8:15am 
Welcome (video) 

8:30am 
Mireille BousquetMélou 
A minisurvey on walks in a cone


I will review some more or less recent results on the
enumeration of walks confined to a cone, with an
emphasis on algebraicity properties.
pdf
video

9:00am 
Thomas Prellberg 
Staircase polygons revisited: an open question by Richard Brak


Nearly 30 years ago I was working on enumeration of
lattice polygons, such as staircase polygons, with
respect to area and perimeter. For staircase polygons,
there is a generating function solution in terms of
qdeformed Bessel functions, which differentiates with
respect to perimeter steps in the horizontal and
vertical direction. While very elegant, this solution
does not reflect that the answer must be symmetric
under exchange of horizontal and vertical steps, which
bothered Richard. In this talk I revisit this problem
and present such a generating function. This involves a
foray into qdeformed algebraic functional equations, a
subject I first encountered when working with Richard
and Tony.
pdf
video

9:30am 
Stuart Whittington 
Selfavoiding walks interacting with a surface and subject to a force


Selfavoiding walks interacting with a surface
constitute a useful model of polymer adsorption. We
present some rigorous results about selfavoiding walks
interacting with a surface and subject to a force that
can desorb the walk. We give results about the free
energy that establish the form of the phase diagram,
and extend this to the cases of uniform stars and
uniform combs. This is joint work with Buks van
Rensburg.
pdf
video

10:00am 
E. J. Janse van Rensburg 
Pulling spiders


In this talk I give a brief overview of some basic methods for obtaining free energies of cubic lattice models of adsorbing and pulled polymers in terms of the free energies of adsorbing and pulled selfavoiding walks. In addition to pulling adsorbing spiders (these are models of adsorbing star polymers pulled in their central node, and with legs intersecting the adsorbing plane), I will also briefly look at the free energies of other models. The phase diagrams of some of the models will also be discussed. This work was done jointly with Stu Whittington, and with Chris Soteros.
pdf
video

10:30am 
Morning tea 
11:00am 
Gary Iliev 
Localization of semiflexible polymers near a penetrable interface


In this talk, we will look at directed walk models related to bilateral Dyck paths interacting with two immiscible solvents and a penetrable interface. The paths will also carry a "stiffness" parameter that decorates pairs of collinear steps.
By varying the energy and stiffness parameters, we build up a picture of the phase diagram and understanding of the phase behaviour of such polymeric systems.
pdf
video

11:30am 
Chris Soteros 
Entanglements in lattice polygons in tubes


Lattice polygon models are useful for exploring the probability of knotting and
linking in polymers. I will review some recent exact and Monte Carlo results
regarding how the probability of a given knot or link type scales with polygon
size for polygons in tubular subsets of the simple cubic lattice. Exact and
theoretical results for the smallest tube that admits nontrivial knots (the
infinity x 2 x 1 tube) confirm a conjecture that the entropic critical exponent
goes up by one for each prime factor in the knotdecomposition. TransferMatrix
MonteCarlo evidence indicates that the same scaling form holds for some other
small tube sizes. Much of this work was done in collaboration with Nick
Beaton, Jeremy Eng, Kai Ishihara, Puttipong Pongtanapaisan, Rob Scharein, Koya
Shimokawa and Mariel Vazquez.
pdf
video

12:00pm 
Andrew Rechnitzer 
Trials and tribulations of preserving topology


Monte Carlo simulations are a big part of understanding the statistical properties of knots. Unfortunately, if one wishes to study curves of fixed knot types then there are very few methods available.
This work, with Nick Beaton and Nathan Clisby, is an attempt to adapt existing algorithms to polygons in R3 of fixed topology. It is very much a work in progress, but I will report on our attempts at trying to coerce the (very fast) pivot algorithm to respect topology.
pdf
video

12:30pm 
Lunch 
1:30pm 
Judyanne Osborn 
Richard Brak as a role model


Richard Brak was my PhD supervisor, and the best role model I could think of for a young academic, or any academic. I will reflect on some of what I learnt from him, how the world and academia is the richer for his having been in it, and some of what I see as his legacy.
pdf
video

2:00pm 
Tony Guttmann 
Spiral walks on the triangular lattice


One of the problems Richard worked on for his PhD was
that of spiral SAWs on the triangular lattice. At
around the same time I was working on an extension of
this problem in collaboration with George Szekeres, and
I will describe these problems.
pdf
video

2:30pm 
Iwan Jensen 
Odds and ends about osculating paths


We present some odds and ends regarding osculating
paths with 4 and 5 walkers. Exact enumerations are used
to calculate the exact generating function for walkers
in watermelon and star configurations and some critical
properties are extracted.
pdf
video

3:00pm 
Afternoon tea 
3:30pm 
Aleks Owczarek 
SAW in a box


We present a study of selfavoiding walks on the square lattice restricted to a
square box of side L weighted by a length fugacity without restriction of their
end points. The model admits a phase transition between an ‘empty’ phase, where
the average length of walks are finite and the density inside large boxes goes
to zero, to a ‘dense’ phase, where there is a finite positive density. We prove
various bounds on the free energy and develop a scaling theory for the phase
transition based on the standard theory for unconstrained polymers. We compare
this model to unrestricted walks and walks whose endpoints are fixed at the
opposite corners of a box, as well as Hamiltonian walks. We use Monte Carlo
simulations to verify predicted values for three key exponents.
pdf
video

4:00pm 
Nicholas Beaton 
The powered Catalan numbers


Much of Richard’s most recent research was dedicated to
understanding bijections between different
combinatorial structures. In work with Mathilde Bouvel,
Veronica Guerrini and Simone Rinaldi we studied a
sequence which we called the “powered Catalan numbers”
(OEIS A113227) which count, among other things, several
different classes of vincular patternavoiding
permutations, a class of patternavoiding inversion
sequences, two classes of (partially) directed lattice
paths, and a class of labelled trees. I will discuss
some of these objects and the various bijections
between them.
pdf
video

4:30pm 
Jan de Gier 
The onetransit model


I will discuss joint work with Richard regarding a Dyck
path type model with contact energies above and below a
horizontal line. The statistical mechanical partition
function of this model gives the stationary
distribution of the asymmetric exclusion process with
open boundaries.
pdf
video

5:00pm 
Closing remarks 