Seminar Calendar
for events the day of Tuesday, February 23, 2010.

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Questions regarding events or the calendar should be directed to Tori Corkery. 
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Tuesday, February 23, 2010

Topology seminar
11:00 am   in Altgeld Hall 241,  Tuesday, February 23, 2010
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Submitted by bertg.
Qayum Khan (Notre Dame)
Rigidity of connected sums of certain 4-manifolds
Abstract: We establish the topological s-cobordism surgery sequence for any closed oriented 4-manifold X that is homotopy equivalent to a connected sum X_1 # ... # X_n of certain factors X_i. Here, it suffices that the fundamental group G_i of each X_i is "good" in the sense of Freedman--Quinn. More generally, each X_i must have an exact s-cobordism surgery sequence. As a corollary, if each X_i is aspherical and each G_i satisfies the Farrell--Jones Conjecture, then X is topologically s-rigid. The methods use topological cobordisms and homology rather than direct surgeries.

Graduate Student Algebraic Geometry Working Seminar
1:00 pm   in 347 Altgeld Hall,  Tuesday, February 23, 2010
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Submitted by mim2.
Mee Seong Im   [email] (UIUC Math, 1-3PM)
Higher Order Deformation (Part 5)
Abstract: We will begin by Jimmy Shan presenting the following paper: Linearizing Flows and a Cohomological Interpretation of Lax Equations by P.A. Griffiths. He will cover Hamiltonian System/Lax Equations, Spectral Curves, Eigenvector Mapping, and Griffiths' Linearizing Theorem. We will then continue with our study of deformation theory from Hartshorne's book. We will study obstructions to deformations of schemes, dimensions of families of spatial curves, and analyze a nonreduced component of the Hilbert scheme. This concludes Chapter 2 of Hartshorne. We will spend the next few weeks carefully studying Compact Complex Surfaces by Wolf Barth and Higher-Dimensional Algebraic Geometry by Olivier Debarre. If we have time, we will return to moduli theory and global deformation theory in Hartshorne's book.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 23, 2010
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Submitted by w-henson.
no meeting this week

Number Theory Seminar
1:00 pm   in 241 Altgeld Hall,  Tuesday, February 23, 2010
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Submitted by jarouse.
Kenneth Stolarsky (UIUC Math)
I was right about cubes!
Abstract: My 1978 conjecture about cubes (and higher powers) with remarkably few ones in their base 2 expansion has been proved (Hare, Laishram, and Stoll). A proof will be sketched, along with a selective survey of digital problems and results. Over several generations digital mathematics has seen swings from frequent contempt to acceptance and now to remarkable respect, the latter due in part to recent work of Mauduit and Rivat. Its role in mathematical culture will be discussed.

Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, February 23, 2010
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Submitted by sba.
Ralph Alexander (UIUC Math)
Helly's Theorem
Abstract: The classical Theorem of Helly (1921) states: Consider a finite collection of convex bodies in Euclidean N-space such that the intersection of any (N+1) of these bodies is not empty. Then the intersection of the entire collection is not empty. This talk will include several proofs and generalizations of Helly's theorem. A closely related theorem of Radon also will be discussed

Graduate Analysis Seminar
4:00 pm   in 243 Altgeld Hall,  Tuesday, February 23, 2010
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Submitted by wgreen4.
Kelly Funk (UIUC Math)
Measure Preserving Homeomorphisms of the Torus: Part I
Abstract: This series of talks is based on a lecture by Frederic Le Roux given at the Università di Udine e Scuola Normale Superiore in Pisa, Italy. In this part of the talk I will discuss Lax's Theorem which says that any volume preserving homeomorphism may be uniformly approximated by a dyadic permutation. The proof of this result is based on the combinatorial Marriage Lemma and is simpler than the older proof based on the Ergodic Theorem. I will also discuss the genericity of topological transitivity, which is a consequence of Lax's Theorem. This talk should interest graduate students in a variety of areas and will be accessible. Everyone is encouraged to attend!!