References for IMR 2005

Details of IMR 2005 activities

Mathematics Graduate Program

Get ID card, Advance to GO. (Monday morning)
On Monday morning, we hope that most students will deal with some initial administrative details. These include getting keys to offices, registering for courses, filling out various financial forms, and getting a university ID card (which will also be a library card). We also hope to take a picture of each of you, for display in the department and possibly on the web.

Please find Chuck Weibel or Carla Ortiz in the Graduate Office (Hill 306) to have your picture taken.
International students: Check in at the International Center on the College Avenue campus. Attend workshops as necessary (such as the Employment Workshop to learn about I-9 and W4 forms and to apply for a social security card). You also should find out about PALS (English as a Second Language) and possibly some meetings about TA training.
Check your department mailbox in Hill 315. You may also have a personal mailbox in the post office, but you are responsible for mail in your department mailbox. Tuition remission cards will be in your department mailbox by 8/29/2005.
See Risa Hynes in Hill 322 for a computer account.
See Lynn Braun in Hill 311 for a key to your office (you will need to give a five dollar deposit).
If you have a TA appointment please see Lynn Braun in Hill 311 and give her your payroll papers and learn about the Health Benefits workshop (and then turn in your health benefits papers to Ms. Braun).
If you are a Fellow turn in paperwork to Lynn Braun in Hill 311.

Just do what you can in the morning!

The Lectures

1. Metric spaces: to Rⁿ ... and beyond!

Topic
The most common topological spaces are metric spaces and Rⁿ is a nice example of a metric space. We'll review some definitions such as compact, connected, complete, and continuous (and anything else beginning with c) and examples.
Buzz Lightyear's Pizza Planet is probably a metric space, in spite of the Evil Emperor Zurg.

Lecturer
Professor Siddhartha Sahi is an expert in representations of Lie Groups, as well as Price-mediated trade, the velocity of money and Jack MacDonald polynomials.

2. The Inverse Function Theorem

Topic
The Inverse and Implicit Function Theorems are fundamental tools in the study of many problems in geometry (the local structure of manifolds, advertising for lecture 3) and analysis (bifurcation problems and the solvability of ODEs and PDEs, advertising for lecture 5). The context of these theorems, their statements and a few typical applications will be provided. If there is unbounded time, the infinite-dimensional versions may surface.

Lecturer
Professor Avi Soffer studies non-linear partial differential equations which arise in mathematical physics. He is also interested in Spectral Scattering, which studies things "that can appear and disappear." (Who do you call? Ghostbusters!)

3. Manifolds

Topic
Any surface in R³ of the form z=f(x,y) is a manifold, and so is any curve in Rⁿ, but manifolds are much more. The Implicit Function Theorem lets you certify them. Stokes' Theorem, the classical groups, spheres and donuts all play a role here, and some are edible.

Lecturer
Professor Steve Ferry is an expert on classification problems in manifolds and shapes. He will not tell you about Hilbert cube manifolds and homology manifolds unless you ask. But I definitely think you should ask him about Penguins and the BC Blues.

4. Linear algebra

Topic
A useful synopsis of linear algebra: vector spaces, linear transformations, eigenv{alue|ector}s, etc.

Lecturer
Professor Robert Wilson has received awards recognizing his teaching, research, and service to the university. During 2005-6 he will be our acting CHAIR. One of his major research achievements, jointly with Richard Block, was classifying the mod p simple Lie algebras. He is now working on noncommutative geometry and quasideterminants.

5. Differential Equations

Topic Ordinary differential equations (ODE's) provide a pleasant application of the abstract Contraction Mapping Theorem on metric spaces. A form of local existence and uniqueness can be efficiently verified. Usually, solutions must always exist. The situation with partial differential equations is very different, as was verified by Hans Lewy.

Lecturer
Board of Governors Professor Michael Vogelius is interested in Partial Differential Equations and Numerical Analysis. Ask him what he knows about "crack identification."

6. The Axiom of Choice

Topic
The Axiom of Choice and its familiar equivalents, such as Zorn's Lemma, are used in many "constructions" in analysis, algebra, and topology. This lecture will choose some of them.
References: A "home page" for the Axiom of Choice; or a systematic exposition by Professor Ken Ross.
Professor Ocone's notes are here.

Lecturer
Professor Daniel Ocone is an expert on Stochastic processes, and he has investigated applications in mathematical biology and mathematical finance. He will be teaching Financial Math 642:621 this semester.

7. The Classical Lie Groups

Topic GL_n, SL_n, O_n, U_n, S³, etc.
These groups of linear transformations occur and reoccur in almost all areas of mathematics. You should meet them now so when you re-encounter them the occasion will be a friendly one.

Lecturer
Professor Chris Woodward is an accomplished teacher and researcher. Ask him about honeycombs... or Wireless networks.

First class: Complex Variables

Topic
Oh yeah, classes. Now it begins...
The first class covers the algebra of complex numbers and complex-valued functions.

The rest of the course covers: analytic functions, the Cauchy-Riemann equations, power series, Cauchy's Theorem, zeros and singularities of analytic functions, maximum modulus principle, conformal mapping, Schwarz's lemma, the residue theorem, Schwarz's reflection principle, the argument principle, Rouché's theorem, normal families, the Riemann mapping theorem, properties of meromorphic functions, the Phragmen-Lindelof principle and elementary properties of harmonic functions.

Lecturer
Professor Hector Sussmann (You really should click on this link to find out more!)

The Glimpses

Probability and Combinatorics

Topic
Some combinatorics will be introduced, including graphs and tournaments. Then a couple of examples of combinatorial problems will be given in which probability is a useful tool.

Lecturer
Bill Cuckler is studying Graph Theory and working with Jeff Kahn; and will defend his Rutgers thesis next Spring. He likes tournaments, and is a very fast runner for our Mayday Race team. One anagram of his name is Curckle; probably there are others.

Schrödinger's Windows

Topic
TK

Lecturer
Chris Stucchio is a fourth-year graduate student in Mathematical Physics, and will defend his Rutgers thesis next Spring. His thesis advisor is Avi Soffer. He insists that this is all a mistake.

PDE's

Topic
∂y/∂t and so on...
more TK

Lecturer
Qinian Jin is a 4th-year graduate student in Partial Differential Equations, and will defend his Rutgers thesis next Spring. His thesis advisor is Yanyan Li.

Number Theory

Topic
A survey of popular topics in Number Theory. Tools used for number theoretic research come from several main subjects. L-functions, Modular forms and Elliptic curves, to name a few. I hope to acquaint the audience with some of the main ideas.

Lecturer
Roman Holowinsky is a 5th-year graduate student in analytic Number Theory, and his home page still requires some modification. His thesis advisor is Henryk Iwaniec, the winner of the 2002 AMS Cole Prize in Number Theory.

Other Stuff in the Schedule

Administrative "stuff" (Monday afternoon)
During this time we hope that most students will deal with more administrative details. These include getting keys to offices, registering for courses, filling out various financial forms, and getting a university ID card (which will also be a library card). We also hope to take a picture of each of you, for display in the department and possibly on the web.

International students Check in at the International Center on the College Avenue campus. Attend workshops as necessary (such as the Employment Workshop to learn about I-9 and W4 forms and to apply for a social security card). You also should find out about PALS (English as a Second Language) and possibly some meetings about TA training.
All students
- Check your department mailbox in Hill 315. You may also have a personal mailbox in the post office, but you are responsible for mail in your department mailbox.
- Tuition remission cards will be in your department mailbox by 8/29/2005.
- See Risa Hynes in Hill 322 for a computer account.
- See Lynn Braun in Hill 311 for a key to your office (you will need to give a five dollar deposit).
- Please see Chuck Weibel or Carla Ortiz in the Graduate Office (Hill 306) to have your picture taken so we can begin to recognize you.
- If you have a TA appointment please see Lynn Braun in Hill 311 and give her your payroll papers and learn about the Health Benefits workshop (and then turn in your health benefits papers to Ms. Braun).
- If you are a Fellow turn in paperwork to Lynn Braun in Hill 311.
You will also need to register and have your photograph taken for your Rutgers identification card. For this you will need the Tuition remission cards mentioned above.

Is this enough?

Our computers & software (Tuesday after lunch)
This presentation will give a brief overview of the computing environment of the Math Department and the University. Particular attention will be given to items of interest to math graduate students.

Lecturer
Sam Coskey is a second-year graduate student. He was an undergraduate at the University of Washington. His nickname is Spaceghost. More relevantly, he is the current graduate student representative to the Math Department's Computing Committee.

More Administrative "stuff" (Wednesday afternoon)
At 1:00 (Wednesday), Teresa Delcorso will give a presentation on applying for Competitive Fellowships and other pots of money.
Please attend; it could be worth $10,000 to you!

Breakfast! (Thursday morning)
We will try to supply an agreeable breakfast (this means free food, which is usually interesting to graduate students).
Wake up!

Final Administrative "stuff" (Thursday afternoon)
Surely you haven't done all the red tape yet. Take another whack at it!

Lunch (Monday and Thursday at High Noon)

We will try to supply an agreeable lunch (this means free food, which is usually interesting to graduate students). Discussion at lunch on Monday should include most students' advisors, who can help students decide on initial registration for courses.

Move in; Relax

You may need this time to move into your lodgings.
Have fun, and please help one another.

	Four-Square Four Square rules Make a square and number squares 1-4. Get a ball that bounces well. The game begins with player number one dropping the ball and hitting it politely into any of the other squares. The person standing in that square lets the ball bounce in their square, before hitting it to any other square. The game continues until the ball is hit out of bounds or a player can not retrieve the ball. At Rutgers, a new number one comes into play each time. If the player in square number n loses, each of the players in squares less than n move up one square. (Other rules require player number one moves to square four.)
	Other ad hoc rules will be revealed by Paul Ellis at random moments, especially those about "offending the sensibilities." ;)

Aerobie

Aerobie is a relaxed soccer-style game played with an aerobie (a plastic annulus with aerodynamic properties like a frisbee has). We play by any of several sets of rules. Bill Cuckler will recruit you to play regularly with the Rutgers Aerobie Team if you let him.

NB@night

On Tuesday, we will attempt to tour a bit of downtown New Brunswick at night. Professor Simon Thomas, who knows the finer points of New Brunswick, will try to act as a sort of tour guide. The evening will begin with dinner at 7 PM. We shall see what happens next!

Party! Party?

You should get e-mail about this. One of these will happen Wednesday.

There is another party, whose attendance is almost restricted to graduate students, is usually given by the (now) second-year students for the entering and now first-year students. This will happen later on. I hope that more information will follow about this.