Program for A Tour of Combinatorics and Statistical Mechanics: In Memory of Richard Brak
Note that the schedule below is provisional, and may be adjusted to accommodate speaker preferences.
The program will be progressively updated as talk titles and abstracts are received.
Date: Monday, 7 February, 2022.
Venue: Evan Williams Theatre in the Peter Hall Building, University
of Melbourne. All talks will be shown
simultaneously online.
Times are given in AEDT, that is Australian Eastern Daylight Time,
which is UTC+11:00.
Click on talk title links to view the corresponding abstract (if available).
8:15am 
Welcome 

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.

9:00am 
Thomas Prellberg 
TBA

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.

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.

10:30am 
Morning tea 
11:00am 
Gary Iliev 
TBA

11:30am 
Chris Soteros 
TBA

12:00pm 
Andrew Rechnitzer 
TBA

12:30pm 
Lunch 
1:30pm 
Judyanne Osborn 
Richard Brak as 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.

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.

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.

3:00pm 
Afternoon tea 
3:30pm 
Aleks Owczarek 
Critical scaling of lattice polymers confined to a box without endpoint restriction


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.

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.

4:30pm 
Jan de Gier 
TBA

5:00pm 
Closing remarks 
8:15am 
Welcome 

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.


9:00am 
Thomas Prellberg 
TBA


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.


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.


10:30am 
Morning tea 

11:00am 
Gary Iliev 
TBA


11:30am 
Chris Soteros 
TBA


12:00pm 
Andrew Rechnitzer 
TBA


12:30pm 
Lunch 

1:30pm 
Judyanne Osborn 
Richard Brak as 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.


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.


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.


3:00pm 
Afternoon tea 

3:30pm 
Aleks Owczarek 
Critical scaling of lattice polymers confined to a box without endpoint restriction

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.


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.


4:30pm 
Jan de Gier 
TBA


5:00pm 
Closing remarks 