The model of higher categories given by Joyal's model structure for quasi-categories has univalent universes of coCartesian fibrations. This subsumes the existence of univalent universes of Kan fibrations proved by Voevodsky. Furthermore, the existence of such universes can be used as an alternative to the yoga of homotopy coherent nerves to prove all the essential features of higher category theory, giving a (directed) type theoretic approach to the foundations of higher categories.
https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.htmlUpdated on Mar 26, 2020 10:57 AM PDT
To join this or any of the MSRI hosted talks this week please use the following link.
So far, we have primarily discussed factorization homology of E_n-algebras (informally referred to as "factorization homology alpha"). For E_n-algebras in spaces, this admits a generalization to (∞,n)-categories (informally referred to as "factorization homology beta"). In the case that n=1, this has been extended further to enriched (∞,1)-categories. In this talk, I will explain both factorization homology beta and enriched factorization homology in dimension 1. I will also discuss its functoriality, leading to the cyclotomic structure on topological Hochschild homology (THH). This represents various joint works among David Ayala, John Francis, Nick Rozenblyum, and myself.Updated on Mar 30, 2020 11:20 AM PDT
Created on Mar 26, 2020 03:49 PM PDT
Updated on Mar 30, 2020 02:03 PM PDT
Updated on Mar 27, 2020 08:32 AM PDT
Created on Mar 26, 2020 03:49 PM PDT
Created on Mar 26, 2020 03:51 PM PDT
https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.htmlCreated on Mar 26, 2020 10:53 AM PDT
Updated on Mar 27, 2020 08:33 AM PDT
The African Diaspora Joint Mathematics Workshop (ADJOINT) will take place at the Mathematical Sciences Research Institute in Berkeley, CA from June 15 to June 26, 2020.
ADJOINT is a two-week summer activity designed for researchers with a Ph.D. degree in the mathematical sciences who are interested in conducting research in a collegial environment.
The main objective of ADJOINT is to provide opportunities for in-person research collaboration to U.S. mathematicians, especially those from the African Diaspora, who will work in small groups with research leaders on various research projects.
Through this effort, MSRI aims to establish and promote research communities that will foster and strengthen research productivity and career development among its participants. The ADJOINT workshops are designed to catalyze research collaborations, provide support for conferences to increase the visibility of the researchers, and to develop a sense of community among the mathematicians who attend.
The end goal of this program is to enhance the mathematical sciences and its community by positively affecting the research and careers of African-American mathematicians and supporting their efforts to achieve full access and engagement in the broader research community.
During the workshop, each participant will:
- conduct research at MSRI within a group of four to five mathematicians under the direction of one of the research leaders
- participate in professional enhancement activities provided by the onsite ADJOINT Director
- receive funding for two weeks of lodging, meals and incidentals, and one round-trip travel to Berkeley, CA
After the two-week workshop, each participant will:
Updated on Feb 27, 2020 10:51 AM PST
- have the opportunity to further their research project with the team members including the research leader
- have access to funding to attend conference(s) or to meet with other team members to pursue the research project, or to present results
- become part of a network of research and career mentors