Seminars Arun Ram

I have an interest in combining the many strengths in Melbourne (and Australian) mathematics and the stream of seminars will be important to this goal. The following is something of a seminar blog.

• Algebra-Geometry-Topology seminar page Semester II 2009
• Algebra-Geometry-Topology seminar page Semester I 2009
• Seminar page 2009
• Seminar page 2008
• Algebra-Geometry-Topology seminar page 2008
• Department seminar page
• Department colloquium page

January 2010 Seminar Blog

• 7 June 2010 13:00 Room 215
  
  Christian Korff (Glasgow) Statistical vertex models, combinatorics and enumerative geometry
  
  Abstract: Under suitable boundary conditions on the square lattice the partition functions for vicious and infinitely-friendly walkers generate respectively Gromov-Witten and sl(n) WZNW fusion coefficients. The latter are the structure constants of two rings which have received much attention in representation theory, combinatorics, algebraic geometry and physics. In my talk I will focus on the formulation of the sl(n) WZNW fusion ring as an integrable model. The transfer matrix can be expressed as generating function for analogues of symmetric polynomials in a noncommutative alphabet, the local affine plactic algebra. The latter is an affine version of the algebra first introduced by Lascoux and Sch"utzenberger in the context of the Robinson-Schensted-Knuth correspondence. Using the Bethe ansatz ones shows that the fusion product (the OPE of two primary fields in the WZNW CFT) is given by the action with an affine plactic Schur polynomial on a row configuration of the lattice model and derives in an elementary way the celebrated Verlinde formula. I will explain the connection of the walker model with the phase model of Bogoliubov, Izergin and Kitanine and show that both models are obtained in a special crystal limit of the XXZ spin chain with infinite spin. The respective transfer matrices are related by Baxter's TQ equation in the crystal limit.
  
  
• 15 June 2010 14:15 Room 215
  
  Scott Provan (North Carolina) Sudoku: Strategy Versus Structure
  
  Abstract: Sudoku puzzles have become wildly popular in just the last few years, and quite a school has developed around classifying solution strategies for Sudoku puzzles. We give a simply-described set of strategies that solves about 90% of all Sudoku puzzles. This strategy class has two interesting properties: one associated with the formulation of these puzzles as a set of interlocking assignment problems, and the other with their representation as the unique nonnegative solution to the associated set of assignment equations. We discuss this strategy, and indicate some interesting research problems in the area.
  
  
• 15 June 2010 13:00 Room 215
  
  Arun Mani (Monash) The Tutte polynomial and the Potts model in square lattices
  
  Abstract: The Tutte polynomial of a graph is a polynomial in two variables, $x,y$, that is of central importance in many counting problems. The Potts model partition function is known to be computationally equivalent to an evaluation of the Tutte polynomial along the curve $(x-1)(y-1) = q$ for integer values of $q$. The asymptotic growth of the Tutte polynomial (and the Potts model) of a square lattice as its dimensions tend to infinity are often of special interest in combinatorics and statistical physics. In this talk we introduce a family of inequalities for the Tutte polynomial of square lattices, and apply them to obtain non-trivial one-sided bounds for a limit describing this growth when $x, y \geq 1$.
  
  
• 15 June 2010 13:00 Room 213
  
  Cayley Finn (Melbourne) The asymmetric simple exclusion process with non-diagonal boundary conditions
  
  Abstract: The asymmetric simple exclusion process (ASEP) is a model describing the diffusion of hard core particles along a one-dimensional chain of sites. With periodic boundary conditions the number of particles is conserved and the spectrum of the transition matrix of this integrable system can be determined by standard bethe ansatz techniques. By introducing a non-diagonal twist matrix, the boundary conditions change to allow creation and annihilation of particles. In this talk I will describe a method of Galleas for determining the spectrum of such a system from functional relations contained in the Yang-Baxter algebra.
  
  
• 1 June 2010 14:15 Doug McDonnell 309
  
  Maurice Chiodo (Melbourne) Finding non-trivial splittings in groups, and similar results in geometry
  
  Abstract: It is well known that there is no algorithm to decide if a finitely presented group splits as a non-trivial free product, nor is there an algorithm to decide if a closed 4-manifold can be written as a connect sum of two non simply connected summands. In this talk I will show that, even if we know that a given finitely presented group splits as a non-trivial free product, we cannot always algorithmically split it. I will use this to show an analogous result in geometry: even if we know that a given closed 4-manifold splits as a connect sum of two non simply connected summands, we cannot always algorithmically split it.
  
  
• 1 June 2010 13:00 Room 213
  
  Alex Lee (University of Melbourne) Matrix models and random surfaces
  
  Abstract: Statistical mechanical partition functions involving matrices, otherwise known as matrix models, can be interpreted as generating functions of random surfaces, that is, discrete surfaces built by gluing together polygons in various configurations. In this context, expectation values of traces are generating functions of random surfaces with boundaries and these functions then obey what are known as loop equations for the matrix model. Finally, I will mention applications of matrix models to counting quadrangulations of surfaces.
  
  
• 31 May 2010 13:00 Babel Middle Theatre
  
  Alistair Savage (Ottawa) Quiver grassmannians, quiver varieties and the preprojective algebra
  
  Abstract: Quivers play an important role in the representation theory of algebras with key ingredients of the theory being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or preprojective algebra. In this talk, we study these objects in detail. We show that the quiver grassmannians corresponding to submodules of certain injective modules are isomorphic to the lagrangian quiver varieties of Nakajima which have been well studied in the context of geometric representation theory. We then refine this result by finding quiver grassmannians which are isomorphic to the Demazure quiver varieties, and others which are isomorphic to the graded/cyclic quiver varieties defined by Nakajima. The Demazure quiver grassmannians also allow us to construct injective objects in the category of locally nilpotent modules of the preprojective algebra. We conclude by relating our construction to a similar one of Lusztig using projectives in place of injectives. This is joint work with Peter Tingley.
  
  
• 27 May 2010 14:15 Old Arts B
  
  Amnon Neeman (Australian National University) The Auslander trace
  
  Abstract: Many years ago Auslander noticed that, for an isolated Gorenstein singularity, there is a natural trace defined on homomorphisms between certain pairs of modules. A conjectural formula was given recently by Kapustin and Li, using physics heuristics. We will discuss Murfet's mathematical proof of the formula.
  
  
• 25 May 2010 14:15 Room 215
  
  San Ming Zhou (Melbourne) Gossiping and routing in second-kind Frobenius graphs
  
  Abstract: Two kinds of Cayley graphs associated with finite Frobenius groups exhibit interesting routing properties, making them attractive candidates (at least in theory) for modelling interconnection networks. In this talk I will focus on gossiping and routing in second-kind Frobenius graphs. In the case when the kernel of the Frobenius group involved is abelian of odd order, we find the exact value of the minimum gossiping time for such a graph under the store-and-forward, all-port and full-duplex model and prove that the graph admits optimal gossiping schemes with the following properties: messages are always transmitted along shortest paths; each arc is used exactly once at each time step; at each step after the initial one the arcs carrying the message originated from a given vertex form a perfect matching. In the case when the kernel of the Frobenius group is abelian of even order, we give an upper bound on the minimum gossiping time under the same model. As examples we will discuss a family of second-kind Frobenius graphs which contains all Paley graphs and connected generalized Paley graphs. This talk is based on joint work with Xin Gui Fang at Peking University.
  
  
• 25 May 2010 13:00 Room 213
  
  Peter Forrester (University of Melbourne) The KP Hierarchy and Algebraic Geometry
  
  Abstract: In this talk some analogies between exact partition functions in two-dimensional lattice gauge theory, and Yang-Mills theory on the sphere, with non-intersecting Brownian walkers will be pointed out. The implications of known analysis of the field theory partition functions for the non-intersecting Brownian walkers will be developed.
  
  
• 24 May 2010 14:15 Babel Middle Theatre
  
  John Enyang (Melbourne) Jucys-Murphy elements and the representations of partition algebras
  
  Abstract: Beginning with a presentation for the partition algebras given by Halverson and Ram, we provide a recursive definition for a large family of commuting (Jucys-Murphy) elements in the partition algebras, together with an integral Murphy-type basis for the partition algebras, with respect to which the commuting family acts triangularly. Consideration of the eigenvalues obtained by the triangular action of the Jucys-Murphy elements on the Murphy basis will show that this recursively defined commuting family of Jucys-Murphy elements coincides exactly with the family of commuting elements given diagrammatically by Halverson and Ram. Our presentation will conclude with a discussion of further applications of the Jucys-Murphy elements in the study of the representations of the partition algebras.
  
  
• 18 May 2010 14:15 Room 215
  
  Andrei Kelarev (Ballarat) Cayley Graphs, Finite State Automata and Group Automata
  
  Abstract: Cayley graphs are closely related to the concepts of finite state automata and group automata. In particular, finite state automata are generalisations of the Cayley graphs, since every Cayley graph can be regarded as a finite state automaton. Group automata form an important subclass of the class of all finite state automata. On the other hand, Cayley graphs are capable of accomplishing all tasks performed by the finite state automata. These relations lead to new open questions concerning the influence of the theoretical properties of the Cayley graphs on their possible applications in directions where finite state automata have been used, including such areas as bioinformatics, data mining, computer graphics, and internet security.
  
  
• 18 May 2010 13:00 Room 213
  
  Gus Schrader (Melbourne) The KP Hierarchy and Algebraic Geometry
  
  Abstract: will review the correspondence (discovered by Krichever, Mumford, and many others) between certain algebro-geometric data and solutions of the KP hierarchy. We will see that the KP system is related to the classical problem of classifying commutative rings of ordinary differential operators. If time permits, I will discuss the application of this theory by Mulase and Shiota to the Schottky problem of characterising Jacobian varieties.
  
  
• 18 May 2010 12:00 Russell Love
  
  Michael Wheeler (Melbourne) New results on the one-dimensional Heisenberg magnet
  
  Abstract:The one-dimensional Heisenberg magnet was introduced in 1928 as a model for a chain of interacting spin-1/2 particles. Although the eigenstates of this model were found by Bethe as early as 1931, the Heisenberg magnet continues to be a widely studied quantum integrable system. One important area of study is the calculation of inner products between eigenstates and more general states of this model. In this talk I will discuss some of the methods appearing in my thesis for calculating such inner products. I will show that certain special inner products provide solutions to the infinite set of partial differential equations which comprise the Kadomtsev-Petviashvili hierarchy, providing a new link between quantum and classical integrable models.
  
  
• 11 May 2010 13:00 Room 213
  
  Gus Schrader (Melbourne) The KP Hierarchy and Algebraic Geometry
  
  Abstract: will review the correspondence (discovered by Krichever, Mumford, and many others) between certain algebro-geometric data and solutions of the KP hierarchy. We will see that the KP system is related to the classical problem of classifying commutative rings of ordinary differential operators. If time permits, I will discuss the application of this theory by Mulase and Shiota to the Schottky problem of characterising Jacobian varieties.
  
  
• 11 May 2010 12:00 Russell Love
  
  Abby Thompson (UC Davis) Surgery on knots in a Surface x Interval
  
  Abstract: Given a knot K in a 3-dimensional space, one can remove a neighborhood N of K and then reinsert N in a non-trivial way, resulting in a new space. This is "surgery" on K, and is a basic topic of study in 3-manifolds. We examine surgery on knots in 3-manifolds that have a natural product structure, and relate it to manifolds that can (or cannot) be obtained by surgery on 2-component links in the 3-sphere. This work is joint with M. Scharlemann.
  
  
• 11 May 2010 14:15 Room 215
  
  Douglas Stones (Monash) The many formulae that count Latin squares
  
  Abstract: A Latin square is an $n \times n$ matrix containing $n$ distinct symbols such that each row and each column contains each symbol exactly once. Latin squares are widely used for designing experiments and in error-correcting codes. However, merely counting Latin squares poses a significant problem and many prior attempts have subsequently been proved faulty. Despite some claims to the contrary, there are many formulae for the number of Latin squares. In this talk, we will give a survey of these formulae and their history which stretches all the way back to MacMahon in 1898!
  
  
• 10 May 2010 15:15 Babel Middle Th
  
  Tharatorn Supasiti (Melbourne) The fundamental groups of Haken n-manifolds
  
  Abstract: Historically, there have been two main approaches in the study of 3-manifolds. In particularly, the approach introduced by Haken is proven successful in computational topology, when restricted to a class of 3-manifolds called Haken manifold. Recently, Foozwell extended some properties of Haken manifolds to higher dimensions, with emphasis on dimension four. In his thesis, he was able to adapt Waldhausen's algorithm to conclude that the topological word problem is solvable for any fundamental group of Haken n-manifold. This prompts the following question: under what condition, is the fundamental group of a Haken n-manifold, word-hyperbolic? In this talk, I will address my current progress on answering this question.
  
  
• 10 May 2010 14:15 Babel Middle Th
  
  Andrei Ratiu (Istanbul Bilgi University) Inner Steiner formula for polytopes with an application to self-affine fractal tilings
  
  Abstract: The recent construction by Lapidus and Pearse of the tubular zeta-function of a self-similar tiling as a certain meromorphic function whose poles are the "complex dimensions" of the tiling and whose sum of residues gives the volume of its inner neighborhood, is an important breakthrough in the theory of fractals. As a first step beyond the world of self-similar fractals, we define the tubular zeta-function of a self-affine tiling and apply it to a higher-dimensional analogue of McMullen's generalized Sierpinski carpets. We use the fact that the volume of the inner tube of a polytope is a piecewise polynomial function, which would be the inner counterpart of the well-known classical Steiner formula for convex bodies.
  
  
• 4 May 2010 14:15 Room 215
  
  Michael Payne (Melbourne) Colouring the Plane
  
  Abstract: The Chromatic Number of the Plane problems asks for the least number of colours required to colour the plane so that points distance one apart receive different colours. Created in 1950, the problem has resisted all attempts to improve on the initial bounds (between 4 and 7) found soon afterwards. Of course, faced with such resistance mathematicians have studied many variations on the problem and found some interesting results. I will talk about some such variations, namely the study of measurable colourings, graphs whose measurable and general chromatic numbers differ, colourings of large subgraphs of the plane, and perhaps more if time permits.
  
  
• 4 May 2010 13:00 Room 213
  
  Richard Brak (Melbourne) What do rings have to say about lattice greens functions?
  
  Abstract: Prompted by Tonys talk last week I wondered what could be said in general about the class of functions lattice greens function belong to. There are two theorems that can be proved algebraically using ring theory. I'll discuss these, their connection to the constant term representation and, time permitting a non-commutative constant term generalisation. The latter is interesting (to me at least) as it is related to free groups and a (slightly) unexpected path problem.
  
  
• 20 April 2010 14:15 Room 215
  
  Keri Morgan (Clayton School of Information Technology) Chromatic factorisation and Galois groups of chromatic polynomials
  
  Abstract: The chromatic polynomial P(G,k) gives the number of proper k-colourings of a graph G. This polynomial is also studied in statistical mechanics where the limit points of the zeros give possible locations of physical phase transitions. We say P(G,k) has a chromatic factorisation, if P(G,k)=P(H1,k)P(H2,k)/P(Kr,k) for some graphs H1 and H2 and some r>=0. Any clique-separable graph, that is, a graph that can be obtained by identifying an r-clique in H1 with an r-clique in H2, has a chromatic factorisation. A graph is said to be strongly non-clique-separable if it is neither clique-separable nor chromatically equivalent to any clique-separable graph. We identified strongly non-clique-separable graphs that have chromatic factorisations. We give an overview of some of our results on these chromatic factorisations including giving an infinite family of strongly non-clique-separable graphs that have chromatic factorisations. We then give a summary of the Galois groups of chromatic polynomials of degree at most 10. We are interested in identifying the relationships between graphs that have chromatic polynomials with the same Galois group. We give some families of graphs that have chromatic polynomials with the same Galois group.
  
  
• 20 April 2010 14:15 Room 215
  
  Kyle Pula (Denver) Anti-Ramsey Theory for Cycles in Complete Graphs
  
  Abstract: This talk will survey results in anti-ramsey theory for cycles. Specifically, we'll look at edge-colorings of complete finite graphs that lack rainbow cycles of prescribed lengths. (A subgraph is rainbow if its edge-colors are pairwise distinct.) The talk will be a gentle survey of results in this area with no particular background required.
  
  
• 22 April 2010 14:15 Babel Middle Theatrette (106)
  
  Jim Shank (Kent) Rings of Invariants and Varieties of Representations
  
  Abstract: Suppose that G is a finite group, F is a field and V is finite dimensional representation of G over F. The action of G on V induces an action on the dual V^* which extends to an action by algebra automorphisms on the symmetric algebra S:=S(V^*). The subring of fixed points, S^G, is known as the ring of invariants of V. For fixed G, F, and dim(V), the representations of G can be paramterised by an algebraic variety. I will discuss the resulting parameterisation of invariant rings, using modular representations of elementary abelian p-groups as illustrative examples.
  
  
• 20 April 2010 13:00 Room 203
  
  Tony Guttmann (Melbourne) Green Functions, Ramanujan's identites and Apéry's proof
  
  Abstract: In this rambling and disconnected talk I will discuss some recent work I've done on Lattice Green Functions, and its unexpected connection with number theory, by virtue of its connection with some Ramanujan type formulae for $1/\pi,$ and to Ap\'ery's proof of the irrationality of $\zeta(3)$. Zero knowledge is required apart from knowing what an ordinary differential equation is, knowing the definition of the Reimann zeta function, the constant $\pi,$ the concept of irrationality, plus the basic axioms of arithmetic.
  
  
• 20 April 2010 12:00 Russell Love
  
  Klemens Fellner (Cambridge and Vienna) Aggregation-pattern in non-local equations with locally-repulsive interaction potentials
  
  Abstract: We study non-local evolution equations for a density of individuals, which interact through a given symmetric potential. Such models appear in many applications such as swarming and flocking, opinion formation, inelastic materials, .... In particular, we are interested in interaction potentials, which behave locally repulsive, but aggregating over large scales. A particular example for such potentials was recently given in models of the alignment of the directions of filaments in the cytoskeleton. We present results on the structure and stability of steady states. We shall show that stable stationary states of regular interaction potentials generically consist of sums of Dirac masses. However the amount of Diracs depends on the interplay between local repulsion and aggregation. In particular we shall see that singular repulsive interaction potentials introduce diffusive effects in the sense that stationary state are no longer sums of Diracs but continuous densities.
  
  
• 15 April 2010 14:15 Babel Middle Theatrette
  
  Daniel Nakano (University of Georgia) Differentiating the Weyl generic dimension formula and support varieties for quantum groups
  
  Abstract: In this talk I will explain how to compute the support varieties of all the irreducible modules for the small quantum group u_{zeta}(g) where g is a simple, complex Lie algebra and zeta is an l-th root of unity larger than the Coxeter number. This calculation employs the prior calculations and techniques of Ostrik and of Nakano--Parshall--Vella, in addition to deep results involving the validity of the Lusztig character formula and the positivity of parabolic Kazhdan-Lusztig polynomials for the affine Weyl group. Analogous results are provided for the first Frobenius kernel G_1 of a reductive algebraic group scheme G defined over the prime field F_p. This is joint work with C. Drupieski and B. Parshall.
  
  
• 13 April 2010 14:15 Room 215
  
  Grant Cairns (La Trobe) Thrackles and related graph drawings
  
  Abstract: A thrackle is a drawing of a finite graph in which every pair of edges meet exactly once, either at a common vertex or at a transverse crossing. The pentagram is a simple example. This talk outlines joint work with Yury Nikolayevsky in which we use homologocal ideas to examine Conway's thrackle conjecture.
  
  
• 13 April 2010 12:00 Russell Love
  
  Xu-Jia Wang (ANU) Optimal transportation and Monge-Ampere equation
  
  Abstract: I will first recall the development of optimal transportation, which was first introduced by Monge in a paper of 1781. Then I will introduce the dual functional of Kantorovich which led to the modern theory of existence and uniqueness of optimal mappings. The regularity of optimal mappings involves the study of Monge-Ampere type equations and substantial progress was achieved in the last two decades.
  
  
• 30 March 2010 13:00 Room 203
  
  Wendy Baratta (Melbourne) Getting Macdonald Polynomials into Shape: Prescribed Symmetry Macdonald Polynomials and Constant Term Identities
  
  Abstract: Macdonald polynomials with prescribed symmetry can be obtained from the nonsymmetric Macdonald polynomials via symmetrisation, antisymmetrisation and normalisation. By computing the explicit form of the normalisation with respect to the constant term inner product we provide a derivation of a special case of a conjectured q-constant term identity.
  
  
• 30 March 2010 14:15 Room 215
  
  Nick Wormald (Waterloo) Load balancing and random graphs
  
  Abstract: A general problem area involves job assignments. There is a set of jobs to be assigned to processors (i.e. things that can deal with the jobs). We wish to assign the jobs such that, roughly speaking, all processors are kept as busy as possible. Various problems arise by imposing different constraints and objective functions can be imposed. I will discuss some of these, and in particular, a connection to a problem concerning orientations of graphs or hypergraphs. Thus, when can a graph's edges be oriented so that the maximum indegree is at most k? How can we find such an orientation quickly? This setting gives rise to problems on thresholds, and algorithms, for random graphs and hypergraphs. The talk will include some recent work with Jane Gao.
  
  
• 30 March 2010 12:00 Russell Love
  
  Ian Wanless (La Trobe) Matrix permanents
  
  Abstract: The permanent is a function on matrices, from the same family as the determinant. Since being introduced by Cauchy in 1812, it has found a wealth of applications in areas like probability, particle physics, algebra and combinatorics. For example, the permanent arises in many counting problems that involve permutations or matchings in bipartite graphs. Much of the 20th century study of permanents was driven by van der Waerden's conjecture about which doubly stochastic matrix minimises the permanent. This "simple" conjecture took over 50 years to solve, and in the meantime spawned several related conjectures that remain open to this day. This colloquium will give a general overview of the study of permanents. It will survey some of the most important known results and interesting open problems. The survey will be broad rather than deep, and hence suitable for non-specialists.
  
  
• 25 March 13:00 Room 213
  
  Robion Kirby (Berkeley) Broken fibrations on 4-manifolds
  
  Abstract: Theorem: Every map from an n-manifold to the 2-sphere or 2-disk is homotopic to a broken fibration, and any two such are related by a simple set of moves. The talk will explain the terms in the theorem, give reasons why the theorem may be useful, describe its antecedents and relations to symplectic 4-manifolds, and maybe more.
  
  
• 29 March 14:15 Babel Middle Theatre
  
  Claas Röer (National University of Ireland, Galway) Commensarations of Thompson's group F
  
  Abstract: In the framework of linear systems of q-difference equations, one may consider the connection data to be defined by the asymptotics of a set of fundamental solutions. We consider the associated linear problem for a q-analogue of the fifth Painleve equation, which is a $2 \times 2$ example of a linear system which is not handled by the theory "regular" systems of q-difference equations. We will construct a set of rational transformations that change the asymptotics, and hence, changes the connection data. From this procedure, we construct a group of symmetries of the underlying Painleve equation.
  
  
• 25 March 13:00 Alice Hoy 102
  
  Chris Ormerod (La Trobe) A Riemann-Hilbert type approach to systems of linear q-difference equations
  
  Abstract: In the framework of linear systems of q-difference equations, one may consider the connection data to be defined by the asymptotics of a set of fundamental solutions. We consider the associated linear problem for a q-analogue of the fifth Painleve equation, which is a $2 \times 2$ example of a linear system which is not handled by the theory "regular" systems of q-difference equations. We will construct a set of rational transformations that change the asymptotics, and hence, changes the connection data. From this procedure, we construct a group of symmetries of the underlying Painleve equation.
  
  
• 9 March 14:15 Old Geology 2
  
  Sergio Fenley (Florida State and IAS) Ideal boundaries of pseudo-Anosov flows and applications to large scale structure of flows and foliations
  
  Abstract: We consider the asymptotic structure induced by a pseudo-Anosov flow in the universal cover of the underlying 3-manifold. First we show that the orbit space can be compactified to a closed disc. Then we consider untwisted flows: This means that no closed orbit is freely homotopic to the inverse of another orbit. In this case we use the dynamics of the flow to produce a flow ideal boundary to the universal cover of the manifold. The main result is that the action of the fundamental group G of the manifold on the flow ideal boundary is a uniform convergence group. This implies that G is Gromov hyperbolic and the action of G on the flow ideal sphere is conjugate to the action of G on its Gromov ideal boundary. This implies that untwisted pseudo-Anosov flows are quasigeodesic. This also has consequences for the asymptotic behavior of certain foliations.
  
  
• 9 March 13:00 Room 213
  
  Nick Beaton (Melbourne) Enumerating some classes of lattice polygons
  
  Abstract: The problem of counting the number of self-avoiding polygons on a lattice is quite difficult (to put it mildly). One approach is to study sub-classes which satisfy some given restrictions (eg. directedness or prudence). In this talk I will discuss some of these sub-classes, the methods used to count them, and some recent interesting results.
  
  
• 9 March 2010 12:00 Russell Love
  
  Joel Hass (UC Davis) Simplicial harmonic maps of surfaces
  
  Abstract: Harmonic maps have proven useful in the study of negatively curved manifolds. We will discuss the idea of a simplicial harmonic map, introduced in recent joint work with Peter Scott. These combine aspects of the smooth and discrete settings and give a simple yet powerful method to control the geometry of families of surfaces,. We will indicate both topological and computational applications.
  
  
• 2 March 13:00 Room 213
  
  Jan De Gier (Melbourne) Constant terms and multivariate polynomials
  
  Abstract: Certain multivariate polynomials, including specialised non-symmetric Macdonald polynomials and parabolic Kazhdan-Lusztig elements, can be given in terms of constant term expressions. These are equivalent to inhomogeneous multiple contour integrals occurring in the works of Jimbo and Miwa. I will discuss a Bethe Ansatz type derivation of these expressions from first principles.
  
  
• 25 Febuary 2010 14:15 Russell Love
  
  Stephen McAteer (Melbourne) MathML: LaTeX is Not the Only Fruit
  
  Abstract: LaTeX has been a staple of mathematical publication for a some time now, however it is not designed with online publication in mind. Enter MathML; Mathematical Markup Language. MathML produces beautiful mathematics, fully integrated into a webpage. I will give a brief introduction into the language, by the end of which audience members should be able to start creating their own gorgeous mathematical webpages without the need to link to a PDF every time a formula appears. I will also discuss some other advantages MathML has over other standards such as searchability and ease of production.
  
  
• 23 Febuary 2010 13:00 Russell Love
  
  Pongphat Taptagaporn (Melbourne) Symmetric Tilings and Enumeration in the Aztec Diamond
  
  Abstract: We extend the ideas of enumerating the perfect matchings of the Aztec Diamond to those with certain reflectional symmetries. First we solve the -invariant case using the graph factorization theorem, and also solve the previously open problems of enumerating <t> and <r²,t>-invariant Aztec Diamonds. Furthermore, we provide algorithms to generate these symmetric cases and show that the complexity of these problems are in P.
  
  
• 22 Febuary 2010 14:15 Russell Love
  
  Andrei Kelarev (Ballarat) Applications of Finite State Systems and Ring Constructions
  
  Abstract: The talk is devoted to a broad overview of previous results and recent work on finite state systems and ring constructions motivated by their applications in data mining, information theory and internet security.
  
  
• 18 February 2010 14:15 Room 213
  
  Marcelo Aguiar (Texas A&M) Quantum groups and Hopf algebras in combinatorics
  
  Abstract:This talk will review the construction of quantum groups (deformations of simple Lie algebras) via quantum symmetric algebras, and explain how it can be extended by introducing a combinatorial structure in the form of a species, as defined by Joyal. This will lead us into the consideration of Hopf monoids in species, a notion that will be defined and for which examples will be given. Very little knowledge of any of the above notions will be assumed.
  
  
• 15 Febuary 2010 14:15 Russell Love
  
  Stefan Tillmann (U Queensland) Spinning, Straightening and the Recognition of Closed Hyperbolic 3-Manifolds
  
  Abstract: I'll talk about joint work with Feng Luo (Rutgers) and Tian Yang (Rutgers) on using Thurston's hyperbolic gluing equations in the context of triangulations of closed 3-manifolds: We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are Thurston's spinning construction and a volume rigidity result attributed by Dunfield to Thurston, Gromov and Goldman. As an application, together with work of Francaviglia, this greatly simplifies the rigorous algorithmic detection and description of hyperbolic structures on closed 3-manifolds due to Casson and Manning.
  
  
• 15 February 2010 13:15 Room 213
  
  Luigi Cantini (LPT, ENS, France) Combinatorial properties of the O(1) loop model
  
  Abstract: The interplay between statistical mechanics and combinatorics has always been of great interest both for physicists and for mathematicians. In this talk, motivated by the remarkable conjecture of Razumov and Stroganov, which states that the properly normalized components of the ground state of the O(1) loop model enumerate classes of Alternating Sign Matrices, we present the combinatorial properties of this ground state for different boundary conditions. The crucial role of integrability through the quantized Knizhnik-Zamolodchikov (qKZ) equations will be exploited. Particular attention will be paid to the case where the model is defined on a strip in which case the sum of the components of the refined ground state is given by a doubly weighted enumeration of Cyclically Symmetric Transpose Complement Plane Partitions (CSTCPP).
  
  
• 27 January 2010 14:00 Russell Love
  
  Daniel Delbourgo (Monash) Exceptional zero formulae for L-functions of elliptic curves
  
  Abstract: TBA
  
  
• 27 January 2010 11:00 Russell Love
  
  Alina Bucur (MIT, IAS, UCSD) Multiple Dirichlet series
  
  Abstract: TBA
  
  
• 27 January 2010 9:30 Russell Love
  
  Kiran Kedlaya (MIT, IAS, UCSD) The probability that a complete intersection is smooth (after Poonen)
  
  Abstract: TBA
  
  
• 20 January 2010 17:30 Rivett Theatre, Redmond Berry Building
  
  Persi Diaconis (Stanford University) Adding numbers and Shuffling cards
  
  Abstract: he usual method of adding two or more integers creates 'carries' as we go along. For 'typical numbers' these carries form a Markov chain with an 'Amazing' transition matrix (Holte). This same matrix comes up in analyzing the usual method of riffle shuffling playing cards. I will explain carries, shuffling and the connection. This is joint work with Jason Fulman.
  
  
  
  
  
  
  
• 19 January 2010 13:15 TBA
  
  Susan Holmes (Stanford University) Comparing Trees using Distances, Trees and Multidimensional Scaling
  
  Abstract: Distances between trees have useful applications in combining phylogenetic trees built from multiple genes and in studying trees built from bootstrap samples and Bayesian posterior distributions. Until recently, computations of the distance between trees was intractable. We have developed an R package to compute the distance between trees based on a polynomial algorithm by M. Owen and S. Provan. Using this distance we are able to project trees from data with varying mutation rates, compare hierarchical clustering trees for Microarrays, and study influence functions for the data used to build the trees. The main tool for using the distances is multidimensional scaling, although the original tree metric delivers a treespace which is not Euclidean, it is itself negatively curved, the Euclidean approximations provided by MDS are very useful for making low dimensional graphics of tree projections. (This is joint work with John Chakerian)
  
  
• 5 January 2010 14:15 Russell Love
  
  Dan Mathews (University of Nantes) Chord diagrams and contact-topological quantum field theory
  
  Abstract: We consider the topological quantum field theory properties of sutured Floer homology, as introduced by Honda--Kazez--Matic. In the ``dimensionally reduced" case of product manifolds, the computation of sutured Floer homology and contact elements reduces to that for solid tori with longitudinal sutures. The SFH of such manifolds forms a ``categorification of Pascal's triangle", and contact structures correspond bijectively to chord diagrams, or sets of disjont properly embedded arcs in the disc; contact elements form distinguished subsets of $SFH$ of order given by the Narayana numbers. We find natural ``creation and annihilation operators'' which allow us to define a QFT-type basis of each $SFH$ vector space, consisting of contact elements. Sutured Floer homology in this case reduces to the combinatorics of chord diagrams. We prove that contact elements are in bijective correspondence with comparable pairs of basis elements with respect to a certain partial order, and in a natural and explicit way. The details of this description have intrinsic contact-topological meaning, and give rise to interesting category-theoretic, simplicial and algebraic structures.