Mark your calendars for our mini-conference, which will take place on Thursday, February 15, all afternoon in 1147 Mathematical Sciences Building.

There will be inspiring talks by GGAM faculty, a poster session, and a reception with Lunar New Year celebration.

Schedule:

1:10–1:30 Talk – Bruno Nachtergaele: Quantum States of Matter — Unravelling Hidden Structure

1:40–2:00 Talk – Shu-Hua Chen: Effects of Assimilating Aerosol Optical Depth (AOD) Observations on Dust and Weather Forecasts over North Africa and the East Atlantic

2:00–2:20 Talk – Steve Shkoller: PDE methods for numerical shock wave collision, contact discontinuity evolution, and noise removal

2:20–3:00 Coffee break / Poster Session

3:00–3:20 Talk – Janko Gravner: Long-range growth models

3:20–3:40 Talk – Sharon Aviran: patteRNA: transcriptome-wide search for functional RNA elements via structural data signatures

3:40–4:00 Talk – Alan Hastings: Spatio-temporal dynamics in ecology

4–6 GGAM Reception and Lunar New Year celebration (jointly with Dept. of Mathematics) – in MSB courtyard


Abstracts:


Bruno Nachtergaele: Quantum States of Matter — Unravelling Hidden Structure

At atomic and subatomic scales, matter is described by mathematical models based on the laws of quantum mechanics. Entanglement, the single most characteristic feature of quantum mechanics, gives rise to rather unintuitive effects that are not found in the physical world we experience by direct observation. The superfluid and superconducting states are just two of the best known examples. We will discuss another type of quantum matter and a topic of intense current interest: topological order and the emergence of a new type of particles called anyons, and give a glimpse of the wide range of mathematics that is successfully used to unravel the secrets of these new states of matter.

Shu-Hua Chen: Effects of Assimilating Aerosol Optical Depth (AOD) Observations on Dust and Weather Forecasts over North Africa and the East Atlantic

In this study, three data assimilation (DA) methods were used to investigate the impact of assimilating Aerosol Optical Depth (AOD) observations on dust and weather forecasts over North Africa and the East Atlantic. DA cycles were carried out every 6 hour for one-month cycling period of June 2015 using GSI 3D-Var, EnKF, and hybrid methods, and 72-h forecasts initialized by each cycle’s analysis were made. We verified analyses and forecasts of all DA experiments using reanalysis and satellite data.

Some basic statistics (e.g., observation minus background vs. observation minus analysis) show that all observations (conventional, satellite radiance, and AOD) are appropriately assimilated in all DA experiments. Both meteorological and dust forecasts are improved with the assimilation of AOD observations through the correction of dust and thus dust-cloud-radiation interactions. The hybrid experiment performs better than the 3D-Var and EnKF experiments. Although the difference between the EnKF and 3D-Var experiments is not significant, both meteorological and AOD fields in the EnKF experiment are slightly closer to the observations than those in the 3D-Var experiment. This is because taking full advantage of AOD observations via flow-dependent background error covariance in the EnKF experiment leads to more accurate description of meteorological fields as well as dust fields via dust-physics interaction.

Steve Shkoller: PDE methods for numerical shock wave collision, contact discontinuity evolution, and noise removal

I will show a number of movies describing a novel numerical method for multi-dimensional shock wave collision and high-frequency noise removal, which is based on ideas from the analysis of PDE.

Janko Gravner: Long-range growth models

The talk will review results on long range growth models, which are inspired by incompatibilities in genotype spaces. The main questions are: under what conditions does the initial set grow to fill the available space and how fast does it do so? The methods typically involve extremal combinatorics.

Sharon Aviran: patteRNA: transcriptome-wide search for functional RNA elements via structural data signatures

Establishing a link between RNA structure and function remains a great challenge in RNA biology. The emergence of high-throughput structure profiling experiments is revolutionizing our ability to decipher structure, yet principled approaches for extracting information on structural elements directly from these data sets are lacking. We present patterRNA, an unsupervised pattern recognition algorithm that rapidly mines RNA structure motifs from profiling data. We demonstrate that patterRNA detects motifs with an accuracy comparable to commonly used thermodynamic models and highlight its utility in automating data-directed structure modeling from large data sets.

Alan Hastings: Spatio-temporal dynamics in ecology

I will highlight the importance of this topic and show how ideas from mathematics play such a key role in understanding spatial ecology. I will emphasize both how process leads to pattern and the problem of inferring process from pattern.