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Capillary networks are prevalent in nature and biology, playing a crucial role in systems like animal vasculature and plant capillaries, with broad applications in medicine and science. However, many aspects of how these networks regulate and control flow remain unresolved. While the basic principles of capillary networks and their functions are well understood, ongoing research seeks to uncover how these systems dynamically respond to environmental changes, adapt to varying conditions, and whether they retain a memory of past states. Developing a model system for capillary networks allows us to pose exciting new questions, such as: "Can capillary networks store memory?"Building such a model presents two key challenges. First, the need to dynamically modify the nature of bonds within the networks and understand its impact on transport. Second, designing networks capable of evolving in response to external stimuli. Successfully addressing these challenges could transform our ability to actively control macroscale flow by manipulating local bonds within the networks.Here, a novel experimental model of capillary networks is proposed, consisting of hundreds of interconnected liquid diodes. Like electrical diodes, these microscale surface structures direct liquid flow in specific directions while preventing reverse flow. However, under certain conditions, liquid diodes may fail, permitting bidirectional flow and introducing bonds of varying properties within the capillary network.This system will allow us to investigate whether the wetting state of liquids in the network depends on its actuation history—essentially exploring whether capillary networks can exhibit memory. This question opens up new possibilities, including the potential to encode information within these networks, analyze how transport responds to external stimuli, study the interplay between global actuation and local fluid dynamics, explore the coupling between mechanics and flow, and better understand how information propagates through capillary systems.

Some of the most important open problems in group theory concern whether all groups can be metrically approximated by certain classes of groups. In particular, it is currently unknown whether there exist groups that are not (linear) sofic, hyperlinear, or MF.

 

We introduce the general problem of approximation of groups, as well as the related problem of stability, which asks whether almost homomorphisms from a group are close to actual homomorphisms. We recall a cohomological tool for stability introduced by De-Chiffre, Glebsky, Lubotzky, and Thom, which was used to prove the existence of groups that are not Frobenius-norm approximated. Moreover, we propose a weaker notion of semi-stability, which relates the different classes of approximated groups, and discuss how this cohomological tool can be adapted for this purpose.

 

For more details, check out our website.

We look forward to seeing you in one or both sessions next Monday.

The questions “How did life on Earth begin?” and “Are we alone in the universe?” are arguably two of the most intriguing in science. While until recently these questions tended to be relegated to the “too difficult” box, the attempts to answer them have now become extraordinarily vibrant and dynamic frontiers of science. I will describe how the quest for cosmic life follows two parallel, independent lines of research: cutting-edge laboratory studies aimed at determining whether life can emerge from pure chemistry, and advanced astronomical observations searching for signs of life on other planets and moons in the solar system and around stars other than the Sun. I will examine how using knowledge acquired through ingenious chemical experimentation, geological studies, advanced astronomical observations, and imaginative theorizing researchers have managed to delineate a plausible pathway leading from the formation of the Earth to the appearance of the early biological cells.  

Traumatic brain (TBI) injuries result in profound local hypoperfusion, ischemia, chronic inflammation and refractory seizures(post-traumatic epilepsy (PTE)), and restrict drug delivery to the site of impact so that peripheral treatment alone would have limited access to the site of injury during the most critical phases of neurotrauma. Cannabidiol (CBD), the major non-psychotropic cannabinoid, has anti-convulsant, anti-inflammatory, anti-nociceptive, antioxidant, and immuno-suppressive properties not fully understood. In pre-juvenile rats, microinjection of CBD attenuated kainate(KA)-induced seizures to a greater extent than intraperitoneal injection, indicating that local drug administration was more effective. In adult rats after experimental TBI, our modified CBD-infused implant applied extradural with oil injection supplementation restored vestibulomotorand cognitive functions compared to systemic treatment alone. We questioned whether the CBD or the low concentrations of THC in the extract was responsible for behavioral and cellular recovery.We hypothesized that an optimal ratio of cannabidiol (CBD) to tetrahydrocannabinol (THC) is required to protect against neuropathological consequences following TBI greater than either substance alone. Varied CBD:THC extract concentrations were compared with hempCBD lacking THC (CBD0). Neurons, glia, and parvalbumin interneurons (PV-INs) were evaluated. Weight loss was observed following high doses of THC dominant cannabis, THC100:1. Neuroscoresand vestibulomotorperformance were restored more with CBD:THC300:1-10:1. However, THC dominant treatments resulted in early onset to spontaneous seizures post-TBI. In a non-reward T-maze, the CBD10:1group had the highest alternation rates; TBI + vehicle, CBD0, CBD1:1, and THC100:1treatment groups had the lowest. The novel object recognition memory task showed CBD300:1treated animals had the best performance, while TBI or THC100:1treated groups had the worst. The forced swim test (FST) showed immobility time was highest after TBI and lowest after THC100:1treatment. The elevated plus maze (EPM) revealed the CBD0group spent the most time in closed arms. Both tests indicate that reduced anxiety was THC dependent. All combinations resulted in reduced injury but CBD10:1and THC20:1gave the most protection and THC100:1the least. Reduced anxiety level was THC dependent but higher doses were pro-convulsant cautioning THC dosing. Reduced GFAP labeling was highest with CBD dominant cannabis supporting its neuroprotective role against inflammation. Rescue of diminished bilateral PV-INs was observed within the hippocampus and medial prefrontal cortex (mPFC) with CBD dominant treatment (CBD300, CBD0) supporting their anticonvulsant effect. Loss of PV-INs with THC dominant treatment supports their proconvulsant effect. Thus, CBD and THC have different beneficial therapeutic effects indicating an optimal concentration ratio is critical for optimal neuropathological therapeutics.Light refreshments before the seminar

Suppose $u_j$ is an orthonormal basis of eigenfunctions of the Laplacian on a compact Riemannian manifold, and consider the probability measures $|u_j|^2 dvol$. The quantum ergodicity theorem of Shnirelman, Zelditch and Colin de Verdiere, states that if the geodesic flow on the manifold is ergodic then there is a density one subsequence of these measures that equidistributes. What about the remaining eigenfunctions? The quantum unique ergodicity conjecture of Rudnick and Sarnak states that for hyperbolic manifolds (or more generally for negatively curved manifolds), any sequence of measures as above equidistributes.  In 2006 Lindenstrauss proved that this is true for Hecke—Maass forms on congruence surfaces. These are eigenfunctions of both the Laplacian and the Hecke operators, which are discrete averaging operators coming from the arithmetic structure of the manifold. 

We will discuss our extensions of Lindenstrauss’ results to the three and (partially) four dimensional cases. One of the challenges that arise in the higher dimensional case is to rule out concentration of measure on totally geodesic submanifolds. We will focus on this issue and our new methods for showing non-concentration. 

Based on joint works with Alexandre de Faveri and Lior Silberman.