Seminar Calendar
for events the day of Thursday, February 2, 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 2, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by ford.
 Daniel Fiorilli (IAS Princeton)On how the first term of an arithmetic progression can influence the distribution of an arithmetic sequenceAbstract: We will show that many arithmetic sequences have asymmetries in their distribution amongst the progressions mod q. The general phenomenon is that if we fix an integer a having some arithmetic properties (these properties depend on the sequence), then the progressions a mod q will tend to contain fewer elements of the arithmetic sequence than other progressions a mod q, on average over q. The observed phenomenon is for quite small arithmetic progressions, and the maximal size of the progressions is fixed by the nature of the sequence. Examples of sequences falling in our range of application are the sequence of primes, the sequence of integers which can be represented as the sum of two squares (or more generally by a fixed positive definite binary quadratic form) (with or without multiplicity), the sequence of twin primes (under Hardy-Littlewood) and the sequence of integers free of small prime factors. We will focus on these examples as they are quite fun and enlightening.

Lunch Seminar on NetMath
12:05 pm   in 102 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by gfrancis.
 Bruce Carpenter   [email] (Mathematics/Urbana)The Pedagogy of NetMathAbstract: The NetMath online instructional model attempts to integrate three things: courseware designed to help students learn mathematics by dynamic exploration and visualization, the incorporation of a computer algebra system for students to perform calculations and write full explanations of their solution process, and a learning management system to streamline administration of the course and promote communication between students, instructors, and mentors. We will discuss each of these in detail by presenting the current system and its challenges as well as surveying possible innovations to improve instruction.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by kapovich.
 Albert Fisher (University of Sao Paulo)A flow crossection for Moeckel's theorem on continued fractionsAbstract: We construct a cross-section to the principal congruence modular flow which is represented as a skew product transformation over the natural extension of the Gauss map. This leads to a new proof of Moeckel's theorem on rational approximants. For an irrational number $x$ in the unit interval with continued fraction expansion $[n_0 n_1...]$, let $p_k/q_k=$[n_0 n_1..n_k] be the rational approximants for $x$. Writing these in lowest terms, they can be of three types: $\frac{O}{E}$, $\frac{E}{O}$, or $\frac{O}{O}$ where $O$ stands for odd and $E$ for even. Moeckel's theorem states that the frequency of each of these exists almost surely. What is unusual in the proof is that this does not follow directly from the ergodic theorem applied to an observable on the Gauss map (the shift on continued fractions): one must first enlarge the space. Moeckel's approach makes use of the geodesic flow on a three-fold cover of the modular surface, together with a geometric argument for counting the time that geodesics spend in cusps. Ergodicity of the flow is automatic (via the Hopf argument) but the counting is somewhat involved. Later Jager and Liardet found a second purely ergodic theoretic proof, constructing a skew product over the Gauss map. There the counting is direct, but the proof of ergodicity is more difficult. Our proof unifies the two earlier arguments, inheriting these strong points of each.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by aimo.
 Robert Kaufman (UIUC Math)Renorming of Banach spaces - a metrical propertyAbstract: A bounded set S in a metric space has a radius, defined by closed disks containing S. When the infimum of radii is realized by a closed disk, S is "centered". Theorem: A nonreflexive Banach space X can be renormed so that some set {a,b,c} in X is not centered. This provides a second (or third) proof of the renorming theorem of W. Davis and W. Johnson (1973).

2:00 pm   in 241 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by lukyane2.
 Ser-Wei Fu (UIUC Math)Length Spectra and Deformation FamiliesAbstract: This is a practice talk for the preliminary exam. I will define and describe the spectral rigidity problem and talk about known results. The talk will be focused on clearly defining every object and giving examples to illustrate a new approach to the problem. To be specific, two main topics that will be discussed are flat metrics and train tracks on surfaces.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, February 2, 2012
 Del Edit Copy
Submitted by beder.
 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, hence a smooth structure, if and only if the Kaehler module is reflexive.