Course Syllabus

Contact Information

Instructor: Michael Jablonski (for weeks 1-5), Peter Patzt (for weeks 6-11), Ricardo Mendes (for weeks 12-16)

Office Hours:  Mondays and Thursdays at 10:30-11:30am on Zoom and by appointment via Calendly

When meeting remotely, use this Zoom link.

Email: mjablonski@math.ou.edu, ppatzt@ou.edu, ricardo.mendes@ou.edu

Class meeting:  MWF 1:30-2:20pm.

Course Details for weeks 6-11

This part of the course is a 5-week introduction to group cohomology.  I will use some of the Algebraic Topology sequence as prerequisites. 

 

Course Materials

Most of the material will be found in greater detail in the textbook "Cohomology of Groups" by Kenneth S. Brown and in Chapter 6 of the textbook "An introduction to homological algebra" by Charles A. Weibel. There are more references that can be found in the tentative schedule. Please email me if you have trouble getting access to any of these course materials. 

Grades and Homework

Put in some effort and get a good grade. There will be weekly homework assignments. Hand in at least one solution per sheet to show your effort. I will try to give feedback on the homework. 

 

 

Course Details for weeks 1-5

This part of the course is a 5-week introduction to de Rham cohomology.  The only prerequisite is to have finished the topology qualifying course.

 

Course Materials

If you'd like a reference text, see Bott & Tu's book on differential forms.  If you would like a copy of my notes, talk to me and we will negotiate on you texing up notes as the price!

Grades

Homework will be given weekly.  The homework will come with many hints and you are welcome to get all the help you need in office hours.  Come to class, take homework seriously, and your grade will be fine.

Course Policies

Masks

Masks are required for in-person attendance.  I expect that you will wear a high quality mask, e.g. N-95 or equivalent.  For more on this and the justification behind it, see the announcement posted on Canvas.  If you are unable/unwilling to wear a mask to class, I will not ask any questions.  We will work together to find a way to accommodate your needs.

Communication

Office hours will not be held in person until covid rates are under control.  During this time, office hours will be on Zoom.  If and when possible, I expect that everyone turn their video on during Zoom meetings so that we can interact more fully. 

Please note, lectures on Zoom or in-person are the copyright of the professor and cannot be recorded without prior, written permission.

The best way to reach me is by email.  You can expect a reply within 24 hours during the work work (Monday - Friday).  I will also use email to contact you.  I encourage you to check email at least once a day, preferably once in the morning and once in the evening.  (Even further, I encourage you to not check it too much so that it doesn't consume your time!)

Life in the pandemic continues to be stressful and challenging for all of us - and in different ways.  We should all be patient with each other as we navigate the shifting landscape.  There will be new challenges, but surely new opportunities, as well, that we can take advantage of.

Late Policy

As a rule, I do not accept late assignments as it disrupts the grading process for everyone else.  That said, I will consider it in unusual circumstances. 

Attendance and make-up exams

Students are expected to attend every lecture. If you miss a lecture, then you should contact a classmate for a copy of their notes and any assigned homework. Make-up exams are very rarely given. If there is a reasonable and verifiable excuse, it will be considered.

When not to come to class:  if you are ill, feeling under the weather, or recently exposed to a sick person, then do not come to class.  It doesn't matter if it is a cold, allergies, or covid, don't come when you are not healthy.

Academic misconduct

All cases of suspected academic misconduct will be referred to the Office of Academic Integrity for investigation under the University’s Academic Misconduct Code. The penalties can be quite severe.  If, at some point, you have made a bad decision, know that classmates are engaging in misconduct, or find yourself in an ambiguous or uncomfortable situation, my advice is to come talk to me ASAP.

 

 

Course Details for weeks 12-16

Some topics on the geometry of metric spaces will be covered. A tentative list:

  • intrinsic, length and geodesic spaces, Hopf-Rinow Theorem;
  • examples and constructions of length spaces;
  • curvature and the Gauss-Bonnet Theorem;
  • spaces of constant curvature;
  • triangle comparison and metric spaces with lower or upper curvature bounds (i.e., Alexandrov spaces and CAT(k)-spaces);
  • Hausdorff and Gromov-Haudorff metrics (on the "space" of all compact metric spaces);
  • geometry of Alexandrov spaces: tangent cones, space of directions, etc.

References: I am using mainly 3 sources for preparing lectures:

  • the book "Metric spaces of non-positive curvature" by Bridson and Haefliger
  • the book "A course in metric geometry" by Burago, Burago, and Ivanov
  • the notes "From Euclid to Alexandrov; a guided tour" by A. Petrunin, A. Yashinski.
  • I've also started looking at a book that is still being written, and looks good: Alexander, Kapovitch, Petrunin - "Alexandrov Geometry: Foundations", available at https://arxiv.org/abs/1903.08539

 

University Academic Policies and Student Support

Course Catalog 

Search the OU Course Catalogue.

Student Handbook

Please familiarize yourself with the OU Student Handbook.

Online Library

Access digital materials and other resources at OU Libraries.

Temporary Student Attendance Policy during COVID.

https://ou.edu/together/instructional-faculty/attendance

Academic Misconduct

In addition to the course conduct policies outlined by your professor in the Course Syllabus in the online classroom, please review the Graduate Student Handbook. 

It is the responsibility of each student to be familiar with the definitions, policies, and procedures concerning academic misconduct. The Student Code is available from the Office of the Vice President for Student Affairs, and is contained in the Student's Guide to Academic Integrity.

This site also defines misconduct, provides examples of prohibited conduct, and explains the sanctions available for those found guilty of misconduct.

Plagiarism 

Plagiarism is the most common form of academic misconduct at OU. There is basically no college-level assignment that can be satisfactorily completed by copying. OU's basic assumption about writing is that all written assignments show the student's own understanding in the student's own words. That means all writing assignments, in class or out, are assumed to be composed entirely of words generated (not simply found) by the student, except where words written by someone else are specifically marked as such with proper citation. Including other people's words in your paper is helpful when you do it honestly and correctly. When you don't, it's plagiarism. 

For more information about plagiarism, watch this video and then take this short course offered by University Libraries.

Reasonable Accommodation for Disabilities

The University of Oklahoma is committed to providing reasonable accommodation for all students with disabilities. Students with disabilities who require accommodations in this course should contact their professor as early in the semester as possible.

Students with disabilities must be registered with the Disability Resource Center prior to receiving accommodations in this course.

If you have a disability and you would like to make a request for reasonable accommodation, please see the Graduate Student Handbook or get in touch with the Accessibility and Disability Resource Center.

Adjustments for Pregnancy/Childbirth Related Issues

Should you need modifications or adjustments to your course requirements because of documented pregnancy-related or childbirth-related issues, please contact me as soon as possible to discuss your options. Generally, modifications will be made where medically necessary and similar in scope to accommodations based on temporary disability.  Learn more about the rights of pregnant and parenting students by consulting the FAQ sheets provided by the Institutional Equity Office.

Title IX Resources  

For any concerns regarding gender-based discrimination, sexual harassment, sexual misconduct, stalking, or intimate partner violence, the University offers a variety of resources, including advocates on-call 24/7, counseling services, mutual no contact orders, scheduling adjustments, and disciplinary sanctions against the perpetrator. Please contact the Sexual Misconduct Office at 405-325-2215 (8-5, M-F) or OU Advocates at 405-615-0013 (24/7) to learn more or to report an incident. 

Religious Holidays

It is the policy of the University to excuse absences of students that result from religious observances and to provide for the rescheduling of examinations and additional required classwork that may fall on religious holidays without penalty. It is the responsibility of the student to make alternate arrangements with the instructor at least one week prior to the actual date of the religious holiday.

Copyright Policy

It is illegal to download, upload, reproduce, or distribute any copyrighted material, in any form and in any fashion, without permission from the copyright holder or his/her authorized agent. The University of Oklahoma expects all members of its community to comply fully with federal copyright laws. If such laws appear to have been violated by any user, the university reserves the right (1) to terminate that user’s access to some or all of the university’s computer systems and information resources and (2) to take additional disciplinary actions as deemed necessary or appropriate. Repeat offenders will be sanctioned and their privileges terminated.

Registration and Withdrawal

If you choose to withdraw from this course, you must complete the appropriate University form and turn the form in before the deadline. If you stop attending the course and doing the coursework without doing the required paperwork, your grade will be calculated with missed homework and examination grades entered as zero. This could result in receiving a grade of F in the course. Deadlines are shown in the Academic Calendar, which is available from the Office of the Registrar.

Student Grievances

In addition to any policies outlined related to submitting an informal or formal grievance by your professor in the Course Syllabus in the online classroom, please review the Student Handbook for more information about the process of submitting a formal grievance.