Events for 11/15/2019 from all calendars

Lines in the curriculum: A persistent obstruction to achievement connecting algebra and geometry

Time: 12:30PM - 1:30PM

Location: BLOC 220

Speaker: Michael Fried, University of California at Irvine

Description: The topic of lines in the curriculum has conceptual teaching difficulties that you can't solve only by applying the typical blue-ribon interventions:

1. better prepared teachers; and
2. assuring students have perfect educational beginnings.

• The subject, lines, passes through many different conceptions moving from 3rd grade to 12th grade and then to sophomore college classes. So much so, that a great 3rd grade teacher, or sound understanding of the number line won't suffice for a student's ultimate success on related math concepts.
• There is a wipeout problem. One not covered alone by increasing resources in 1st year calculus. We document that an epiphany is possible with administration in The Howard Thompson Story . We document a remedy with – not necessarily exceptional – students in Interactive E-Mail Assessment, MAA Vol. on Assessment, B. Gold, S.Z. Keith, and W.A. Marion, eds., #49, Wash. DC, 1999, 80-84.
• Technology – I(nteractive) Q(uestionnaire)s (IQs) – appears here in a surprising way, to gather information from an ordinary class, run by an ordinary instructor. The style of programming is less critical than the form of the curricular assessment

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Sohrab Shahshahani, UMass Amherst

Title: Asymptotic stability of harmonic maps on the hyperbolic plane under the Schrodinger maps evolution

Abstract: We consider the Cauchy problem for the Schrodinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studied case on the Euclidean plane is the existence of a rich new family of finite energy harmonic maps. These are stationary solutions, and thus play an important role in the dynamics of Schrodinger maps. The main result is the asymptotic stability of (some of) such harmonic maps under the Schrodinger maps evolution. More precisely, we prove the nonlinear asymptotic stability of a finite energy equivariant harmonic map Q under the Schrodinger maps evolution with respect to non-equivariant perturbations, provided that Q obeys a suitable linearized stability condition. This is joint work with Andrew Lawrie, Jonas Luhrmann, and Sung-Jin Oh.

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Jurij Volcic, Texas A&M University

Title: The Procesi-Schacher conjecture and positive trace polynomials

Abstract: Hilbert’s 17th problem asked whether every positive polynomial can be written as a sum of squares of rational functions. An affirmative answer by Artin is one of the cornerstones of real algebraic geometry. Procesi and Schacher in 1976 developed a theory of orderings and positivity on central simple algebras with involution and posed a H17 problem for a universal central simple $*$-algebra of degree $n$. It has a positive answer for $n=2$. Recently we proved that the answer for $n=3$ is negative. Nevertheless, we obtained several positivity certificates (Positivstellensätze) for trace polynomials on semialgebraic sets of $n\times n$ matrices. The talk will be a gentle introduction to this mix of central simple algebras, invariant theory and real algebraic geometry.

Seminar on Banach and Metric Space Geometry

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Chris Gartland, University of Illinois at Urbana-Champaign

Title: Markov Convexity of Model Filiform Groups

Abstract: The Ribe program is the research program concerned with generalizing local properties of Banach spaces to biLipschitz invariant properties of metric spaces. Among such generalizations that have been found is the notion of Markov p-convexity, proven by Mendel-Naor to generalize uniform p-convexity. One of the first important spaces for which this invariant has been calculated is the Heisenberg group, proven by Li to be Markov p-convex for every p ≥ 4 and not Markov p-convex for any p<4. In this talk, we'll start with background on Carnot groups and model filiform groups - a class of Carnot groups containing the Heisenberg group - and then explain how to use random walks on graphs to compute their Markov convexities.

Student Working Seminar in Groups and Dynamics

Time: 3:00PM - 4:00PM

Location: BLOC 605AX

Speaker: Konrad Wrobel

Title: Compact Extensions of Szemeredi Factors