Section 3.10 in Stewart's textbook that will help you to develop a conceptual understanding to differentials. You can also learn the knowledge from Ghrist Lecture 12 and Ghrist Lecture 15. Some practice problems can be found in Demidovich Section 2.6.1. Problem 712 to 745 are relevant, with solutions available.

• Lecture 8 (Sep. 17, 2018): Lecture Notes, Details
  For practice problems in the textbook, you can use Wolfram Alpha to check your solution.
  Caution: Do not attempt to use the step-by-step solutions generated by Wolfram Alpha in your problem set. Computers work on these integrals with an approach that is very different from what we human would do. It is very easy for us to recognize that.

• Lecture 9 (Sep. 19, 2018): Lecture Notes, Details
  Please see Section 9.4 for an explicit solution to the logistic model. You will find that it is less informative than what can be seen from the qualitative method.

• Lecture 10 (Sep. 21, 2018): Lecture Notes, Details
  Due to the conference I am currently attending, I had limited time and thus did not include a lot of details. In case you need me to include more details, please send me an email. I'll update the notes later when I have time.
  As I can observe from class and from email correspondences, people are starting to sacrifice sleep for other aspects of life. I strongly urge you not to do that, as I don't want you to regret in the same way I do when you reach my age.
  Plese read the recent research by Dr. Spira et. al regarding the relation between daytime sleepiness and alzheimer. Please also wathc the TED talk for the background concepts.

• Lecture 11 (Sep. 24, 2018): Lecture Notes. Please find details in the textbook.
  Please go over the graphs of common functions and figure out a way to understand them. Please also go over function transformations to see how to shift, stretch, compress and reflect the graph of a function.
  Please find the graphs of x^n on the following Desmos illustration (which is far better than my iPad drawing.)
  For solving polynomial inequalities, please go over Page 3 to 5 of my old note and the MathIsFun Note on solving quadratic inequalities.

• Lecture 12 (Sep. 26, 2018): Lecture Notes. I did not do any example in class. Please try the examples in the book.
  Please find Newton's law of cooling in Example 3 of Section 3.8 of Stewart. Here is a scan for your convenience.
  Please also take some time to try the Lab Project of Taylor Polynomials on Page 258 of Stewart. Here is a scan for your convenience. We will use Taylor polynomial to explain the error bounds on Friday. The knowledge will appear again when we discuss Taylor series. So it does not hurt to get a headsup now.

• Lecture 13 (Sep. 28, 2018): Lecture Notes, Supplementary Notes.
  The derivation of error bounds of left endpoint rule, right endpoint rule and midpoint rule can be found here (the writing should be futher improved.)
  Please find the derivations of errors bounds of trapezoidal rules here (organized by Ed Bender, UCSD.)

• Lecture 14 (Oct. 1, 2018): Lecture Notes. Details
  Please review L'Hospital's rule by going over Stewart 4.4. Here is a scan of the section.

• Lecture 15 (Oct. 3, 2018): Lecture Notes (did not actually cover in class).
  Here is the solutions to some problems I was asked during the office hours.
  The first midterm will be held on Thursday night 7PM - 8:30PM in Davis Auditorium. Good luck!

• Lecture 16 (Oct. 5, 2018): Lecture Notes (did not actually cover in class).
  I just managed to cover Part 1 to Part 3.3. Part 3.4 is too important to rush through. I'll leave it for the next lecture.

• Lecture 17 (Oct. 8, 2018): Lecture Notes (last time). Lecture Notes
  We just started to talk about geometric series. This special type of series is of great importance. Please make sure you have good knowledge to it.

• Lecture 18 (Oct. 10, 2018): Lecture Notes (last time). Lecture Notes (supposed to be for today)
  We did not even finish the lecture notes for last time, not to mention the notes supposed for today.
  Please read the textbook 11.1 to 11.3 at home. All the example problems I have been doing is from the textbook. For the next lecture, I intend to cover 11.3 and 11.4 altogether. I will go over the notes for 11.3 in a fast pace. Please treat it as a review instead of a lecture.
  Here is some hints to Problem 7.8.2 and 11.1.36. Hopefully they help.
  The scan of the exams will be sent to you at 7PM. Please report any issues on grading by 11:59PM. For fairness to students in other sections, issues reported after that will result in no change of grades.

• Lecture 19 (Oct. 16, 2018): Lecture Notes.
  

• Lecture 20 (Oct. 22, 2018): Lecture Notes.

• Lecture 21 (Oct. 24, 2018): Lecture Notes. Sorry for the delayed website update. My fall break is basically spent in bed struggling with cold, fever and serious coughing. I wish your fall break had been much better than mine.

• Lecture 22 (Oct. 26, 2018): Worksheet (by Prof. Addicott). Solutions
  Here is a collective table of facts that can be used to test the convergence of a series. This is probably better than the class handout, as comments are provided for each method. Also please find a flow chart that shows the general procedure in determining the convergence of a series. This helps you to determine where to start and what to do when stuck.

• Lecture 23 (Oct. 29, 2018): Lecture Notes.

• Lecture 24 (Oct. 31, 2018): Lecture Notes.

• Lecture 25 (Nov. 2, 2018): Lecture Notes.
  I wrote a set of notes that summarizes the common inequalities used in this class. Hopefully it helps to gain some confidence.

• Lecture 26 (Nov. 5, 2018): Handout, Details I should cover in class.
  As Nov. 6 is the election day, the problem set for this week will be due on Friday, instead of on Wednesday.

• Lecture 27 (Nov. 7, 2018): Lecture Notes
  I made some modifications in this final version. Please compare it with your notes in class.
  Please find the scan of review for Chapter 11 and go over the concept check section. Also you can use Problem 40 - 58 to check your understanding towards power series. In case you are stuck or have a question, don't hesitate to ask.
  Dr. Smith will be holding a review session on Sunday night. You are strongly advised to attend.

• Lecture 28 (Nov. 9, 2018): Lecture Notes
  

• Lecture 28 (Nov. 9, 2018): Lecture Notes

• Lecture 29 (Nov. 12, 2018): Lecture Notes

• Lecture 30 (Nov. 14, 2018): Lecture Notes (same as previous, as I did not finish the notes)

• Lecture 31 (Nov. 16, 2018): Lecture Notes

• Lecture 32 (Nov. 26, 2018): Lecture Notes

• Lecture 33 (Nov. 28, 2018): Lecture Notes

• Lecture 34 (Nov. 30, 2018): Lecture Notes

• Lecture 35 (Nov. 26, 2018): Lecture Notes

• Lecture 36 (Nov. 26, 2018): Lecture Notes

• Lecture 37 (Nov. 26, 2018): Lecture Notes

Past Courses

Fei Qi
Room 416, Dunham Laboratories
Department of Mathematics
Yale University
10 Hillhouse Avenue
New Haven, CT USA 06511