On March 24th, we are organising a symposium titled "Unexpected Connections", with talks that fit all study directions.

There will be two parallel sessions. The schedule is as follows:

After the symposium, there will be a reception at the Vagant from 17:00 until 18:30.

The speakers have been kind enough to write a short abstract of their talks:

Lisa Tran - "Controlling the bulk from the surface: liquid crystal pattern formation and assembly"

Liquid crystals are ubiquitous in modern society. These materials are the basis of the modern display industry because of their unique properties. They can be manipulated with electric fields, can alter light, and are deformable, elastic fluids --- all properties that are important for engineering a pixel. Yet, liquid crystalline ordering can occur across length scales from nanometric, molecular assemblies to even the centimeter-scale. Although most people associate LCs with displays, they are also pervasive in larger-scaled, living systems. And despite their wide applications, the structures that liquid crystals can form are yet to be completely understood. Current research aims to elucidate these structures. Geometrical constraints can generate patterns and defects – localized, “melted” regions of disorder that can lower the distortion in the system and that can be used to assemble inclusions. Defects can be controlled by using microfluidics to create water-in-liquid crystal-in-water double emulsion droplets – confining the liquid crystal into spherical shells [1]. Molecular configurations are controlled by the topology and geometry of the system and by varying the concentration of surface-active molecules (surfactants) at the liquid crystal interface.

In this talk, I examine defect structures in this system using both experiments and simulations. Beyond equilibrium configurations, I will present recent results where changing the surfactant concentration can strain the system, producing hierarchical, periodic patterns that are also found in biomaterials [2]. I will then present experiments where surface-active particles are used in place of traditional surfactants to pattern them at the liquid crystal-water interface [3, 4]. I end by surveying ongoing experiments in my group that probe the role of surface control for patterning liquid crystal structures across length-scales. These organizing principles provide insight on pattern formation in biological materials, the mechanisms of which can be leveraged for designing bio-inspired technologies.

[1] L. Tran, et. al., Phys. Rev. X (2017) 7:041029.

[2] M.O. Lavrentovich and L. Tran, Phys. Rev. Research (2020) 2:023128.

[3] L. Tran, et al., Science Advances (2018) 4, 10, eaat8597.

[4] L. Tran, K.J.M. Bishop, ACS Nano (2020) 14, 5, 5459 -5456.

Frits Beukers- “The secrets of Riemann's zeta-function”

The distribution of the prime numbers is an ancient mystery, which is still full of unanswered ques. tions. In 1859 Bernard Riemann published a famous ten page paper in which he showed that this distribution is for a large part orchestrated by the zeros of what is now called the Riemann zeta-function.

In this lecture we shall discuss Riemann's conjecture, one of the most notorious problems in pure mathematics, and the striking empirical relationship of the set of zeros with spectra of quantum systems from physics

Carla Groenland - “Graph reconstruction”

Can we reconstruct a network from local snapshots? More formally, the graph reconstruction conjecture (1942) states that a graph on at least three vertices is determined( up to isomorphism) by the multiset of its subgraphs obtained by removing one vertex (plus incident edges). I will survey some of the known results and will show how one can tellw hether the graph is connected from much smaller subgraphs via a result about the real zeros of complex polynomials.

Ro Jefferson - “Physics ∩ Machine Learning”

Machine learning has become both powerful and ubiquitous, but remains a black box whose internal workings are still largely unclear. In this talk, I will discuss some interesting connections between ideas in physics and deep neural networks in particular, whicho collectively motivate a physics-based approach towards a theory of deep learning.

Frank Staals - "Geometric Algorithms for Trajectory Analysis"

Technology such as the Global Positing System (GPS) has made tracking people, animals, or objects easy and cheap. As a result there is a large amount of trajectory data capturing this movement available, and an increasing demand on tools and techniques to analyze such data. We will consider such an analysis tasks, and develop efficient algorithms to perform them automatically. In particular, we will consider the task of segmenting a trajectory. We will formalize the problem, identify relevant geometric properties, and then see how we can use these properties to obtain efficient algorithms for trajectory segmentation.

Rob Bisseling - "Parallel algorithms for finding friends and partners in social networks"

Social networks typically contain many triangles, which means that your friends have a high probably also to be friends of each other. Recommender systems suggest new and sometimes surprising friendship connections, based on finding potential triangles in the network.

In this talk, we will look at the problem of counting triangles in huge networks, and carrying this out efficiently on a parallel computer. We will discuss how to find new connections, and how to match with a suitable partner from among your friends based on the connectivity of the network and the attractions between its members.