Geometry and Topology Seminar

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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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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This talk will be on Zoom:https://us02web.zoom.us/j/83920631646?pwd=cWZRWjllZWEvdjVSNVhTdUxMMGlwUT09 I will start explaining that Hamiltonian reduction can be understood as a particular instance of Lagrangian intersections, within the framework of shifted symplectic geometry. One can see this first part of the talk as…
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Homotopy localizations with respect to arbitrary (possibly proper) classes of maps are known to existin suitably structured model categories assuming the validity of Vopenka’s principle from set theory.Through recent progress in large cardinal theory, we prove that the existence of…
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Given a commutative ring or ring spectrum, there is a functor from finite sets to commutative rings sending a set to the tensor product of copies of the ring (or ring spectrum) indexed by that set.  The Loday construction extends…
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