Title: Mathematical Knowledge for Teaching Chemistry

Date: 02/26/2018

Time: 12:00 PM - 1:00 PM

Place: 252 EH

Progress toward STEM degree depends not only on completing required mathematics courses but also being able to successfully use mathematics to support learning in science courses. Introductory college chemistry courses are often the first place where inadequate preparation in mathematics impedes students’ learning in science. In this talk, Drs. Posey and Bieda will share their efforts to strategically incorporate mathematics support for students in Introductory Chemistry. Our findings suggest important implications for developing students’ conceptual understanding in mathematics courses. We will also share what we have learned about forging and sustaining an interdisciplinary research project.

Title: Taking the long way home: Orbits of plane partitions

Date: 02/27/2018

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Plane partitions are piles of cubes stacked in the corner of a room. P. Cameron and D. Fon-der-Flaass (1995) studied a simple action on such piles, whose dynamics are nonetheless quite mysterious. In particular, repeating this action will always eventually return the original pile, but sometimes the voyage is much longer than expected. Motivated by some deep problems in algebraic geometry, H. Thomas and A. Yong (2009) introduced a suite of combinatorial algorithms on certain grids of numbers. In particular, there is a beautiful K-theoretic promotion operator, which again has some mysteriously large orbits, despite its simple combinatorial definition. We'll see how these two mysteries are in fact the same mystery, and use this relation to explain special cases of both actions. (Based on joint work with Kevin Dilks and Jessica Striker)

Speaker: Jennifer Langer-Osuna, Stanford University

Title: Fostering productive and inclusive collaborative mathematics classrooms

Date: 02/28/2018

Time: 1:45 PM - 3:15 PM

Place: 252 EH

Student-led group work is an increasingly common activity in K-12 mathematics classrooms. Students are expected to debate ideas, justify conjectures, and come to consensus on reasonable approaches to solving problems. Yet several studies have shown that some students become unduly influential, while others' contributions are routinely marginalized. This talk pursues the question, how can collaborative mathematics classrooms foster both equity and productivity? To do so, this talk begins with an exploration of the role of authority relations during collaborative math activity, followed by new design research, in partnership with local schools, based on the results of earlier, exploratory work. The talk closes by contextualizing these projects in a broader body of work focused on examining classrooms designed to equitably engage students from diverse backgrounds in intellectually productive mathematical activity.

We relate fillability of two link exteriors,
and the question when two links admit homeomorphic
surface systems to (a refinement of) Milnor’s triple
linking numbers. This extends a theorem of Davis-Roth
to include also links with non-vanishing linking numbers.
This is joint work with C. Davis, P. Orson, and M. Powell.

Title: Optimal Large Deviation Theory for analytic quasi-periodic Schr\"odinger cocycle and H\"older regularity of the Lyapunov exponent

Date: 03/01/2018

Time: 3:00 PM - 4:00 PM

Place: C517 Wells Hall

Abstract:
We consider 1-d discrete quasi-periodic Schr\"odinger equations and the associated Schr\"odinger cocycles. Suppose the potential is real analytic function with bounded extension, assume positive Lyapunov exponents. We prove some refined Large Deviation Theory (LDT) for any irrational frequency in an exponential regime with respect to the Lyapunov exponent. The large deviation estimates imply some optimal H\"older continuity results of the Lyapunov exponents and the integrated density of states. For small Lyapunov exponent regime, we show that the local H\"older exponent is independent of energy E for Liouville frequency. In the large coupling regime, we show that the local H\"older exponent is independent of the coupling constant. Previously, such coupling independency is only known in the case where the potential is a trigonometric polynomial with (Strong) Diophantine frequency.

Title: Upper cluster algebras and choice of ground ring

Date: 03/01/2018

Time: 3:10 PM - 4:00 PM

Place: C329 Wells Hall

Cluster algebra structures often appear naturally in coordinate rings of algebraic varieties. In many cases the coordinate ring ends up being isomorphic to the corresponding upper cluster algebra. The choice of ground ring the cluster algebra is generated over determines if the cluster algebra consists of regular functions on the algebraic variety. We will discuss how to the choice of ground effects wether or not the cluster algebra coincides with its upper cluster algebra.

Title: Algorithms for mean curvature motion of networks

Date: 03/01/2018

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Motion by mean curvature for networks of surfaces arises in a variety of
applications, such as the dynamics of foam and the evolution of
microstructure in polycrystalline materials. It is steepest descent
(gradient flow) for an energy: the sum of the areas of the surfaces
constituting the network.
During the evolution, surfaces may collide and junctions (where three or
more surfaces meet) may merge and split off in myriad ways as the
network coarsens in the process of decreasing its energy. The first idea
that comes to mind for simulating this evolution -- parametrizing the
surfaces and explicitly specifying rules for cutting and pasting when
collisions occur -- gets hopelessly complicated. Instead, one looks for
algorithms that generate the correct motion, including all the necessary
topological changes, indirectly but automatically via just a couple of
simple operations.
An almost miraculously elegant such algorithm, known as threshold
dynamics, was proposed by Merriman, Bence, and Osher in 1992. Extending
this algorithm, while preserving its simplicity, to more general
energies where each surface in the network is measured by a different,
possibly anisotropic, notion of area requires new mathematical
understanding of the original version, which then elucidates a
systematic path to new algorithms.