coordinator | phone # | office | |
---|---|---|---|

Renato Feres | 5-6752 | Cupples I, 17 | feres@math.wustl.edu |

** Objective: ** The extended graduate orientation program is an optional,
but strongly recommended,
activity for the beginning graduate students. The main purposes are to introduce incoming
students to the style and pace of our graduate courses, bringing everybody up to
speed when Fall classes begin; and help create from the very beginning
a supportive social environment of graduate students,
faculty, and staff, in which we can all work most effectively.

** Course: ** The core of the orientation program is a minicourse
and group work activities about some mathematics subject.
This is not meant to be a remedial course, and does not necessarily cover topics that will
be seen again in the qualifying courses. For this year I have chosen the topic of
p-adic analysis. (More on the topic below.)

** Dates, times, and locations: **
Most activities will take place in Cupples I, room 199. Lunch at room 200. Bring your lunch!
The place has a refrigerator, microwave oven and other amenities for general use.
Mary Ann will provide some cool beverage, chips and cookies.

The minicourse will run from August 10 till August 14, with classes on Monday (8/10), Wednesday (8/12), and Friday (8/14).

There will be a morning (10:00AM - 12:00PM) and an afternoon session (2:00PM - 4:00PM). Each session consists of one hour of lecture and one hour of group work. Tuesdays and Thursdays will be devoted to homework, with the students responsible for organizing their own time.

On Friday the 14th we will have lunch at Bluebarry Hills, together with the staff and some of the faculty.

** Text: ** The course will be based on the text: "p-adic analysis compared with real,"
by Svetlana Katok. **Do not buy it!** Free copies will be provided to you at the beginning of classes or earlier after
your arrival.

** Tentative list of topics: **
We are familiar with the idea of constructing the real numbers by completion of
the field of rational numbers. This takes one from the realm of arithmetic to analysis.
But the completion can also be done using the less familiar p-adic norms, leading
to whole new fields with which we can do algebra, calculus, geometry, etc. This minicourse
introduces the subject of p-adic analysis, while comparing and contrasting it
with the familiar real analysis. We will cover a subset of the following list of topics:

- Completion of normed spaces;
- The field of p-adic integers and p-adic rationals;
- Arithmetic and algebraic properties of p-adic numbers;
- The topology of the field of p-adic rationals;
- Elements of analysis over p-adic fields;
- p-adic functions.