Julie Bergner’s Research Page
My research interests include homotopy theory, algebraic topology, and applications to
representation theory and other algebraic areas. My publications thus far have covered topics
such as:
·
Models for homotopy theories/(∞, 1)-categories, especially simplicial categories and complete Segal spaces
·
Relationships between these
models
·
Groupoid versions of these models
·
Multi-sorted algebraic
theories, and how they provide new perspectives on simplicial
categories, group actions, and operads
·
Diagrams encoding algebraic
structures, especially ones that are simpler than those given by algebraic
theories
Current projects include:
§ Using complete Segal spaces to generalize Toën’s derived Hall algebra construction
§ Generalizing homotopy
fiber products of model categories to more general homotopy
limits and colimits, and showing they are compatible
with the standard definitions within the complete Segal space model
§ Interpreting the Deligne
conjecture in terms of diagrams of complete Segal spaces
§ Generalizing rigidification
results for algebras over algebraic theories to algebras over limit theories
(joint work with Bernard Badzioch)
§ Writing a nice manuscript on Dwyer-Kan simplicial localizations
This quarter I am organizing a seminar
on Cobordism and Topological Field Theories, in which we are working through Lurie’s proof of
the Cobordism Hypothesis.
In November, John Baez and I are
organizing a special session on homotopy theory and
higher algebraic structures at the AMS Western Section Meeting here at UC
Riverside. Information can be found here.
http://www.math.ucr.edu/~jbergner/research.htm Last
updated: 4 September 2009