Seminar Calendar
for events the day of Thursday, October 18, 2012.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2012          October 2012          November 2012
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1       1  2  3  4  5  6                1  2  3
2  3  4  5  6  7  8    7  8  9 10 11 12 13    4  5  6  7  8  9 10
9 10 11 12 13 14 15   14 15 16 17 18 19 20   11 12 13 14 15 16 17
16 17 18 19 20 21 22   21 22 23 24 25 26 27   18 19 20 21 22 23 24
23 24 25 26 27 28 29   28 29 30 31            25 26 27 28 29 30
30


Thursday, October 18, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, October 18, 2012
 Del Edit Copy
Submitted by ford.
 Michael Filaseta (Univ. South Carolina Math.)49598666989151226098104244512918Abstract: If $p$ is a prime with decimal representation $d_{n} d_{n-1} \dots d_{1} d_{0}$, then a theorem of A. Cohn implies that the polynomial $f(x) = d_{n} x^{n} + d_{n-1}x^{n-1} + \cdots + d_{1}x + d_{0}$ is irreducible. One can view this result as following from the fact that if $g(x) \in \mathbb Z[x]$ with $g(0) = 1$, then $g(x)$ has a root in the disk $D = \{ z \in \mathbb C: |z| \le 1 \}$. On the other hand, that such a $g(x)$ has a root in $D$ has little to do with $g(x)$ having integer coefficients. In this talk, we discuss a perhaps surprising result about the location of a zero of such a $g(x)$ that makes use of its coefficients being in $\mathbb Z$ and discuss the implications this has on generalizations of Cohn's theorem. A variety of open problems will be presented. This research is joint work with a former student, Sam Gross.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, October 18, 2012
 Del Edit Copy
Submitted by kapovich.
 Alex Furman (University of Illinois at Chicago)Classifying lattice envelopes for (many) countable groupsAbstract: Let $\Gamma$ be a given countable group. What locally compact groups $G$ contain a lattice (not necessarily uniform) isomorphic to $\Gamma$ ? In a joint work with Uri Bader and Roman Sauer we answer this question for a large class of groups including Gromov hyperbolic groups and many linear groups. The proofs use a range of facts including: recent work of Breuillard-Gelander on Tits alternative, works of Margulis on arithmeticity of lattices in semi-simple Lie groups, and a number of quasi-isometric rigidity results.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 18, 2012
 Del Edit Copy
Submitted by aimo.
 Raanan Schul (SUNY Stony Brook)Lipschitz Functions vs. ProjectionsAbstract: We discuss joint work with Jonas Azzam. All Lipschitz maps from $R^7$ to $R^3$ are orthogonal projections''. This is of course quite false as stated. It turns out however, that there is a surprising grain of truth in this statement. We show that all Lipschitz maps from $R^7$ to $R^3$ (with 3-dimensional image) can be precomposed with a map $g:R^7\to R^7$ such that $f\circ g$ will satisfy, when we write the domain as $R^4\times R^3$ and restrict to $E$, a large portion of the domain, that $f\circ g$ will be constant in the first coordinate and biLipschitz in the second coordinate. Geometrically speaking, the map $g$ distorts $R^7$ in a controlled manner, so that the fibers of $f$ are straightened out. Our results are quantitative. The target space can be replaced by any metric space! The size of the set $E$ on which behavior is good is an important part of the discussion and examples such as Kaufman's 1979 construction of a singular map $[0,1]^3$ onto $[0,1]^2$ are an important enemy. On route we will discuss a new extension theorem which is used to construct the bilipschitz map $g$, improving results of Jones (88) and David (88). In particular, if $g:R^7\to R^7$ is a Lipschitz map, then it agrees with a globally defined biLipschitz map $\hat{g}:R^7\to R^7$ on a large piece of the domain. This was previously known only by increasing the dimension of the target space of $\hat{g}$ (David and Semmes, 91).

2:00 pm   in 241 Altgeld Hall,  Thursday, October 18, 2012
 Del Edit Copy
Submitted by collier3.
 Seth Wolbert (UIUC Math)Stacks in Differential GeometryAbstract: A stack over the category of smooth manifolds is a structure that can be used to generalize the deconstructive (i.e., via restriction) and reconstructive (i.e.,via gluing) properties seen in fiber bundles. This talk is designed to give a gentle introduction to these structures and some of their nice properties. Given time, we will also discuss the stack of transport functors and how parallel transport induces an equivalence of categories between this stack and the stack of principal G-bundles with connections.

Groupoids and Stacks
3:00 pm   in 345 Altgeld Hall,  Thursday, October 18, 2012
 Del Edit Copy
Submitted by lerman.
 Rui Fernandes (UIUC Math)Introduction to Lie groupoids (continued)Abstract: More fun with Lie groupoids

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, October 18, 2012
 Del Edit Copy
Submitted by jvalidas.
 Howard Osborn (UIUC Math)New facets of Kaehler DerivativesAbstract: If a commutative algebra over a field of characteristic zero is isomorphic to a function algebra with values in the field, and if the unit element is the only nonzero idempotent, then the universal Kaehler derivative annihilates only the elements that correspond to constant functions. This result is used to show that the cotangent spaces of the algebra are mutually isomorphic, and that such an algebra has the analog of a smooth atlas if and only if its Kaehler module is reflexive.

Mathematics Colloquium
4:00 pm   in Altgeld Hall 245,  Thursday, October 18, 2012
 Del Edit Copy
Submitted by kapovich.
 Alex Furman (University of Illinois at Chicago)Groups with good pedigrees, or superrigidity revisitedAbstract: In the 1970s G.A. Margulis proved that certain discrete subgroups (namely lattices) of such Lie groups as SL(3,R) have no linear representations except from the given imbedding. This phenomenon, known as superrigidity, has far reaching applications and has inspired a lot of research in such areas as geometry, dynamics, descriptive set theory, operator algebras etc. We shall try to explain the superrigidity of lattices and related groups by looking at some hidden symmetries (Weyl group) that they inherit from the ambient Lie group. The talk is based on a joint work with Uri Bader.