UIUC Dept. of Mathematics Seminar Calendar

      July 2004             August 2004           September 2004   
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
              1  2  3    1  2  3  4  5  6  7             1  2  3  4
  4  5  6  7  8  9 10    8  9 10 11 12 13 14    5  6  7  8  9 10 11
 11 12 13 14 15 16 17   15 16 17 18 19 20 21   12 13 14 15 16 17 18
 18 19 20 21 22 23 24   22 23 24 25 26 27 28   19 20 21 22 23 24 25
 25 26 27 28 29 30 31   29 30 31               26 27 28 29 30

Wednesday, September 22, 2004

Math 600 (formerly Math 500)
4:00 pm in 243 Altgeld Hall, Wednesday, September 22, 2004

Del

Edit

Copy

Submitted by msaran.

Clifton Ealy [email] (UIUC Math)
Model Theory, Stability Theory, and Beyond
Abstract: One of the most active areas of research within model theory is that known as stability theory. I will describe what a stable theory is, and what sort of questions are considered in the study of stable theories. Time permitting, I will speak briefly about attempts to extend the results of stability theory to more general contexts.

Wednesday, September 29, 2004

Wednesday, October 6, 2004

Wednesday, October 13, 2004

Math 600 (formerly Math 500)
4:00 pm in 243 Altgeld Hall, Wednesday, October 13, 2004

Del

Edit

Copy

Submitted by msaran.

Robert Smith (UIUC Math and Veterinary Pathobiology)
Using mathematics to clean up the environment: Impulsive differential equations as applied to sewage treatment and toxic waste cleanup.
Abstract: Self-cycling fermentation is a computer-aided process used for culturing microorganisms. Applications include water purification, treatment of sewage, and the cleanup of toxic waste. We consider a model of growth of a single species in the fermentor, assuming a single limiting nutrient, with the level of this nutrient as the triggering factor. The model is formulated in terms of impulsive ordinary differential equations. The model predicts that either the system fails and the population of microorganisms essentially washes out, or more favourably, the fermentor cycles indefinitely, with one impulse per period, maintaining a positive, though oscillatory, number of cells. The predicted outcome is based on a threshold criterion that can be determined in terms of biologically relevant parameters. An analytic expression for the cycle time is also derived. Using this expression, it is shown that the total yield over a specified time period depends on the choice of the optimal emptying/refilling fraction, and a method for determining the optimal emptying/refilling fraction is given. We also prove that, under certain conditions, two species can coexist on a single nonreproducing nutrient. We provide numerical simulations that suggest coexistence of three species is also possible and that competitor-mediated coexistence can occur in this case.

Tuesday, October 19, 2004

Math 600 (formerly Math 500)
4:00 pm in 347 Altgeld Hall (NOTE CHANGE from usual room AND usual day), Tuesday, October 19, 2004

Del

Edit

Copy

Submitted by msaran.

Khye Loong Yew (UIUC Math)
Some uses of tensor products in functional analysis
Abstract: Out of the fourteen "natural tensor norms" classified by Grothendieck in his 1956 Resume, the injective and projective ones proved their usefulness rather quickly through simple examples involving vector valued function spaces. This talk seeks to illustrate how Grothendieck further linked them to the important notions of compactness and approximation property of Banach spaces. The categorical flavor involved allows direct generalization of these concepts to operator spaces. If time permits, tensor products of operator algebras will also be discussed. This talk is fairly self-contained with all necessary definitions and results stated.

Wednesday, October 27, 2004

Wednesday, November 3, 2004

Math 600 (formerly Math 500)
4:00 pm in 243 Altgeld Hall, Wednesday, November 3, 2004

Del

Edit

Copy

Submitted by msaran.

Naeem Sheikh and Kyung Won Hwang (UIUC Math)
Intersection Families and the Polynomial Method
Abstract: You have a family F of subsets of {1,...,n} such that the size of any set in F is in K and the size of intersection of any two sets in F is in L, where K and L are some specified sets of non-negative integers. What is the maximum cardinality of F? The answer, of course, depends on conditions imposed on K and L. Ray-Chaudhri and Wilson proved a simple version of this problem in 1975. Later, Babai gave a proof of their result using polynomials and linear independence. It is this method that interests us. We show how we have been using this method to attack various such problems (both open and solved problems). Accessible to all graduate students.

Wednesday, November 10, 2004

Math 600 (formerly Math 500)
4:00 pm in 243 Altgeld Hall, Wednesday, November 10, 2004

Del

Edit

Copy

Submitted by msaran.

Jinjia Li [email] (UIUC Math)
Intersection multiplicity and Fitting invariant
Abstract: The positivity part of Serre's conjecture on intersection multiplicity has remained open for almost half a century. My talk will start with an introduction on this fascinating subject. Then, I will introduce the definition of Fitting invariant and discuss some basic properties. Finally, I will briefly show how to use Fitting invariant to prove a special case of the positivity part of Serre's conjecture. This talk should be accessible to a general mathematical audience with no prior knowledge in commutative algebra.

Wednesday, November 17, 2004