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30 Mathematics Departmental Presentation 2026
Mathematics Departmental Presentation 2026 Speaker: Adrian Chitan, Junqi Liu, Rujing Zhao (Western) "TBA" Time: 15:30 - 17:00 Room: MC 107 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Graham Denham (Western) "Katz's proof of Rota-Heron-Welsh (cont'd)" Time: 15:30 - 16:30 Room: MC 108 |
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1 Transformation Groups Seminar
Transformation Groups Seminar Speaker: Kumar Shukla (Western) "Reisner's criterion II" Time: 15:30 - 17:00 Room: MC 108 We present a proof of Reisner's criterion, which characterizes when the Stanley-Reisner ring of a simplicial complex is Cohen–Macaulay in terms of the homology of the links of in the complex. |
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Geometry and Topology
Geometry and Topology Speaker: Tim Campion (Johns Hopkins University) "Cubical subdivision" Time: 15:30 - 16:30 Room: MC 107 We study the test model structure (as well as a “projective" variant) on several categories of cubical sets (cubical sets with or without connections / symmetries / reversals), study their monoidal properties, and establish Quillen equivalences among them and to simplicial sets and topological spaces. With this groundwork in place, we then consider (on most of these cubical sites) cubical subdivision — an analog of simplicial subdivision (which is even better because it is strong monoidal!). This leads to a cubical analog of Kan’s $\mathrm{Ex}^\infty$ functor which we show to be a functorial fibrant replacement with good properties. As a corollary, we obtain cubical approximation theorems for various flavors of cubes. |
Mathematics Departmental Presentation 2026
Mathematics Departmental Presentation 2026 Speaker: Vladimir Gorchakov, Deepak Sadanandan, Mac Martin (Western) "TBA" Time: 15:30 - 17:00 Room: MC 107 |
Geometry and Topology
Geometry and Topology Speaker: Tim Campion (Johns Hopkins University) "The categorified Berkovich spectrum (a lowbrow approach)" Time: 15:30 - 16:30 Room: MC 108 The set $M(A)$ of multiplicative seminorms on a commutative ring $A$ carries a natural topology. By considering completions of $A$ with respect to these seminorms, Berkovich obtained a structure sheaf of $\mathcal O_A$ of "analytic" functions on $M(A)$. We consider (the rudiments of) a categorification of Berkovich’s theory, associating to every symmetric monoidal stable infinity category $\mathcal A$ a topological space $M(\mathcal A)$ and sheaf of categories $\mathcal O_{\mathcal A}$. We emphasize the concrete nature of these objects. For example, for $k$ a field and any $r > 0$ the function
$$N_{r,k}: \mathsf{Ob}(\mathsf{Sp}^\mathrm{fin}) \to \mathbb{R}_{\geq 0}$$
$$ X \mapsto \sum_i \mathrm{dim} H_i(X; k) r^i$$
is a point in $\mathcal M(\mathsf{Sp}^\mathrm{fin})$. Moreover, the skeletal filtration of a spectrum is often a "Cauchy sequence." We carry through the theory far enough to compute $M(\mathsf{Sp}^\mathrm{fin})$ (which the reader familiar with chromatic homotopy theory may now guess). |
Department Meeting
Department Meeting Speaker: (Western) "Department meeting" Time: 15:30 - 16:30 Room: MC 108 |
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