UIUC Dept. of Mathematics Seminar Calendar

      March 2012             April 2012              May 2012      
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Thursday, April 12, 2012

Special Topology Seminar
11:00 am in 241 Altgeld Hall, Thursday, April 12, 2012

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Submitted by franklan.

Daniel Cohen (Louisiana State University)
Topological complexity of configuration spaces
Abstract: The topological complexity of a space is a homotopy type invariant motivated by the motion planning problem from robotics. We discuss this invariant in the context of configuration spaces of ordered points on orientable surfaces.

Number Theory
11:00 am in 241 Altgeld Hall, Thursday, April 12, 2012

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Submitted by berndt.

Hei-Chi Chan (University of Illinois at Springfield)
Some questions related to the Rogers-Ramanujan continued fraction
Abstract: The Rogers-Ramanujan continued fraction is defined by \[ R(q):= \cfrac{ q^{1/5} }{ 1+\cfrac{ q}{ 1+\cfrac{ q^2 }{ 1+\cfrac{ q^3 }{ \ddots } } } } , \] with $|q|<1$. In this talk, we will look at some results and open questions related to $R(q)$. We will also look at some related concepts, such as the Rogers-Ramanujan identities, $t$-cores, and boson-fermion correspondence. Among other things, we will look at the following integral: \[ \sqrt{4 \phi + 3 } \,\, - \,\phi = 1 + \exp \left( -\frac{1}{5} \int_{e^{-2\pi}}^1 \frac{ (1-t)^5 (1-t^2)^5 (1-t^3)^5 \cdots \, }{ (1-t^{5}) (1-t^{10}) (1-t^{15}) \cdots \, } \cdot \frac{dt}{t} \right) , \] where $\phi:=(1 + \sqrt{5})/2$ is the Golden Ratio.

NetMath Lunch Seminar
12:05 pm in Altgeld Hall, Thursday, April 12, 2012

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Submitted by gfrancis.

George Reese and Ken Travers [email] (Education, UIUC)
MSTE Past, Present, and Future
Abstract: In this talk we will give background on the Office for Mathematics, Science, and Technology Education (MSTE). The Office was created in 1993 with a goal to catalog and promote math, science, and technology education programs at the University. Since then, the mission has evolved to one of public engagement that emphasizes partnerships with K-12 schools to integrate technology and improve curriculum. In this talk Reese and Travers will highlight some of the key collaborations MSTE has had and discuss future directions.

Group Theory Seminar
1:00 pm in Altgeld Hall 347, Thursday, April 12, 2012

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Submitted by kapovich.

Hao Liang (University of Illinois at Chicago)
Centralizers of finite subgroups of the mapping class group and almost fixed points in the curve complex
Abstract: Let S be an orientable surface of finite type, MCG(S) the mapping class group of S, C(S) the curve complex of S and H a finite subgroup of MCG(S). By the hyperbolicity of C(S), there exists points in C(S) whose H-orbit has diameter at most 6\delta; We call such points H-almost fixed points. We prove that there exists a constant K depending only on S so that if the diameter of the set of H- almost fixed points is greater than K then the centralizer of H in MCG(S) is infinite. I will start by explaining the proof of the analogous statement for hyperbolic groups, then I will explain the extra ingredients needed for the case of mapping class groups.

Analysis Seminar
2:00 pm in 243 Altgeld Hall, Thursday, April 12, 2012

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Submitted by aimo.

Kai Rajala (University of Jyväskylä, Finland)
Optimal assumptions for discreteness
Abstract: A celebrated theorem of Reshetnyak's says that a non-constant Sobolev mapping F of R^n is discrete and open if K_F=|DF|^n/det(DF) is uniformly bounded. In view of applications to non-linear elasticity theory, geometric function theory, and certain PDE:s, it is desirable to find the minimal analytic assumptions under which one can conclude discreteness and openness. In dimension two, Iwaniec and Sverak proved that it suffices to assume K_F to be locally integrable. We discuss higher-dimensional versions of the Iwaniec-Sverak theorem due to Manfredi and Villamor, and others, and present our joint work with Stanislav Hencl, showing that the expected sharp higher-dimensional version does not hold.

Commutative Ring Theory Seminar
3:00 pm in 243 Altgeld Hall, Thursday, April 12, 2012

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Submitted by beder.

Paulo Mantero (Purdue Math)
Liaison classes of non-licci ideals
Abstract: A vast part of literature on liaison via complete intersections adresses questions relative to licci ideals, that is, ideals that are in the linkage class of a complete intersection. For a non-licci ideal I, there are few results describing the structure of the linkage class of I, most of them dealing with the case of height 2 ideals (Rao, Lazarsfeld, Ballico-Bolondi-Migliore, Perrin, Martin-Descamps, Nagel, etc.). In particular one would like to find distinguished elements in every linkage class. In this talk we introduce a theoretical definition for `minimal' ideals in any even linkage class. We show that, under reasonable assumptions, these ideals exist and are essentially unique. Among all ideals in an even linkage class, these ideals minimize homological invariants (e.g. Betti numbers, multiplicity). We provide several concrete situations where one can identify these minimal elements (e.g. determinantal ideals or ideals with homogeneous linear resolutions are minimal in their respective even linkage classes). If time permits, I will show an application to producing more evidence towards the Buchsbaum-Eisenbud-Horrocks Conjecture.