University of Haifa – החוג למתמטיקה, אוניברסיטת חיפה
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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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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Recording: https://us02web.zoom.us/rec/share/i0GSXYC62VZ68cvBAUV0NgTUPNwqxhwyqWt0bCFbb4EhmRiQ61Ni_OqHzZWJZyn.CHIdEHASwtqlGrp2
Many topological spaces including smooth manifolds and algebraic varieties can be triangulated, but the explicit triangulations are often unknown or too big to be of practical interest. We will take a look at this problem from the viewpoint of algebraic…
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I will report on joint work with Robert Burklund in which we remove finiteness assumptions from a theorem of Mandell. Specifically, we show that the canonical functor from p-adic,nilpotent spaces to (E∞-) coalgebras over F¯p is fully faithful. Recording:https://us02web.zoom.us/rec/share/qlTnQPOI-W7GyhRTkK3DB5PZdP1WiEgcOsHaZ661TmES9VsoM_pqHWgFji4whSJd.0MWjSTm7kOZ12uaH
A linear operator on a Hilbert space is called Fredholm if its kernel and cokernel are finitedimensional. As was shown in classical works of Atiyah, J¨anich, and Singer, the space of bounded Fredholm operators represents even K-theory; its subspace consisting…
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For every n and a fixed prime p, we construct a new congruence for the orbifold Euler characteristic of a group which we call the chromatic congruence at the height n. Here the word “chromatic” refers to the chromatic stable…
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I will put forward a possible generalization of Dugger’s theorem on universal homotopy theories, in enriched homotopy theory, following previous work of Dugger and Shipley for the case of enrichment over Abelian groups. I will discuss what can be done…
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In this talk, I will introduce the notion of Poincar´e duality spaces in the equivariantsetting for finite groups and discuss an approach relating equivariant Poincar´e duality withPoincar´e duality on the fixed points. Time permitting, I will also indicate how one…
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While encoding the homotopy invariants in a model category, one approach (due to Heller and Grothendieck) is to determine certain higher invariants in the homotopy categories of all small diagram categories. In this talk, we provide an explicit approach to…
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