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This paper summarizes the discussions which took place during the PITT-PACC Workshop entitled “Non-Standard Cosmological Epochs and Expansion Histories,” held in Pittsburgh, Pennsylvania, Sept. 5–7, 2024. Much like the non-standard cosmological epochs that were the subject of these discussions, the format of this workshop was also non-standard. Rather than consisting of a series of talks from participants, with each person presenting their own work, this workshop was instead organized around free-form discussion blocks, with each centered on a different overall theme and guided by a different set of Discussion Leaders. This document is not intended to serve as a comprehensive review of these topics, but rather as an informal record of the discussions that took place during the workshop, in the hope that the content and free-flowing spirit of these discussions may inspire new ideas and research directions.
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Problems in Arithmetic Topology
We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF workshop on “Arithmetic Topology.” Three problem sessions were hosted during the workshop in which participants proposed open questions to the audience and engaged in shared discussions from their own perspectives as working mathematicians across various fields of study. Participants were explicitly asked to provide problems of various levels of difficulty, with the goal of capturing a cross section of exciting challenges in the field that could help guide future activity. The problems, together with references and brief discussions when appropriate, are collected below into three categories: (1) topological analogues of arithmetic phenomena, (2) point counts, stability phenomena and the Grothendieck ring, and (3) tools, methods and examples.
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- PAR ID:
- 10284071
- Date Published:
- Journal Name:
- Research in the mathematical sciences
- Volume:
- 8
- ISSN:
- 2197-9847
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s40687-021-00264-5
