Seminar Calendar
for events the day of Tuesday, November 1, 2011.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, November 1, 2011

Topology Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, November 1, 2011
 Del Edit Copy
Submitted by franklan.
 Bruce Williams (University of Notre Dame)K-theory of endomorphisms

Number Theory
1:00 pm   in 241 Altgeld Hall,  Tuesday, November 1, 2011
 Del Edit Copy
Submitted by berndt.
 Bruce Reznick (UIUC)Linearly dependent powers of quadratic formsAbstract: Given a positive integer $d$, let $\Phi(d)$ denote the smallest $r$ so that there exist $r$ pairwise non-proportional complex quadratic forms $q_i(x,y) = a_i x^2 + 2b_i x y + c_i y^2$ with the property that $\{q_i^d\}$ is linearly dependent. We are interested in computing $\Phi(d)$ and characterizing the minimal sets. For example, when $d=2$, the essentially unique minimal set comes from the Pythagorean parameterization: $\{x^2 - y^2, x y , x^2 + y^2\}$. Using a classical map of Felix Klein, the three pairs of linear factors of these quadratics are associated with the three pairs of antipodal vertices of the regular octahedron. For more details, see the bulletin board. There will be no more than 15 minutes overlap in the material presented in the two seminars.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, November 1, 2011
 Del Edit Copy
Submitted by kkirkpat.
 Kay Kirkpatrick   [email] (UIUC Math)Fractional Schrodinger equations and long-range interactions in biopolymersAbstract: We consider a general class of discrete nonlinear Schrodinger equations (DNLS) on the 1-D lattice with mesh size h. In the continuum limit when h goes to zero, we prove that the limiting dynamics are given by a nonlinear Schrodinger equation (NLS) with the fractional Laplacian as the dispersive operator. In particular, we obtain that fractional powers between 1/2 and 1 arise from long-range lattice interactions when passing to the continuum limit, whereas the NLS with the usual Laplacian describes the dispersion in the continuum limit for short-range or quick-decaying interactions (e.g., nearest-neighbor interactions). Our results rigorously justify certain NLS models with fractional Laplacians proposed in the biophysics literature. Joint work with Enno Lenzmann and Gigliola Staffilani.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, November 1, 2011
 Del Edit Copy
Submitted by sabok.
 Todor Tsankov (Paris 7)Automatic continuity of homomorphisms for continuous groupsAbstract: It is an interesting phenomenon that for many Polish groups, the algebraic structure of the group "remembers" the topology. This can be given many meanings; perhaps the strongest is the following automatic continuity property: every homomorphism into a separable group is continuous. This property can be thought of as a strengthening of the well-studied in model theory small index property: a Polish group has the small index property iff every homomorphism into S_infty is continuous. The automatic continuity property was introduced by Kechris and Rosendal, who also developed a technique for verifying it. More recently, their technique was generalized to the continuous setting by Ben Yaacov, Berenstein and Melleray and that allowed a new kind of "two-step" proofs of automatic continuity, most notably for the unitary group and the automorphism group of a standard probability space, examples which were inaccessible by previous methods.

Geometry Seminar (joint with Algebra-Geometry-Combinatorics Seminar)
2:00 pm   in 243 Altgeld Hall,  Tuesday, November 1, 2011
 Del Edit Copy
Submitted by sba.
 Bruce Reznick (UIUC)Linearly dependent powers of quadratic formsAbstract: Given a positive integer $d$, let $\Phi(d)$ denote the smallest $r$ so that there exist $r$ pairwise non-proportional complex quadratic forms $q_i(x,y) = a_i x^2 + 2b_i x y + c_i y^2$ with the property that $\{q_i^d\}$ is linearly dependent. We are interested in computing $\Phi(d)$ and characterizing the minimal sets. For example, when $d=2$, the essentially unique minimal set comes from the Pythagorean parameterization: $\{x^2 - y^2, x y , x^2 + y^2\}$. Using a classical map of Felix Klein, the three pairs of linear factors of these quadratics are associated with the three pairs of antipodal vertices of the regular octahedron.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, November 1, 2011
 Del Edit Copy
Submitted by nevins.
 David Treumann (Northwestern University)Skeleta from Newton polytopesAbstract: Thom's Morse-theoretic proof of the Lefschetz hyperplane theorem shows that an affine variety of complex dimension n is homotopy equivalent to a cell complex of real dimension n. Recent ideas of Ruan and Kontsevich suggest that this cell complex--the "skeleton" of the variety--should carry a sheaf of dg categories (the sheaf of Fukaya categories). I will discuss work with Zaslow about what these skeleta and sheaves look like for a large class of varieties, and the role they play in mirror symmetry.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, November 1, 2011
 Del Edit Copy
Submitted by west.
 Lawrence H. Erickson (UIUC Computer Science)Locating a robber on a graph via distance queriesAbstract: A cop wants to locate a robber hiding among the vertices of a graph. A round of the game consists of the robber moving to a neighbor of its current vertex (or not moving) and then the cop scanning some vertex to obtain the distance from it to the robber. If the cop can at some point determine where the robber is, then the cop wins. If the robber can avoid this forever, then the robber wins. We prove that the robber wins on graphs with girth at most $5$. We prove a conjecture of Seager by showing that the cop wins on a subdivision of an $n$-vertex graph $G$ when each edge is subdivided into a path of length at least $\min\{3^{\mu(G)},n\}$, where $\mu(G)$ denotes the metric dimension of $G$. For grids and complete bipartite graphs, the threshold is lower. (Joint work in REGS with Ilkyoo Choi, Michelle Delcourt, James Carraher, and Douglas B. West.)