[ugrads] math club this weekend & next weekend

Michael J. Pelsmajer pelsmajer at iit.edu
Wed Oct 26 13:36:41 CDT 2005


Friday there are two interesting talks, Saturday
there is a math contest (held at IIT), and next
weekend there is a undergraduate math conference. 
And then of course there's the Pumpkin Launching
Contest.  Specifics follow: 

Friday at noon on Keating Field
Math Club, as part of a CSL team
Pumpkin Launching Contest.  Dig it.

My personal advice about math talks is that 1) you
shouldn't worry about not understanding everything.
 2) Bring something to do and sit in the back, so
that when you can no longer follow you can quietly
do some work. 3) Remember: Only the speaker
understands it all!

Especially for former/current Math 454 students:
Friday, Oct 28 3:30pm

Hemanshu Kaul
(University of Illinois at Urbana-Champaign)

"New Results in Graph Packing"


A number of basic problems in graph theory can be
stated as packing
problems. Let G1 and G2 be graphs of order at most
n, with maximum degree
D_1and D_2, respectively. We say that G1 and G2 pack
if their vertex sets
map injectively into {1,...,n} so that the images of
the edge sets are
disjoint. The concept of graph packing generalizes
various extremal graph
problems, including problems on fixed subgraphs
(such as the Hamiltonian
Cycle problem), forbidden subgraphs (Turan-type
problems), and equitable
coloring. The study of packings of graphs was
started in the 1970s by
Sauer and Spencer, and by Bollobas and Eldridge.
Graph packing results
have also been widely applied to the study of
computational complexity of
graph properties.

In 1978, Sauer and Spencer showed that if 2D_1*D_2<
n, then G1 and G2
pack. Sauer-Spencer theorem is sharp, and we (with
A. Kostochka) extend it
by characterizing the extremal graphs. This result
can thought of as a
small step towards the well-known Bollobas-Eldridge
graph packing
conjecture (1978): if (D_1+1)(D_2+1)<= n+1, then G1
and G2 pack. If true,
this conjecture would be sharp, and would be a
considerable extension of
the Hajnal-Szemeredi theorem on equitable colorings.
The conjecture has
only been proved when D_1<=2, or D_1=3 and n is
huge. We (with A.
Kostochka and G. Yu) prove the best current result
towards this
conjecture, further extending the Sauer-Spencer theorem.

This guy is a super-big shot in mathematics, and the
talk should
be presented at a level that everyone can get
something out of it.
It's at Loyola, but we are welcome to attend.

Title:  Recent Acquisitions in the On-Line
Encyclopedia of Integer Sequences

Speaker: Neil A. Sloane, AT&T Shannon Labs, Florham
Park, New Jersey

Date: Friday, October 28

Time: 3:00 p.m., Damen Hall 144 (Finnegan Auditorium)

Reception: 2:30 p.m., Damen Hall 350. Special
Halloween refreshments
will be served.

Abstract: The On-Line Encyclopedia of Integer
Sequences is a database
of number sequences that enables users to check if a
sequence that has
arisen in their work has been studied by others. A
typical entry gives
the first 50 or so terms of the sequence, formulae,
references, links,
computer programs for producing the sequence, etc.
To find the OEIS,
Google "sequences".

The OEIS contains over 110,000 sequences and gets
over 20,000 hits per
day. Over a thousand new sequences are added each
month. This talk
will describe some of the most interesting sequences
received in the
past few months, including some that are defined by
very unusual
recurrences. Many open problems will be mentioned.

About the speaker: Dr. Sloane has had major
contributions in the
fields of sphere packing, error-correcting codes and
combinatorics. He
is most known for the remarkable OEIS - check it out at

This Saturday:

27th Annual Virginia Tech Regional Mathematics Contest
>From 8:30a.m. to 11:00a.m., October 29, 2005


Next weekend, we'll drive down Friday and return

Undergraduate Mathematics Day
at the University of Dayton
 REGISTER BY FRIDAY, and TELL ME (pelsmajer at iit.edu).

Finally, thanks to Dr. McCray for speaking today and
to Mike McCourt for doing a whole lot of work.

Michael Pelsmajer
pelsmajer at iit.edu

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