UIUC Dept. of Mathematics Seminar Calendar

    February 2003            March 2003             April 2003     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                    1                      1          1  2  3  4  5
  2  3  4  5  6  7  8    2  3  4  5  6  7  8    6  7  8  9 10 11 12
  9 10 11 12 13 14 15    9 10 11 12 13 14 15   13 14 15 16 17 18 19
 16 17 18 19 20 21 22   16 17 18 19 20 21 22   20 21 22 23 24 25 26
 23 24 25 26 27 28      23 24 25 26 27 28 29   27 28 29 30         
                        30 31

Tuesday, March 18, 2003

Topology Seminar
11:00 am in 345 Altgeld Hall, Tuesday, March 18, 2003

Del

Edit

Copy

Submitted by cpfrench.

Halvard Fausk (Northwestern)
A stable homotopy splitting theorem for finite groups.

Logic Seminar
1:00 pm in 345 Altgeld Hall, Tuesday, March 18, 2003

Del

Edit

Copy

Submitted by evas.

Itay Ben-Yaacov (UIUC Math)
Uncountable categoricity in cats, cont.
Abstract: Cats form a general model theoretic framework that makes it possible to treat in a uniform manner a wide range of classes: elementary classes, Banach-like structures, probability spaces and more. After giving the basic definitions I will speak about notions of topology and abstract distance which are intrinsic to a cat, as well as their relation to true extra-logical metrics. The topology (or metric) allows us to define "complete models", which are the analogue of models of a first order theory, and whose size is measured by their density character rather than by cardinality. It also allows us to define the correct analogues of $\lambda$-stability and Morley Rank, in a manner similar to that of Iovino in Banach spaces. Having developed these tools, we prove that a cat is categorical in one uncountable cardinal if and only if it is categorical in every uncountable cardinal, following ideas found in Shelah's lazy guide.

Geometric Potpourri Seminar
2:00 pm in 243 Altgeld Hall, Tuesday, March 18, 2003

Del

Edit

Copy

Submitted by seminar.

Dr. Wacharin Wichiramala (UIUC Department of Mathematics)
A smaller cover for unit convex arcs
Abstract: An interesting variant of Moser's well-known "worm problem" asks for the convex planar set of least area that can cover all unit convex arcs. Thirty years ago Wetzel noted that an isosceles right triangle T with unit hypotenuse and area 0.2500 is such a cover, and he showed that a small triangle can be clipped from the right angle vertex of T to give a cover with area about 0.2492. At that time he conjectured that the triangle T clipped at the minimum width (0.4389) of the unit broadworm is also a cover. Last year Johnson and Poole found a sophisticated way to prune the isosceles right triangle T near its right angle vertex to form a cover with area about 0.2466. I will describe a barbarian way to clip the triangle T to form a cover with area about 0.2464, thereby bringing the world record back to UIUC.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, March 18, 2003

Del

Edit

Copy

Submitted by west.

Michael Plantholt (Illinois State University, Mathematics)
A combined logarithmic bound on the chromatic index of multigraphs
Abstract: For any multigraph G, the integer round-up phi(G) of the fractional chromatic index fr(G) yields the best general lower bound for the chromatic index chi'(G). For an upper bound, Kahn showed that for any positive constant c there exists a positive integer N such that chi'(G) < (1+c) fr(G) whenever fr(G) > N. We show that for any multigraph G with order n and at least one edge, chi'(G) <= phi(G) + log_3/2 ( min {n+1 , phi(G)} ). Kahn's result follows as a corollary.

Mathematics in Science and Society (MSS)
4:00 pm in 314 Altgeld Hall, Tuesday, March 18, 2003

Del

Edit

Copy

Submitted by duursma.

Andrew Odlyzko [email] (Director, Digital Technology Center, University of Minnesota)
Cryptography and economics
Abstract: Mathematical cryptography has provided a new application area for many areas that had formerly been regarded as belonging to pure mathematics. It has also provided a variety of interesting and important tools for ecommerce. The impact of these tools was widely expected to be revolutionary. Yet so far, although some of these mathematical techniques do play a vital role, most of the optimistic early expectations have been disappointed. The reason for this, which will be explored in this lecture, is that many of these tools, especially those providing strong privacy, conflict with the economic incentives that govern how ecommerce is conducted.