Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 1, 2005.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, February 1, 2005

11:00 am in Altgeld Hall 241,Tuesday, February 1, 2005

Euclidean field theories and K-theory

Elke Markert (Notre Dame)

Abstract: It is a long-standing conjecture that certain spaces of quantum field theory functors form spectra which yield interesting cohomology theories. In particular, spaces of 2-dimensional conformal field theories are supposed to give a geometric model for TMF. S. Stolz and P. Teichner have developed a construction of field theory functors in two cases, 1-dimensional euclidean (EFT), and 2-dimensional conformal (CFT), where the euclidean version is proven to give a spectrum for K-theory. The above conjecture on the 2-dimensional case serves as motivation to study the 1-dimensional one in more detail. In this talk we introduce the main parts of the construction of the EFT functors and give a new connective version of 1-dimensional euclidean theories which yields connective ko-theory.

1:00 pm in 345 Altgeld Hall,Tuesday, February 1, 2005

Ax-Kochen-Ersov type results for valued difference fields, according to Belair, Macintyre, and Scanlon.

Lou van den Dries (UIUC Math)

Abstract: One can extend a large part of the Ostrowski-Kaplansky theory of immediate extensions of valued fields to a wide class of valued difference fields, including in particular fields of Witt vectors with their frobenius. This leads to the results referred to in the title.

1:00 pm in 241 Altgeld Hall,Tuesday, February 1, 2005

Lehmer numbers and Lehmer points

Alexandru Zaharescu (UIUC)

Abstract: We discuss the definition of Lehmer numbers and Lehmer points, and present some asymptotic results on the number of such points.

2:00 pm in Siebel Center 3401,Tuesday, February 1, 2005

Computing coverage via homology

R. Ghrist (UIUC Math)

Abstract: Coverage problems arise in cell phone networks, security systems, and sensor networks. I'll prove how to verify coverage in a system without coordinates, localization, or orientation sensing, and with minimal information about the domain. The criterion is the nonvanishing of an induced map in the homology of the Rips complex of the communication network.

2:00 pm in 243 Altgeld Hall,Tuesday, February 1, 2005

Parallelogram covers for triangles of diameter one.

Prof. Yevgenya Movshovich (EIU Department of Mathematics)

Abstract: In this joint work with Liping Yuan we determine the smallest parallelogram of a given shape that contains all the triangles of diameter one. Since the unit sector of 60 degrees covers all such triangles, the problem becomes a fitting problem: find the smallest parallelogram similar to any given one that contains this sector. It is enough to solve the fitting problem for the unit equilateral triangle; the solution parallelogram will also contain the sector.

3:00 pm in 347 Altgeld Hall,Tuesday, February 1, 2005

Computation of R-transforms

Mingchu Gao (UIUC)

Abstract: We will give a proof of the theorem of the computation of R-transforms by Cauchy transforms of distributions. We will present some examples of the computation of R-transforms.

3:00 pm in 241 Altgeld Hall,Tuesday, February 1, 2005

2-Distance colouring of sparse planar graphs with \Delta+1 colors

Oleg Borodin (UIUC Math (visiting from Institute of Mathematics, Novosibirsk, Russia))

Abstract: A vertex coloring is a 2-distance coloring if every two vertices at distance 1 or 2 have different colours. Clearly, each graph G with maximum degree \Delta needs at least \Delta+1 colors to be 2-distance colored, since it contains a \Delta-star. We consider sufficient conditions, in terms of \Delta and the girth, for a planar graph to be 2-distance (\Delta+1)-colorable. (This is a joint work with A.O.Ivanova, T.K.Neustroeva, and, partly, A.N.Glebov and V.A.Tashkinov.)

3:00 pm in 347 Altgeld Hall,Tuesday, February 1, 2005

Computation of R-transforms

Mingchu Gao (UIUC)

Abstract: We will give a proof of the theorem of the computation of R-transforms by Cauchy transforms of distributions. We will present some examples of the computation of R-transforms.

4:00 pm in 341 Altgeld Hall,Tuesday, February 1, 2005

Solving equations in free groups using extension theorems

Slawomir Solecki (UIUC Math)