University of Haifa – החוג למתמטיקה, אוניברסיטת חיפה
Hochschild homology was originally introduced as an invariant of associative algebras that generalizes the commutator. In subsequent decades, it has been extended both in categorical directions, such as to dg-categories, and in topological ones, such as to ring spectra. These…
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Classically, (∞, 1)-categories are modeled by complete Segal spaces. However, many examples first arise as non-complete Segal spaces, which are then completed abstractly to obtain an (∞, 1)-category. With Nuiten, we construct a model of (∞, 1)-categories in which completeness…
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In this talk, we will survey a collection of questions (and partial answers) regarding the role of symmetry in the inequalities of isoperimetric type. We will speculate why symmetry might help with improving isoperimetric properties, recall the B-conjecture, and will…
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The goal of this talk is to introduce the notion of a Grothendieck (∞, 2)-topos as a presentable (∞, 2)-category satisfying a categorified version of the descent axiom for (∞, 1)- topoi of Rezk-Lurie, which we call fibrational descent.As the…
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We consider the evolutes of plane real-algebraic curves and find lower bounds for the following 4 quantities: (1) the maximal number of times a real line can intersect the evolute of a real-algebraic curve of degree d; (2) the maximal number…
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Abstract: We consider the following dynamics on a connected graph (V,E) with n vertices. Given p>1 and an initial opinion profile f_0: V \to [0,1], at each integer step t >= 1 a uniformly random vertex v=v_t is selected, and the…
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The naive notion of a chain complex makes sense in any pointed category, but its homotopical version is a little more complicated. We define a notion of a tight chain complex in a pointed model or ∞-category M, and describe…
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Abstract: The Combinatorial Invariance Conjecture for Kazhdan–Lusztig polynomials posits that the Bruhat graph associated with two elements in a Coxeter group uniquely determines the corresponding Kazhdan–Lusztig polynomial. This conjecture has been a topic of research for over forty years, with…
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It is well known that cluster structures and Poisson structures in the algebra of regular functions on a quasi-affine variety are closely related. In this talk, I will discuss this connection for Poisson structures defined on a simple simply connected…
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The tangle hypothesis is a variant of the cobordism hypothesis that considers cobordisms embedded in some finite-dimensional Euclidean space (together with framings). Such tangles of codimension k can be organized into an E_k-monoidal d-category, where d is the maximal dimension of the tangles. The tangle hypothesis then asserts that this category…
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