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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.

<p>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.</p><p>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).</p><p>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.</p>

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.

<p>The study of dilute, strongly interacting quantum gases reveals</p><p>universal properties that transcend the specifics of individual</p><p>systems. These features arise from their short-range behavior</p><p>and are encapsulated in a key quantity called the “contact”, which</p><p>quantifies the probability of two particles being in close proximity.</p><p>In this talk, I will introduce the contact theory and its extension to</p><p>nuclear and molecular systems beyond the zero-range limit. I will</p><p>demonstrate its applicability in analyzing nuclear electron</p><p>scattering and photo absorption reactions.</p><p>Additionally, I will discuss how mean-field approximations, such as</p><p>the nuclear shell model, can effectively estimate the contact,</p><p>offering valuable insights into the underlying physics.</p>

<p>Aneuploidy, an imbalanced number of chromosomes or chromosome arms, is a genetic hallmark of cancer cells, yet aneuploidy remains a biological enigma and a missed opportunity for cancer therapy. My lab applies experimental and computational approaches to dissect the basic biology underlying cancer aneuploidy and to study its cellular consequences. In this seminar, I will focus on an unpublished study in which we discovered an important role for a recurrent aneuploidy in driving brain metastasis, revealed the underlying molecular mechanism, and identified a therapeutically-relevant cellular vulnerability that is associated with this common aneuploidy.</p>

<p>In my lecture, I will showcase how designing new materials and exploring their fundamental properties can lead to innovative concepts and practical applications in organic chemistry. We will begin by discussing the synthesis of novel halo-organic compounds that enable the stereoselective catalytic synthesis of biologically relevant chiral organofluorides.</p><p>&nbsp;&nbsp;&nbsp;&nbsp; The talk will primarily focus on the versatile chemistry of N-Heterocyclic Nitrenium ions (NHNs) – the nitrogen-based analogs of ubiquitous N-Heterocyclic Carbenes. We will demonstrate their unique coordination abilities, analyze their properties, and highlight their role in stabilizing elusive species.1,2 Nitrenium ions represent a novel family of nitrogen-based Lewis acids3 and serve as efficient metal-free catalysis, frustrated Lewis pairs partners4 and platform for isolating valuable radicals.5 Finally, we will demonstrate how the fundamental understanding nitrenium properties led to the development of triazenolysis reaction - an <em>aza</em>-version of the canonical alkene ozonolysis.6</p><p></p><p><strong>References:</strong></p><p>[1] <em>Nat. Chem</em>. <strong>2011</strong>, <em>5</em>, 525.</p><p>[2] <em>Chem.Sci.</em> <strong>2014</strong>,&nbsp;<em>5</em>,&nbsp;1305.</p><p>[3] <em>J. Am. Chem. Soc.</em> <strong>2017</strong>, <em>139</em>, 4062.</p><p>[4] <em>Angew. Chem. Int. Ed. </em><strong>2020</strong>, <em>59</em>, 23476.</p><p>[5] <em>J. Am. Chem. Soc. </em><strong>2022, </strong><em>144, </em>23642; <em>J. Am. Chem. Soc. </em><strong>2024</strong>, <em>146</em>, 19474.</p><p>[6] <em>Nat. Chem</em>. <strong>2025</strong>, <em>17</em>, 101.</p>