Speaker: David Webb (Associate Professor of Mathematics Education Executive Director, Freudenthal Institute US University of Colorado Boulder School of Education)

Title: Infusing Active Learning Design Principles in the Undergraduate Calculus Sequence

Abstract: This interactive presentation will provide a brief overview of undergraduate mathematics at the University of Colorado Boulder, and related activities that we and other universities have designed and used in the freshman pre-calculus through Calculus 2 sequence. Using principles of Active Learning, students are encouraged to conjecture, explore and communicate their reasoning in the process of solving mathematics problems. Underlying this approach is research that has demonstrated how students who are involved in active learning techniques can learn more effectively in their classes, resulting in lower DFW rates, increased persistence in subsequent courses, and improved dispositions towards mathematics.

Speaker: Victor Donnay, William Kenan, Jr Professor of Mathematics and Director, Environmental Studies program, Bryn Mawr College

Title: Connecting Math and Sustainability

Abstract: How can we better inspire our students to study and succeed in mathematics? Victor Donnay will discuss his experiences in using issues of civic engagement, particularly environmental sustainability, as a motivator. He will present a variety of ways to incorporate issues of sustainability into math and science classes ranging from easy to adapt extensions of standard homework problems to more elaborate service learning projects. He will share some of the educational resources that he helped collect as chair of the planning committee for Mathematics Awareness Month 2013- the Mathematics of Sustainability as well as his TED-Ed video on Tipping Points and Climate Change. He has used these approaches in a variety of courses including Calculus, Differential Equations, Mathematical Modeling and Senior Seminar.

Title: A curiosity of the trace operator II

Abstract: I’ll discuss the regularity of the trace operator on various smoothness spaces. In short, this is an operator which reduces (roughly) smoothness as measured in L_p by an order of 1/p. Its behavior on Sobolev spaces, especially on the Hilbert spaces W_2^s (i.e., where smoothness is measured in L_2), plays a critical role in approximation theory when boundaries are present, and in the stability, regularity and existence results for weak solutions for PDEs.

Previously I presented a somewhat negative results: that the trace operator from W_2^(1/2) to L_2 is not bounded (although it is bounded from W_2^{s+1/2} to W_2^s when s>0. In this talk, I’ll explain how a minor correction (a so-called “curiosity” according to Hans Triebel) works – namely, by reducing the domain to a certain Besov space and using results from the atomic decomposition of these spaces.

Hilbert’s third problem, scissors congruence, and the Dehn invariant

Speaker: Joe Gerver (Rutgers)

Title: Non-collision singularities in the n-body problem: history and recent progress

Abstract: In the 1890′s, Poincare asked whether, in the n-body problem with point masses and Newtonian gravitation, it is possible to have a singularity without a collision. This might happen, for example, if one or more bodies were to oscillate wildly, like the function sin (1/t). We will go over the history of this problem for the past 120 years, including some recent developments.

Speaker: Michelle Manes (UH Mānoa)

Title: Curve-based cryptography, a tour of recent developments

Abstract: Elliptic curve cryptography (ECC) was first proposed in the mid 1980s, but it took 20 years for ECC algorithms to become widely used. Researchers are currently laying the mathematical foundations for cryptosystems based on genus 2 and more recently on genus 3 curves. If we’re successful, these systems may be widely used in another 10 years or so. Many of the breakthroughs in this area have come from research collaborations forged at the Women in Numbers and Sage Days for Women conferences.

In this talk, I’ll give a brief introduction to the idea of cryptosystems based on the “discrete log problem,” including ECC and higher genus curves. I’ll trace the story of the recent results, and I’ll provide some mathematical details for the most recent work on genus 3 curves.