Seminar Calendar
for events the day of Thursday, February 9, 2012.

.
events for the
events containing

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



Thursday, February 9, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by ford.
 Jimmy Tseng (UIUC Math)Bounded Luroth expansionsAbstract: Luroth series expansions are in a family of various expansions of the real numbers, a family which includes continued fractions. Like for continued fractions, every real number can be expressed as a Luroth expansion. Also like for continued fractions, the digits of a Luroth expansion are generated by a self-map, the Luroth map. The digits are, of course, an encoding of the map and give us a geometric way of looking at the expansion. I will give a sketch of the proof of the following result (joint with B. Mance): the set B of numbers with bounded Luroth expansion, bounded continued fraction expansion, and bounded n-ary expansion for every integer n > 1 is a dense set of full Hausdorff dimension. (Each of these conditions on B would form a superset of zero Lebesgue measure.) The proof is based on applying a technique developed by W. Schmidt (or a later variant made by C. McMullen) to the Luroth map,which has infinite distortion, and is adapted from techniques that I developed in 2009 for cases of bounded distortion.

Lunch Seminar on NetMath
12:05 pm   in 102 Altgeld Hall,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by gfrancis.
 Pat Szuta   [email] (Mathematics/Urbana)IT Innovations in Online Math Development and InstructionAbstract: The University of Illinois has a long history of creating tools for effectively instructing mathematics online. These home-grown systems are often necessary because mathematics rarely fits into industry standards of online instruction. We will discuss how many of the challenges of teaching math online are rooted in technology, and what is currently being done to solve them.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by kapovich.
 Catherine Pfaff (Rutgers - Newark)Constructing and Classifying Fully Irreducible Outer Automorphisms of Free GroupsAbstract: The main theorem of my thesis emulates, in the context of $Out(F_r)$ theory, a mapping class group theorem (by H. Masur and J. Smillie) that determines precisely which index lists arise from pseudo-Anosov mapping classes. Since the ideal Whitehead graph gives a finer invariant in the analogous setting of a fully irreducible $\phi \in Out(F_r)$, we instead focus on determining which of the 21 connected 5-vertex graphs are ideal Whitehead graphs of ageometric, fully irreducible $\phi \in Out(F_3)$. Our main theorem accomplishes this. The methods we use for constructing fully irreducible $\phi\in Out(F_r)$, as well as our identification and decomposition techniques, can be used to extend our main theorem, as they are valid in any rank. Our methods of proof rely primarily on Bestvina-Feighn-Handel train track theory and the theory of attracting laminations.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, February 9, 2012
 Del Edit Copy
Submitted by aimo.
 Kevin Wildrick (University of Bern)Lipschitz constants and differentiability almost everywhereAbstract: Rademacher's theorem that Lipschitz functions are differentiable almost everywhere forms the backbone of results in function theory, geometric measure theory, and geometric topology. A prime example is Cheeger's theorem regarding the existence of differentiable structures on metric spaces supporting a Poincaré inequality. We will review some classical results and then discuss a version of Rademacher's theorem for the "lower" Lipschitz constant, which detects oscillation only on some sequence of scales tending to zero, rather than on all sequences of scales tending to zero. We also provide an example showing the sharpness of the results and the relationship of differentiability to the capacity of points.