# Colloquium

The colloquium typically meets Mondays at 4:00 PM in Room 617 on the sixth floor of Wachman Hall.

The colloquium is preceded by tea starting at 3:30 in the Faculty Lounge, adjacent to Room 617. Click on title for abstract.

• Monday January 23, 2017 at 16:00, Wachman 617
Asymptotic representation theory over Z

Tom Church, Stanford University and IAS

Representation theory over Z is famously intractable, but "representation stability" provides a way to get around these difficulties, at least asymptotically, by enlarging our groups until they behave more like commutative rings. Moreover, it turns out that important questions in topology / number theory / representation theory / ... correspond to asking whether familiar algebraic properties hold for these "rings". I'll explain how these connections work; describe what we know and don't know; and give a wide sampling of concrete applications in different fields. No knowledge of representation theory will be required -- indeed, that's sort of the whole point!

• Monday February 20, 2017 at 16:00, Wachman 617
2-Segal spaces and the Waldhausen S-construction

Julia Bergner, University of Virginia

The notion of a 2-Segal space was recently defined by Dyckerhoff and Kapranov, and independently by Galvez-Carrillo, Kock, and Tonks under the name of decomposition space. Unlike Segal spaces, which encode the structure of a category up to homotopy, 2-Segal spaces encode a more general structure in which composition need not exist or be unique, but is still associative. Both sets of authors above proved that the output of the Waldhausen $S_\bullet$-construction is a 2-Segal space. In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we look at a discrete version of this construction whose output is a 2-Segal set. We show that, via this construction, the category of 2-Segal sets is equivalent to the category of augmented stable double categories. In this talk, I'll introduce 2-Segal sets and spaces, discuss this result and a conjectured homotopical generalization, and, time permitting, look at some other interesting features of 2-Segal spaces.

• Monday March 6, 2017 at 16:00, Wachman 617
TBA

TBA

• Monday March 20, 2017 at 16:00, Wachman 617
Modelling collective cell movement

Philip Maini, Oxford University

Collective cell movement is a phenomenon that occurs in normal development, wound healing and disease (such as cancer). In many cases, the ability of cell populations to move large distances coherently arises due to a structure of "leaders" and "followers" within the population. I will present two such examples: (i) angiogenesis -- this the process by which new blood vessels form in response to injury, or in response to a cancerous tumour's demand for more nutrient. We systematically derive a discrete cell-based model for the "snail-trail" phenomenon of blood vessel growth and show that this leads to a novel partial differential equation model. We compare and constrast this model with those in the literature. (ii) neural crest cell invasion - this is the process by which cells move to target locations within the embryo to begin construction of body parts. Through an interdisciplinary research project we show how a hybrid discrete-cell-based mathematical model, and an experimental model, combine to allow us to gain new insights into this phenomenon.

• Monday April 3, 2017 at 16:00, Wachman 617
TBA

Jason Manning, Cornell University

• Monday April 10, 2017 at 16:00, Wachman 617
TBA

Timo Seppalainen, University of Wisconsin Madison

TBA

• Monday April 17, 2017 at 16:00, Wachman 617
TBA

Joan Birman, Columbia University