Title: Tangent measures (D. Preiss ``Geometry of measure in R^n') - III

Date: 10/10/2016

Time: 1:40 PM - 3:10 PM

Place: C304 Wells Hall

We continue to explore Preiss's paper. We will finish Section 2 by showing that compact tangent cones are connected (in particular, a tangent cone cannot be generated by two different measures) and pass to the study of uniform measures in Section 3.

Title: Two phase free boundary problem of Chris Bishop: how singular integrals and blow up methods solve it.

Date: 10/10/2016

Time: 4:02 PM - 5:00 PM

Place: C517 Wells Hall

This is a report of a joint work with Azzam, Mourgoglou and Tolsa. Harmonic measure was in the focus of attention of many analysts (Bishop, Bourgain, Carleson, Jones, Makarov, Wolff to name a few) in 1985-1995. Beautiful metric properties of harmonic measure were revealed during this period, this concerns especially a 2D case. In higher dimensions the behavior was more enigmatic, and many problems were left for the future. Recently it turned out that the technique of non-homogeneous harmonic analysis developed by (among others) Nazarov-Treil-and the speaker (NTV) is the right tool to clarify several
outstanding questions about harmonic measure in 3 and higher dimensions. We will show how to solve yet another problem formulated by Chris Bishop in 1992.

Title: Positivity and combinatorics of some bases of cluster algebras

Date: 10/11/2016

Time: 1:00 PM - 1:50 PM

Place: C304 Wells Hall

Lots of research of cluster algebras focuses on construction of their natural bases. A desirable property of a good basis is that all elements are universally positive and that all structure constants are positive. In this talk, I will survey some bases that have this property. In particular, I will talk about the theta function bases constructed by Gross, Hacking, Keel and Kontsevich using scattering diagrams and broken lines, and give an explicit combinatorial description of these broken lines in special cases.

Title: What We Still Don’t Know About Addition and Multiplication

Date: 10/11/2016

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

How could there be something we don’t know about arithmetic? It would seem that subject was sewn up in third grade. But here’s a problem we don’t know the solution to: What is the most efficient method for multiplication? And here is another: How many different numbers appear in a large multiplication table? There are many more such problems, largely unsolved, and for which we could use some help!

Speaker: Gregory Larnell, University of Illinois - Chicago

Title: We Real Cool: Reconsidering the Cooling Out Phenomenon in a Remedial Mathematics Education Context

Date: 10/12/2016

Time: 3:30 PM - 4:20 PM

Place: 252 EH

Recognizing the gatekeeping function of mathematics as curricular discipline has been a longstanding subject of mathematics education research and scholarly debate. Difficult and complex questions about how this gatekeeping occurs, however, have been explored less frequently. Furthermore, everyday social occurrences by which mathematics gatekeeping and racialized inequity intersect have received even less attention. In this talk, I will re-introduce and discuss the cooling out phenomenon in education (COPE), a concept that originates in sociology and has re-emerged across several academic disciplines, including higher education. This time, the purpose is to understand how COPE functions amid Black undergraduates’ experiences within remedial mathematics courses. Drawing on two recent studies in which I analyzed series of interviews, I discuss the ways that COPE unfolds amid study participants’ experiences, who and what processes may be involved in COPE, and implications regarding COPE for mathematics education research more broadly.

A 2-knot is defined to be an embedding of S^2 in S^4. Unlike for knots
in S^3, the theory of concordance of 2-knots is trivial. This talk
will be framed around the related concept of 0-concordance of 2-knots.
It has been conjectured that this is also a trivial theory, that every
2-knot is 0-concordant to every other 2-knot. We will show that this conjecture is false, and in fact there are infinitely many 0-concordance classes.
We'll in particular point out how the concept of 0-concordance is
related to understanding smooth structures on S^4. The proof will
involve invariants coming from Heegaard-Floer homology, and we will
furthermore see how these invariants can be used shed light on other
properties of 2-knots such as amphichirality and invertibility.

Title: The ranges of some familiar arithmetic functions

Date: 10/13/2016

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

We consider 4 functions from elementary number theory:
sigma (the sum-of-divisors function), phi (Euler's function),
lambda (Carmichael's universal exponent function), and s (the
sum-of-proper-divisors function). In particular we discuss the
distribution of the values of these functions, and coincidences
of values. Most of the problems considered have a fairly long
history, some over 80 years. We report on recent progress.
(Various parts of this work are joint with Kevin Ford,
Florian Luca, Paul Pollack, and others.)

Speaker: Pierre Gremaud, North Carolina State University

Title: Data analysis for mathematicians: the example of syncope

Date: 10/14/2016

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

We will discuss four important concepts in the analysis of data:
variable importance, surrogate models, classification and clustering.
Each of these concepts will be introduced from scratch with a general
mathematical audience in mind. In particular, we will introduce methods
for nonparametric statistics as well as new results in global
sensitivity analysis.
The material of the talk will be illustrated by the analysis of syncope
data. Syncope refers to a spontaneous and transient loss of
consciousness. It is a prevalent disorder which accounts for over 1
million visits to emergency departments per year in the US alone. There
is currently no agreement on the root causes of that disorder.