Seminar Calendar
for events the day of Thursday, April 5, 2012.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, April 5, 2012

IMSE
10:00 am   in 314 Altgeld Hall,  Thursday, April 5, 2012
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Submitted by seminar.
 Richard Griffith, Ph.D., Senior Manager (Complex Systems for National Security, Sandia National Laboratory)An Overview of Sandia National Laboratories and Our Key Complex Systems National Security ChallengesAbstract: Sandia National Laboratories is a multidisciplinary engineering laboratory dedicated to solving the nation's most difficult national security challenges. Sponsored by the Department of Energy/National Nuclear Security Administration (DOE/NNSA), Sandia has responsibility for the stewardship of the Nation's nuclear weapon stockpile. In addition, the Labs are actively engaged with multiple government agencies to address challenges in nuclear non-proliferation, renewable energy technologies, border and air transit security, conventional military systems, and other important issues. Because many of the key challenges the nation faces are Complex Systems, Sandia has a core capability in complex systems techniques, methods, algorithms, and approaches, and seeks to apply them in unique and creative ways to address these challenges. A number of these complex systems challenges will be discussed, with the intent of identifying faculty and graduate students with aligned research interests.

Number Theory Seminar
11:00 am   in 243 Altgeld Hall,  Thursday, April 5, 2012
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Submitted by ford.
 Jingjing Huang (Penn State Math)Sums of unit fractionsAbstract: The results presented in this talk are joint work of Robert Vaughan with myself. We are mainly concerned with the Diophantine equation $$\frac{a}{n}=\frac1{x_1}+\frac1{x_2}+\cdots+\frac1{x_k}$$ and its number of positive integer solutions $R_k(n;a)$. Now the distribution of the function $R_2(n;a)$ is well understood. More precisely, by averaging over $n$, the first moment and second moment behaviors of $R_2(n;a)$ have been established. Furthermore, we have shown that, after normalisation, $R_2(n;a)$ satisfies Gaussian distribution, which is an analog of the classical theorem of Erdos and Kac. Now, in this talk, I will mainly talk about the following result. Let $E_a(N)$ denote the number of $n\le N$ such that $R_2(n;a)=0$. It is established that when $a\ge3$ we have $$E_a(N)\sim C(a) \frac{N(\log\log N)^{2^{m-1}-1}}{(\log N)^{1-1/2^m}},$$ with $m$ defined in the talk. This result significantly improves a result of Hoffmeister and Stoll. I will explain how to prove this theorem. The next project would be to study the ternary case $k=3$. While the conjecture, by Erd\H{o}s, Straus and Schinzel, that for fixed $a\ge 4$, we have $R_3(n;a)>0$ when $n$ is sufficiently large, is still wide open, here I will talk about some partial results on the mean value $\sum_{n\le N}R_3(n;a)$ if time permits.

Lunch Seminar on NetMath
12:00 pm   in 102 Altgeld Hall (Illinois Geometry Lab),  Thursday, April 5, 2012
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Submitted by gfrancis.
 George Francis   [email] (Mathematics, Urbana)On a Suite of Tools for Online Geometry Courses.Abstract: Absent any single adequate tool for implementing even the most essential online equivalents to standard classroom methods in teaching geometry, my students and I cobbled together a suite of minimally functional tools enabling a now four year old pedagogical experiment. In this presentation I will develop an "axiomatic" wish list of what one needs for an online geometry course. I will illustrate it using the custom tools when possible, and wave my hands when there are none.

Group Theory
1:00 pm   in 347 Altgeld Hall,  Thursday, April 5, 2012
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Submitted by jathreya.
 Jayadev Athreya (UIUC)Radial Density in Apollonian Circle PackingsAbstract: Given an Apollonian Circle Packing (ACP) $P$ and a circle $C_0 = \partial B(z_0, r_0)$ in $P$, color the set of disks in $P$ tangent to $C_0$ red. Take the concentric circle $C_{\epsilon} = \partial B(z_0, r_0 + \epsilon)$. As $\epsilon \rightarrow 0$, what proportion of $C_{\epsilon}$ is red? In joint work with F. Boca, C. Cobeli, and A. Zaharescu, we show that the answer is $3/\pi$.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, April 5, 2012
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Submitted by aimo.
 Pekka Pankka (University of Helsinki, Finland)Almost sure limits of quasiconformally equivalent closed manifoldsAbstract: Suppose $(M_i,p_i)$ is a sequence of pointed closed Riemannian manifolds so that the diameters of $M_i$ grow without bounds. By Gromov's compactness theorem, under conditions on curvature and injectivity radius, this sequence has a subsequence converging in the pointed Gromov-Hausdorff topology to a pointed Riemannian manifold $(X,p)$. But what is $X$ typically like? Under the additional condition that manifolds $M_i$ are uniformly quasiconformally equivalent to a fixed manifold, $X$ is almost surely (in a suitable sense) quasiconformal to either the Euclidean space or a punctured Euclidean space. In this talk I will discuss this and similar results for surfaces and graphs and the relation of these results to the work of Benjamini and Schramm. This is joint work with Hossein Namazi and Juan Souto.

2:00 pm   in 241 Altgeld Hall,  Thursday, April 5, 2012
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Submitted by lukyane2.
 Grace Work (UIUC Math)Ideal Triangulations of Hyperbolic 3-ManifoldsAbstract: In this talk we will see how link complements can be decomposed into finite unions of ideal tetrahedra. From this decomposition we can compute the hyperbolic structure on these manifolds. The tetrahedra provide us with information we can use to compute arithmetic invariants of the manifolds. Our main example will be the complement of the figure-eight knot.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, April 5, 2012
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Submitted by beder.
 Yu Xie (Notre Dame Math)An extension of a Lemma of Huneke to non $m$-primary ideals and formulas for the generalized Hilbert coefficientsAbstract: Let $(R,m)$ be a Cohen-Macaulay local ring and $I$ an $m$-primary ideal. In 1996, Huckaba provided a $d$-dimensional version of a 2-dimensional formula due to Huneke. This formula relates the length $\lambda(I^{n+1}/JI^n)$ to the difference $P(n+1)-H(n+1)$, where $J$ is a minimal reduction of $I$, and $P(n+1)$ and $H(n+1)$ are Hilbert polynomial and Hilbert function of $I$ respectively. We extend the formula further to non $m$-primary ideals and use it to compute the generalized Hilbert coefficients defined by Polini and Xie recently.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, April 5, 2012
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Submitted by kapovich.
 Sijue Wu (University of Michigan)Wellposedness of the two and three dimensional full water wave problemAbstract: We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.