Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 28, 2006.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, February 28, 2006

1:00 pm in 343 Altgeld Hall,Tuesday, February 28, 2006

Adding oscillatory functions to the real field

Chris Miller (Ohio State)

Abstract: We are interested in expanding the real field by oscillatory functions, in particular, those that arise in solving certain kinds of ODEs. Certainly, in some cases (e.g., sin x), we wind up defining Z (the set of all integers), hence any hope of obtaining useful information via model-theoretic methods is lost. On the other hand, there are some oscillatory functions that do generate well-behaved (in a sense that can be made precise) structures; e.g., sin(log x). I will give a necessary condition on functions f such that (R, ,x,f) is o-minimal and (R, ,x,sin f) does not define Z.

1:00 pm in 441 Altgeld Hall,Tuesday, February 28, 2006

Cellular resolutions and Betti numbers

David Lipsky (UIUC Math)

Abstract: I'll give some definitions leading up to cellular resolutions of monomial ideals, and present a few basic propositions about them, all from chapter four of Miller and Sturmfels.

1:00 pm in 241 Altgeld Hall,Tuesday, February 28, 2006

Oscillation of Dedekind sums

Maosheng Xiong (UIUC)

Abstract: This is joint work with Emre Alkan and Alexandru Zaharescu.

2:00 pm in 243 Altgeld Hall,Tuesday, February 28, 2006

The problem of angle bisectors, II.

Prof. Gregory Galperin (EIU Department of Mathematics)

Abstract: In the previous seminar, Prof. J. Wetzel proved the following theorem (based on the ideas of a 1994 Monthly article by P. Minorescu and L. Panaitopol):

Theorem. Any three positive numbers, without qualification, can serve as the lengths of the angle bisectors of precisely one Euclidean triangle (up to congruency).

The speaker will present his own recent proof of the same theorem based on elementary ideas of Euclidean geometry and calculus.

3:00 pm in 243 Altgeld Hall,Tuesday, February 28, 2006

Title: On a theorem of Suslin

Professor Madhav Nori (U Chicago, Mathematics)

Abstract: Title: On a theorem of Suslin Abstract: A theorem of Suslin concerning the homology of the pair (BGL_n(F),BGL_{n-1}(F)) will be reinterpreted through mixed Tate Motives.

3:00 pm in 241 Altgeld Hall,Tuesday, February 28, 2006

Combinatorial problems arising in CR geometry

John D'Angelo (UIUC Math)

Abstract: I will discuss several combinatorial problems arising from the study of CR mappings between spheres and hyperquadrics. All terms in complex geometry will be clearly explained, and the talk will be accessible to people in discrete mathematics.