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:

·        Comparing models for homotopy theories/(∞, 1)-categories, especially simplicial categories and complete Segal spaces

·        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

·        Using complete Segal spaces to generalize Toën’s derived Hall algebras

·        Generalizing homotopy fiber products of model categories to more general homotopy limits and colimits of (∞, 1)-categories

·        An expository paper on (∞, n)-categories and the cobordism hypothesis

·        An expository paper on groupoid cardinality and Egyptian fractions (with Christopher Walker)

·        A criterion for when the Reedy and injective model structures on diagram categories of spaces coincide (with Charles Rezk)

·        Developing and comparing models for (∞, n)-categories (with Charles Rezk)

·        Models for (∞, 1)-operads and group actions on (∞, 1)-categories and (∞, 1)-operads (with Philip Hackney)

·        Developing a theory of topological cluster categories (with Marcy Robertson)

·        Developing and comparing models for equivariant (∞, 1)-categories (with Greg Chadwick)

·        Bredon homology of unitary partition complexes (with Ruth Joachimi, Kathryn Lesh, Vesna Stojanoska, and Kirsten Wickelgren)

·        A way to obtain the Catalan numbers from action graphs (with Gerardo Alvarez and Ruben Lopez)

Publications

Current projects include:

§  A new proof of the comparison between Ɵn-spaces and Ɵn-sets (with Ieke Moerdijk)

§  Understanding the relationship between 2-Segal sets and bicategories (with Angélica Osorno, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer)

Slides from past talks

PhD students:

Jacob West, Higher Auslander-Rieten theory, 2015

Seminars and conferences:

·        Topology seminar 2015-16

·        Topology seminar 2014-15

·        Special session on homotopy theory, October 2014 (co-organized with Angélica Osorno)

·        Topology seminar Fall 2013

·        Special session on homotopy theory and K-theory, November 2013 (co-organized with Christian Haesemeyer)

·        6th Annual Southern California Women in Mathematics Symposium, October 2013 (co-organized with Juhi Jang)

·        Special session on geometric applications of homotopy theory, August 2013, Congress of the Americas (co-organized with Andrés Angel and Marcy Robertson)

·        Topology seminar 2012-13

·        Special session on homotopy theory and commutative algebra, January 2013 (co-organized with Philip Hackney and Inês Henriques)

·        Topology seminar 2011-12 (co-organized with Michael Williams)

·        Topology seminar 2010-11

·        Rational homotopy theory seminar 2010-11 (co-organized with Fred Wilhelm and Philip Hackney)

·        Special session on homotopy theory and K-theory, October 2010 (co-organized with Christian Haesemeyer)

·        Cobordism and topological field theories seminar, 2009-10

·        Special session on homotopy theory and higher algebraic structures, October 2009 (co-organized with John Baez)

Back to Julie’s web page

http://www.math.ucr.edu/~jbergner/research.htm                                   Last updated:  5 October 2015