110.737 -- Topics in algebraic geometry: Archimedean cyclic homology

Spring 2014

Instructor: Caterina (Katia) Consani
Office: 410B Krieger Hall
Phone: (410) 516-5116.
Email: kc@math.jhu.edu

Class Times: MW, 1:30-2:45 pm.
Room: Krieger Hall 204.


References: There is NO official textbook, the instructor will try to develop a self-contained course; however possible references include (but are not limited to):

A. Connes, Noncommutative geometry, Academic Press 1994.

A. Connes, C. Consani, Cyclic homology, Serre's local factors and lambda operations, (preprint 2012).

J-L. Loday, Cyclic homology, Springer 1992.


Outline of the course: This is a semester long graduate course in algebraic geometry dedicated to the introduction of the newly developed notion of "Archimedean cyclic homology" (see A. Connes, C. Consani preprint above) and its applications in arithmetic. Topics expected to be covered include: Hochschild (co)homology, cyclic (co)homology of algebraic schemes, the lambda operations, archimedean cyclic homology.


Prerequisites: notions in abstract and homological algebra, the algebraic geometry of schemes, algebraic number theory, including Hasse-Weil L-functions.


Special Notice: This course is listed as a graduate-level course and will be taught as such even in the presence of undergraduate students or graduate students in other subjects (i.e. without a full undergraduate math major). This means that the instructor will expect a level of scholarly and mathematical maturity appropriate to an advanced graduate student in mathematics. Material will go somewhat quickly at times and students will be expected to pick up some of it on their own. For these reasons the instructor warmly suggest ALL STUDENTS ENROLLED to take notes in class.


Grading: The final grade will be determined from two components: class presence and participation.


Important Note: Classes will be cancelled on Wednesday March 12 and Monday March 24, as the instructor expects to be away.


110.402 Syllabus

Advanced Algebra II
Spring 2014

[Course Homepage]

Basic Information
Course Title Advanced Algebra II
Course Number 110.402
Instructor Caterina Consani (kc@math.jhu.edu), Krieger 410B
Lectures MW 12:00 --1:15 pm, Krieger Hall 308
Section Meetings F 12:00-12:50pm, Krieger Hall 308
Office Hours W 3:30 pm -- 4:30 pm, and by appointment, Krieger 410B
TA Jeffrey Tolliver (tolliver@math.jhu.edu), Krieger 201. Office hours: TBA --.
Course Information
Textbook W. Keith Nicholson, Introduction to Abstract Algebra (Fourth Edition).
Description

This course is the continuation of Advanced Algebra I (110.401). We will cover most sections from Chapter 5 to Chapter 10, not necessarily following the order in the book. See detailed schedule on course homepage (to be updated frequently). Roughly speaking, the course is subdivided into four main parts: Factorization in integral domains (Chapter 5); Introduction to modules, modules over PID and the structure theorem of finitely generated abelian groups (Chapter 7); Advanced topics in Groups: Sylow theorems, Jordan-Holder theorem, solvable groups, etc (Chapter 8-9); Field extensions and Galois theory (Chapter 6 and 10).

The prerequisite for this course is 110.401.

Homework and Exams
Homework

Homework will be assigned every Friday on the course homepage, and will be due on the following Friday in session to the TA. No late homework will be accepted. Collaboration on homework is allowed and encouraged. However, each student must write up his/her solutions to the problems individually and in his/her own words. Copying from another students paper is prohibited. Only selected homework problems will be graded. Homework counts for 40% of your grade.

You might get assistance from our Math Help Room at Krieger 213. The Help Room will be open from 9:00am to 9:00 pm, Monday through Friday.

Exams Policy

There will be one in-class midterm exam scheduled on Friday, March 7 (at session time) and there will be one take-home 2nd midterm exam distributed in session on Friday April 25 and collected in class on Monday April 28. This course has NO FINAL EXAM.

No lecture notes or other study materials will be allowed in the exams. Per department policy, there will be no makeup exams. If you miss the in-class midterm with a valid excuse, then your exam grades will be determined by the 2nd exam and the homework. The grade for an unexcused absence from any exam will be zero.

Grading Policy The grade for this course will be determined as follows.
  • Homework: 40%
  • Midterms: 30% (each)
Special Aid

Students with disabilities or other special needs who require classroom accommodations must first be registered with the disability coordinator in the Office of Academic Advising. To arrange for testing accommodations the request must be submitted to the instructor at least 7 days (including the weekend) before each of the midterms or final exam. You may make this request during office hours, after class or by sending an email to the instructor.

Academic Ethics

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful.
Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies. Ethical violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the Internet and electronic devices unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.
Report any violations you witness to the instructor. You may consult the associate dean of student affairs and/or the chairman of the Ethics Board beforehand. See the guide on "Academic Ethics for Undergraduates" and the Ethics Board Web Site for more information.
You will sign an ethics statement for each exam.