Applied Harmonic Analysis and Data Science (hybrid meeting)

Data science has become a field of major importance for science and technology nowadays and poses a large variety of challenging mathematical questions. The area of applied harmonic analysis has a significant impact on such problems by providing methodologies both for theoretical questions and for a wide range of applications in signal and image processing and machine learning. Building on the success of three previous workshops on applied harmonic analysis in 2012, 2015 and 2018, this workshop focused on several exciting novel directions such as mathematical theory of deep learning, but also reported progress on long-standing open problems in the field

Applied Harmonic Analysis and Sparse Approximation

Efficiently analyzing functions, in particular multivariate functions, is a key problem in applied mathematics. The area of applied harmonic analysis has a significant impact on this problem by providing methodologies both for theoretical questions and for a wide range of applications in technology and science, such as image processing. Approximation theory, in particular the branch of the theory of sparse approximations, is closely intertwined with this area with a lot of recent exciting developments in the intersection of both. Research topics typically also involve related areas such as convex optimization, probability theory, and Banach space geometry. The workshop was the continuation of a first event in 2012 and intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations

Observations of Coherence in Oxygenic Photosynthesis.

The field of two dimensional electronic spectroscopy (2DES) is rapidly advancing, both in theory and implementation to tackle increasingly complex and delicate problems. In the past seven years, observations of coherent or wave-like dynamics in 2D spectra of photosynthetic antenna has captured the imagination of many practitioners in the field, from theorists to experimentalists. Two questions are being raised: what is the origin of coherent dynamics in photosynthesis and, more importantly, do they matter for the function of biological systems? For certain photosynthetic antenna systems there is now considerable evidence and theoretical backing to suggest that coherent dynamics have a positive functional impact on energy transfer. Less explored is how such dynamics may influence charge separation, the primary purpose of photosynthetic reaction centers. Coherent signals are typically weak and difficult to resolve from population dynamics. To address this issue, we developed a method to collect 2DES which has dramatically improved the signal to noise over previous implementations. The new method has been applied to the photosystem II reaction center (PSII RC). The PSII RC is the photosynthetic enzyme uniquely capable of using solar energy to split water. As such it is an important system both for basic plant science and renewable energy generation. With this technique, we find eight coherent modes in PSII RC in the first such report of coherent dynamics on this system. Most of the wave-like motions are assigned to be of vibrational character while four are assigned to a mixture of vibrational and electronic character. Based on supporting simulations it is shown that charge separation is enhanced by the inclusion of such mixed character modes.PhDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/109003/1/fullerf_1.pd