Calendar

Feb
22
Fri
Colloquium: Saverio Spagnolie (U. Wisconsin-Madison) @ Keller 401
Feb 22 @ 3:30 pm – 4:30 pm

Title: Active matter invasion of a viscous fluid and a no-flow theorem

Abstract: Suspensions of swimmers or active particles in fluids exhibit incredibly rich behavior, from organization on length scales much longer than the individual particle size to mixing flows and negative viscosities. We will discuss the dynamics of hydrodynamically interacting motile and non-motile stress-generating particles as they invade a surrounding viscous fluid, modeled by equations which couple particle motions and viscous fluid flow. Depending on the nature of their self-propulsion, colonies of swimmers can either exhibit a dramatic splay, or instead a cascade of transverse concentration instabilities, governed at small times by an equation which also describes the Saffman-Taylor instability in a Hele-Shaw cell, or Rayleigh-Taylor instability in two-dimensional flow through a porous medium. Analysis of concentrated distributions of particles matches the results of full numerical simulations. Along the way we will prove a very surprising “no-flow theorem”: particle distributions initially isotropic in orientation lose isotropy immediately but in such a way that results in no fluid flow anywhere and at any time.

Feb
25
Mon
Geometric Group Theory Seminar @ Keller 413
Feb 25 @ 3:00 pm – 4:00 pm

Devin Murray

Title: Introduction to right-angled Artin groups

Mar
1
Fri
Colloquium: John Calabrese (Rice) @ Keller 401
Mar 1 @ 3:30 pm – 4:30 pm

Speaker: John Calabrese (Rice)

Title:
From Hilbert’s Nullstellensatz to quotient categories

Abstract:
A common theme in algebraic geometry is the interplay between algebra and geometry. In this talk I will discuss a few “reconstruction theorems”, in which the algebra determines the geometry.

Mar
5
Tue
Logic seminar: Quinn Culver
Mar 5 @ 2:45 pm – 3:35 pm

Keller Hall 301

Abstract: My plan is to go through (as much as time will allow of) Measure and Integrals in Conditional Set Theory by Jamneshan et al. with the goal of getting to at least one theorem there that witnesses the merits of conditional set theory.

Mar
8
Fri
Colloquium: Dusko Pavlovic (UHM ICS) @ Keller 401
Mar 8 @ 3:30 pm – 4:30 pm

Speaker: Dusko Pavlovic (UMH ICS)

Title: From Data Analysis to Dedekind-MacNeille Completions of Categories

Abstract: Solutions of mathematical problems are well-known to help with practical applications (to the point of being “unreasonably effective”, as Wigner put it). It is less well-known that practical applications sometimes help solving long standing mathematical problems. I will tell a story of this second kind.

The Dedekind-MacNeille completion of a poset is the smallest complete lattice that contains it, or equivalently the largest complete lattice where each element is both a meet and a join of the elements of the poset. Dedekind devised it to reconstruct the reals as a completion the rationals, and MacNeille generalized it to arbitrary posets. When posets are generalized to categories (so that the partial ordering a<b is expanded into the morphisms a->b), then meets and joins become limits and colimits, and the obvious task arises: generalize the Dedekind-MacNeille completion to categories. The task is thus to embed any given category into a category with all small limits and colimits, in such a way that any limits and colimits that already existed are preserved, and that any new objects that are added are both limits and colimits from the original category. This task was formulated already in the 50s, and it was listed as the most important open problem in Lambek’s 1966 “Completions of Categories” (volume #24 of Springer LNM). Stunningly, in 1972, Isbell proved that already the group Z_4, viewed as a one-object category, cannot be embedded into a bicomplete category where each object is both a limit and a colimit of diagrams built from copies of Z_4. But since the inductive process of adjoining limits to a category obviously settles at various bicompletions, and since it is easy to see that some of these bicompletions must be minimal, Isbell’s negative result just expanded the question: What are minimal bicompletions of categories, and which properties make them minimal? The question remained open for more than 40 years, or almost 60, depending how you count. 

In this talk I will sketch the answer at which we arrived in 2015. It emerged as a special case of a matrix bicompletion construction, developed in a data analysis project. In the meantime, the practical applications of the result have expanded, but some of the mathematical repercussions, and most of the algorithmic issues, have not been settled.

Mar
12
Tue
Logic seminar: Quinn Culver
Mar 12 @ 2:45 pm – 3:35 pm

Keller Hall 301

Abstract: My plan is to go through (as much as time will allow of) Measure and Integrals in Conditional Set Theory by Jamneshan et al. with the goal of getting to at least one theorem there that witnesses the merits of conditional set theory.

Mar
15
Fri
Colloquium: Michael Yampolsky (U. Toronto) @ Keller 401
Mar 15 @ 3:30 pm – 4:30 pm

Speaker: Michael Yampolsky (U. Toronto)
Title: Renormalization of rotation domains

Abstract: Renormalization has emerged as a key theme in low-dimensional dynamics. I will start with a review of renormalization of maps of the circle, and will then discuss applications of renormalization theory to the study of Siegel disks in one and two complex variables.

Mar
22
Fri
AMS Spring Central and Western Joint Sectional Meeting
Mar 22 – Mar 24 all-day