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A subgroup H < G is called confined if there is a compact subset K of G such that every conjugate of H intersects K at some point other than identity. We prove that every confined subgroup of an irreducible lattice in a higher rank semisimple Lie group has finite index. Since a non-trivial normal subgroup is confined, our result extends the Margulis normal subgroup theorem. We do not rely on Kazhdan’s property (T), and instead obtain a spectral gap from the product structure. More generally, we show that any confined discrete subgroup of a higher rank semisimple Lie group satisfying a certain irreducibility condition is a lattice. This extends the recent work of Fraczyk and Gelander, removing the property (T) assumption. Joint work with Uri Bader and Tsachik Gelander.

At every aspect of our lives, function determines structure. Just as new roads are built between developing cities, network wires are laid to accommodate faster communication demands, and social networks form around shared goals, the brain also remodels its connectome to adapt to the continuous and dynamic changes in functional demands.The&nbsp;connectome&nbsp;refers to the functional and structural characteristics of brain connectivity, spanning from the micron level (neural circuits) to the macroscopic level (long-scale pathways). This intricate network, encompassing the white matter and beyond, facilitates the transmission of information across different brain regions. When the integrity of the&nbsp;connectome&nbsp;is compromised, brain function deteriorates. Thus, the&nbsp;connectome&nbsp;is fundamental to everything the brain does.Traditionally, without the tools to explore the&nbsp;connectome&nbsp;in vivo, it was assumed to be stable and fixed. Much of white matter research focused on mapping the geographical structure of the network and its connected areas. However, advances in magnetic resonance imaging (MRI), particularly diffusion MRI, have opened a new window into the in vivo physiology of the white matter and the&nbsp;connectome.By measuring the microstructural properties of white matter, researchers now have the opportunity to investigate its physiology and dynamics. This presentation will demonstrate how the&nbsp;connectome&nbsp;can be measured, outline its macro- and microstructural features, and describe its evolutionary characteristics by comparing the&nbsp;connectomes&nbsp;of 100 different mammalian species. Additionally, we will explore the role of the&nbsp;connectome&nbsp;in brain plasticity and its remarkable dynamics.Light refreshments before the seminar

TheUNC-40 receptor, a homolog of the human DCC receptor, is critical for neuronal development and maintenance, with its dysregulation implicated in neurodegenerative diseases such as Parkinson’s disease. This study investigates the role of UNC-40 in dopaminergic neuron health and degeneration using Caenorhabditis elegans as a model system. Loss-of-function mutations in UNC-40 conferred resistance to 6-hydroxydopamine (6-OHDA)-induced DA neuron degeneration, while stabilization of UNC-40 via mutation in the CPD regulatory site led to spontaneous, selective DA neurodegeneration independent of toxins. Mechanistic analyses revealed that UNC-40 stabilization triggers parthanatos, a caspase-independent cell death pathway driven by mitochondrial oxidative stress. Pharmacological inhibition of PARP-1 and treatment with mitochondrial antioxidants significantly rescued DA neurons from degeneration.suggesting UNC-40 stabilization causes mitochondrial oxidative stress. Remarkably, UNC-40-induced degeneration was sexually dimorphic, affecting hermaphrodites but not males. Transcriptomic analyses revealed significant gene expression changes in hermaphrodites carrying stabilized UNC40, while males exhibited minimal changes, suggesting intrinsic protective mechanisms. UNC-6, a ligand for UNC-40, was identified as a critical external factor modulating this dimorphism; its absence in hermaphrodites rendered them vulnerable, while its presence in males made them unaffected by the stabilization of the receptor. Behavioral assays revealed functional impairments in hermaphrodites with stabilized UNC-40, linked to altered synaptic activity and excitotoxicity. These findings establish UNC-40 as a key regulator of DA neuron health, highlight its role in oxidative stress and synaptic maintenance, and underscore sexually dimorphic vulnerability to neurodegeneration. The parallels between UNC-40 in C. elegans and DCC in humans suggest conserved mechanisms underlying neurodegeneration and point to potential therapeutic targets for diseases like PD.

The Scanning Probe Microscopy (SPM) Unit conducts a diverse range of scientific projects, spanning from the life sciences (e.g., vesicles, cells, and shells) to material science (e.g., crystals and nanoparticles). Beyond 3D topographic imaging, scanning probe microscopy provides a comprehensive understanding of a material by measuring mechanical, electrical, and other properties. Recent advancements in our unit, including correlative AFM-SEM systems and rapid scanning capabilities, expand the AFM's potential for studying dynamic processes and for more efficient data acquisition. Moreover, machine learning methods have been harnessed to improve analysis accuracy.In this talk, I will present the technique and bring examples where AFM has provided critical insight into various scientific fields by illuminating the nanoscale.

Non-equilibrium active matter systems often exhibit self-organized, collective motion that can give rise to the emergence of coherent spatial structures. Prime examples covering many length scales range from mammal herds, fish schools and bird flocks, to insect and robot swarms. Despite significant advances in understanding the behavior of homogeneous systems in the last decades, little is known about the self-organization and dynamics of heterogeneous active matter. I will present results of bioconvection experiments with multispecies suspensions of wild-type bacteria from the hyper-diverse bacterial communities of Cuatro Ciénegas, Coahuila, whose origin dates back to the pre-Cambrian. Under oxygen gradients, these bacteria swim in auto-organized, directional flows, whose spatial scales exceed the cell size by orders of magnitude, demonstrating a plethora of amazing dynamical behaviors, including segregation. I will present evidence supporting the notion that the mechanisms giving rise to these complex behaviors are predominantly physical, and not a result of biological interactions. This research significantly advances our understanding of both heterogeneity in active matter, as well as in the dynamics of complex microbial ecological communities, bringing profound insights into their spatial organization and collective behavior.

We provide the final step in the resolution of Bourgain's slicing problem in the affirmative. Thus we establish the following theorem: for any convex body K in R^n of volume one, there exists a hyperplane H, such that the (n-1)-dimensional volume of the intersection of K with H is at least c. Here c > 0 is a universal constant. Our proof combines Milman's theory of M-ellipsoids, stochastic localization with a recent bound by Guan, and stability estimates for the Shannon-Stam inequality by Eldan and Mikulincer.

Joint work with J. Lehec.

In nature, sequence-specific biopolymers, such as peptides and nucleic acids, are essential to various biological systems and processes. These biopolymers are utilized in materials science to achieve precise property control. Typically, variations in amino acid sequences focus on functional regulation while nucleotides are used for structural control. This raises the question: How can we integrate peptide-based functionality with the spatial precision of DNA nanotechnology for innovative material design? Here, I will present examples illustrating the incredible properties of peptide self-assembly from my PhD, and the remarkable nanoarchitecture design achieved through DNA nanotechnology from my Postdoc. These two key elements establish a vision of utilizing and synergizing peptide functionality with structural control achieved by DNA nanotechnology.Specifically, I will show how subtle changes in the molecular environment influence the morphology and behavior of peptide assemblies such as diphenylalanine crystals and enable control over their growth and disassembly processes, revealing insights into peptide-based material manipulation (Nat. Commun., 2016). Another example is that of the amorphous assemblies of tri-tyrosine peptides, where we linked the molecular arrangement to unique mechanical and optical properties of glass-like peptide structures (Nature, 2024).Next, I will introduce the principles of DNA nanotechnology for advanced structural control. By designing DNA nano-frames capable of self-assembling into organized lattices, we created micron-scale 3D materials. We discovered that a minor modification in DNA linker length induces a crystalline phase transition, from simple cubic to face-centered cubic structures, altering lattice geometry. In addition, we established a method using acoustic waves to achieve scalable and morphologically controllable DNA assemblies at the millimetric scale (Nat. Commun., 2024). This approach highlights how DNA nanotechnology provides unparalleled spatial control, decoupling structural architecture from functional elements such as peptides and nanoparticles. Together, these projects illustrate how peptides and DNA nanotechnology can be potentially integrated to engineer novel materials and enhance our capacity to design materials with tailored properties across scales.

The (hi)story of amenable groups starts with von-Neumann, who tried to explain the Banach–Taraski–Hausdorff paradox. He observed that the paradox is in fact a consequence of what will later be called the "non-amenability" of the free group on two generators. It led him to ask whether it's true that the phenomenon of a group being non-amenable is always a consequence of having F2 as a subgroup. This became known as "von-Neumann's problem", and was settled to the negative be Ol'shanskii in 1950. The story takes a surprising turn 60 years later: in the perspective of measured group theory, Gaboraiu and Lyons provided a "positive" answer to von-Neumann: they showed that any non-amenable group "measure theoretically" contains a free subgroup. I will introduce (and not prove!) the theorem, and show a consequence of it, due to Epstein: a group is non-amenable if and only if it admits uncountably many non-OE actions.

The talk is based on this survey by Houdayer.