Week of December 5, 2021

Mon Dec 6, 2021
12:00pm - Zoom - Probability and Analysis Webinar
Ioana Dumitriu - (UC San Diego)
TBA

https://sites.google.com/view/paw-seminar

4:00pm to 5:00pm - - Applied and Computational Mathematics
Keith Promislow - (Michigan State U.)
TBA
4:00pm - RH 306 and Zoom: https://uci.zoom.us/j/97796361534 - Applied and Computational Mathematics
Keith Promislow - (Michigan State U.)
Packing and Entropy in Amphiphilic Diblock-Polymer Blends

Packing and entropy play crucial roles in self-assembly of structured (di-block, triblock) polymers in solvent.  We revisit the random phase reductions of self-consistent mean field models of Choksi-Ren and Uneyama-Doi, including a longer-range interaction associated to partial charges, we  derive the functionalized diblock phase-field model for the free energy.  We show that reductions of this model connect to the scalar models of Gompper-Schick and Gommper-Goos for oil-water-surfactant microemulsions, and then present an analysis of a blend of long and short polymers, identifying a scaling regime in which geometric singular perturbations techniques and simple micro-local analysis can be applied to show that interdigitations of long and short polymers, evocative of the role of sterols in phospholipid bilayers, can have a stabilizing effect.

Thu Dec 9, 2021
9:00am to 10:00am - Zoom - Inverse Problems
Xue-Cheng Tai - (Hong Kong Baptist University)
Deep neural networks in image processing

https://sites.uci.edu/inverse/

10:00am to 11:00am - https://uci.zoom.us/j/97664033581 - Mathematical Physics
Siegfried Beckus - (University of Potsdam)
The table and the chair: Spectral approximations beyond dimension one

The table and the chair tiling are two aperiodic tilings of the plane that are typical examples of two-dimensional quasicrystals. One way to treat such systems in dimension one, is to approximate these systems by suitable (periodic) approximations. Based on this, we raise the following questions: Is there a general method to approximate spectral properties of a given operator by the underlying geometry or dynamics? If so, can we control the approximations and which spectral properties are preserved? During the talk, we provide a short overview over such results with a special focus on dynamicallydened operator families. We will see as how to apply those results explicitly and what they tell us about the table and the chair tiling. These results are joint works with Ram Band, Jean Bellissard, Horia Cornean, Giusseppe De Nittis, Felix Pogorzelski, Alberto Takase and Lior Tenenbaum.