09:00 AM - 10:00 AM
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Operads in algebraic topology
Kathryn Hess (École Polytechnique Fédérale de Lausanne (EPFL))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
I will define operads and modules over operads, in the context of both chain complexes and topological spaces. I will then describe a number of important examples of these structures arising in algebraic topology and explain their significance and utility.
- Supplements
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Hess
137 KB application/pdf
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10:00 AM - 10:30 AM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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10:30 AM - 10:50 AM
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Braid groups in complex spaces and grassmannians
Simona Settepanella (Hokkaido University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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11:00 AM - 11:20 AM
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Schematic homotopy types of operads
Marcy Robertson (University of Melbourne)
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- Location
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- Video
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- Abstract
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- Supplements
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11:25 AM - 11:45 AM
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Realizability of G-modules: on a dual of a Steenrod problem
Cristina Costoya (Universidade da Coruña)
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- Location
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- Video
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- Abstract
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- Supplements
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11:45 AM - 01:15 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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01:15 PM - 02:15 PM
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Homotopy theory and arithmetic geometry
Kirsten Wickelgren (Duke University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
The solutions in \mathbb{C} to a system of polynomial equations form a nice topological space which is useful even for studying solutions to the polynomials over smaller fields such as R or even Q. To study solutions over Q or characteristic p fields, it is more useful to replace the notion of topological space with an object in a suitable category where one can do homotopy theory, such as the Morel-Voevodsky category for A^1 homotopy theory, and pro-spaces, where one has the étale homotopy type of a scheme. We will define A^1 homotopy theory, étale topological type, and an étale realization between them of Isaksen. We will use this to discuss Grothendieck's anabelian conjectures and obstructions to solutions to polynomial equations
- Supplements
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02:30 PM - 03:30 PM
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Homological stability for families of groups
Nathalie Wahl (University of Copenhagen)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Symmetric groups, braid groups, certain mapping class groups and general linear groups are examples of families of groups known to display a stability phenomenon in their homology. In my talks, I will give an answer to the following questions: What do these examples have in common? When should one expect that a family of groups satisfies homological stability? and how does one check that such a family does indeed stabilize
- Supplements
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Wahl
103 KB application/pdf
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03:30 PM - 04:00 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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04:00 PM - 05:30 PM
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Participant Talks (10 minutes each)
Safia Chettih (University of Oregon), John Harper (Ohio State University), Mona Merling (University of Pennsylvania), Carmen Rovi (Loyola University), Jean Verrette (University of Hawaii at Manoa)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- --
- Supplements
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