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UID:mathcal-6@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Cubical subdivision (Tim Campion - Johns Hopkins University)
DTSTART;TZID=America/Toronto:20260406T153000
DTEND;TZID=America/Toronto:20260406T163000
DESCRIPTION: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.
 <p>
 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.
LOCATION:MC 107
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BEGIN:VEVENT
UID:mathcal-8@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:The categorified Berkovich spectrum (a lowbrow approach) (Tim Campion - Johns Hopkins University)
DTSTART;TZID=America/Toronto:20260408T153000
DTEND;TZID=America/Toronto:20260408T163000
DESCRIPTION: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 $M(A)$.
 <p>
 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."
 <p>
 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).
LOCATION:MC 108
END:VEVENT
BEGIN:VEVENT
UID:mathcal-35@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Lectures on Multiparameter Persistence I: Density-sensitive bifiltrations in TDA (Michael Lesnick - SUNY Albany)
DTSTART;TZID=America/Toronto:20260505T110000
DTEND;TZID=America/Toronto:20260505T120000
DESCRIPTION:
LOCATION:MC 107
END:VEVENT
BEGIN:VEVENT
UID:mathcal-36@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Lectures on Multiparameter Persistence II: Lp-metrics on multiparameter persistence modules (Michael Lesnick - SUNY Albany)
DTSTART;TZID=America/Toronto:20260506T110000
DTEND;TZID=America/Toronto:20260506T120000
DESCRIPTION:
LOCATION:MC 107
END:VEVENT
BEGIN:VEVENT
UID:mathcal-37@shafikov.ca
DTSTAMP:19980119T070000Z
SUMMARY:Lectures on Multiparameter Persistence III: Limit computation via minimal initial functors (Michael Lesnick - SUNY Albany)
DTSTART;TZID=America/Toronto:20260507T110000
DTEND;TZID=America/Toronto:20260507T120000
DESCRIPTION:
LOCATION:MC 107
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