July 7th--10th we will have an Alberta Topology Seminar at the U.Calgary Biogeoscience Institute.
David Blanc (U. Haifa)
Ryan Budney (U.Victoria)
Jim Cruickshank (U.Galway)
Martin Frankland (U.Regina)
Allen Herman (U.Regina)
Weizhe Niu (U.Glasgow)
Arnaud Ngopnang Ngompe (U. Regina)
George Peschke (U.Alberta)
Marcus Pivato (U. Paris 1 Pantheon-Sorbonne)
Manak Singh (U.Regina)
Don Stanley (U.Regina)
Fernando Szechtman (U.Regina)
Walter Tholen (York. U)
7:30am Breakfast.
Morning talks
Speaker: R. Budney, 9am.
Title: An application of Whitehead products.
Abstract: There is a nexus of closely-related spaces: the diffeomorphism group
of a trivial disc-bundle over the circle, the co-dimension 2 trivial knot (and the space of all knots isotopic to it),
and the space of Schoenflies spheres, i.e. co-dimension 1 embedded spheres in an ambient sphere. I will
describe how Whitehead products and the homotopy groups of wedges of spheres give us insights into
these classical problems that were previously either approached via the Dehn lemma (dimension 3) or
with algebraic K-theory (dimension 6 and up).
Speaker: M. Frankland, 10:30am.
Title: Quillen cohomology of divided power algebras over an operad
Abstract: Quillen cohomology provides a cohomology theory for any algebraic structure, for example Andre-Quillen cohomology of commutative rings. Quillen cohomology has been studied notably for divided power algebras and restricted Lie algebras, both of which are instances of divided power algebras over an operad: the commutative and Lie operad respectively. In joint work with Ioannis Dokas and Sacha Ikonicoff, we investigate Quillen cohomology of divided power algebras over an operad P, identifying Beck modules, derivations, and Kaehler differentials in that setup. We also compare the cohomology of divided power algebras over P with that of P-algebras.
12:00pm Lunch
Afternoon talks
Speaker: J. Cruickshank, 1pm.
Title: Lower bound theorems for various classes of simplicial complexes.
Abstract: Face numbers of simplicial complexes have been the object of much research in algebraic combinatorics
over the last 50 years and a lot of effort has been expended on understanding simplicial spheres and manifolds in this context.
Recently there have been some spectacular breakthroughs, culminating with Adiprasito's proof of the McMullen's g-conjecture for
rational homology spheres. I will give a brief survey of some of the highlights in this area, focusing on the connection with the
rigidity theory of graphs and report on recent joint work with Bill Jackson (QMUL) and Shin-ichi Tanigawa (Univ. of Tokyo) on lower
bound theorems for some interesting classes of simplicial complexes.
Speaker: D. Blanc, 2:30pm.
Title: The life and times of George Peschke.
Activities.
6:30pm Dinner.
7:30am Breakfast.
Morning Talks.
Speaker: M. Pivato, 9am.
Title: Autonomy and Metapreferences
Abstract: The standard model of rational choice in economics treats the preferences of the agent as
exogenous. This raises interesting philosophical problems: if an agent cannot choose her own preferences,
then she is not really "autonomous" ---she is condemned to slavishly maximize the preferences which have been
"imposed" on her from the outside. Likewise, we cannot hold her morally responsible for her choices (good or bad),
if these choices are simply the result of maximizing an (unchosen) preference order. But suppose instead that an
agent could choose her preferences. On what basis would she make such a choice? Presumably, on the basis of
"second order" preferences. But how does she choose these second-order preferences? This leads to an obvious
infinite regress. Furthermore, what does rational choice mean when the agent must simultaneously optimize with
respect to first-order, second-order, and higher-order preferences? What happens when her higher-order
preferences come into conflict with her lower-order preferences? In this talk, I will introduce two mathematical
models of such "metapreferences", and discuss possible solutions to these problems. This is a preliminary report on work in progress.
Speaker: A.N. Ngompe, 10:30am.
Title: The Hurewicz model structure on simplicial R-modules.
Abstract: By a theorem of Christensen and Hovey, the category of non-negatively graded chain complexes has a model structure, called the h-model structure or Hurewicz model structure, where the weak equivalences are the chain homotopy equivalences. The Dold-Kan correspondence induces a model structure on the category of simplicial modules. In this paper, we give a description of the two model categories and some of their properties, notably the fact that both are monoidal.
12:00pm Lunch
Afternoon talks.
Speaker: W. Tholen, 1pm.
Title: Smallness in topology.
Abstract: Quillen's notion of small object and the Gabriel-Ulmer notion of finitely presentable or generated object are fundamental in homotopy theory and categorical algebra.
Do these notions always lead to rather uninteresting classes of objects in categories of topological spaces, such as all finite discrete spaces, or just the empty space, as the
examples and remarks in the existing literature may suggest?
This article demonstrates that the establishment of full characterizations of these notions (and some natural variations thereof) in many familiar categories of spaces can be quite
challenging and may lead to unexpected surprises. In fact, we show that there are significant differences in this regard even amongst the categories defined by the standard separation axioms,
with the T1-separation condition standing out. The findings about these specific categories lead us to insights also when considering rather arbitrary full reflective subcategories of
the category of all topological spaces.
Speaker: D. Stanley, 2:30pm.
Title: Which algebras are the cohomology of spaces?
Abstract: TBA
Speaker: G. Peschke, 4pm.
Title: Meaning of the E-infinity terms of the spectral sequence associated to a bigraded exact couple.
Abstract: We explain completely and definitively the meaning of the E-infinity objects of the spectral sequence associated to a connected bigraded exact couple.
Activities.
6:30pm Dinner.
Ryan Budney (ryan.budney@gmail.com)
Jim Cruickshank (james.cruickshank@universityofgalway.ie)