CARMA ANALYSIS AND NUMBER THEORY SEMINAR

Speaker: Dr Hamish Waterer (CARMA, University of Newcastle)
Title: A Bucket Indexed Formulation for Nonpreemptive Single Machine Scheduling Problems
Time & Date: 3:00 pm EST, Tuesday 17 September 2013
Venue: Room V205, Mathematics Building, Callaghan Campus, The University of Newcastle
Also available on the Access Grid network (venue: UNewcastle).

Abstract

An exact bucket indexed (BI) mixed integer linear programming formulation for nonpreemptive single machine scheduling problems is presented that is a result of an ongoing investigation into strategies to model time in planning applications with greater efficacy. The BI model is a generalisation of the classical time indexed (TI) model to one in which at most two jobs can be processing in each time period. The planning horizon is divided into periods of equal length, but unlike the TI model, the length of a period is a parameter of the model and can be chosen to be as long as the processing time of the shortest job. The two models are equivalent if the problem data are integer and a period is of unit length, but when longer periods are used in the BI model, it can have significantly fewer variables and nonzeros than the TI model at the expense of a greater number of constraints. A computational study using weighted tardiness instances reveals the BI model significantly outperforms the TI model on instances where the mean processing time of the jobs is large and the range of processing times is small; that is, the processing times are clustered rather than dispersed.

This research is a joint work with Natashia Boland and Riley Clement.

This talk will be broadcast using Access Grid Technology from The University of Newcastle. To participate in this seminar, book your University's AGR or a university/APAC etc. AGR that you are otherwise able to use. A listing of Access Grid nodes is available at: http://www.accessgrid.org/nodes.

This seminar notice is available on the AMSI Website: Events > AGR Events

Seminar Convenors

• Liangjin Yao liangjinyao@gmail.com
• Matthew Tam matthew.tam@uon.edu.au

If you (and your colleagues) wish to participate, please:

1. book your own AGR (or university/APAC etc. AGR that you otherwise are able to use), and ask your AGR technical people to contact David Allingham David.Allingham@newcastle.edu.au (the AGR technical person at Newcastle University) in advance of the seminar.
2. Advise the seminar convenor: Julianne Turner (juliane.turner@newcastle.edu.au

Contact:

Ms Maaike Wienk
Access Grid Coordinator
Australian Mathematical Sciences Institute
Building 161, C/- The University of Melbourne, Victoria 3010 Australia
P: 03 8344 1776 | F: 03 9349 4106
E: agr@amsi.org.au | W: http://www.amsi.org.au/

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

Professor Venkatesh was a 2011 Institute of Advanced Studies Professor-at-Large.

• Colloquium: Monday 23 Sept, 14:00 (EST time);
  Lecture Theatre 214, Otto Hirschfeld Building 81, University of Queensland, St Lucia.
  Dynamics and the geometry of numbers

Abstract: It was understood by Minkowski that one could prove interesting results in number theory by considering the geometry of lattices in \mathbb{R}ⁿ. (A lattice is simply a grid of points.) This technique is called the “geometry of numbers.” We now understand much more about analysis and dynamics on the space of all lattices, and this has led to a deeper understanding of classical questions. I will review some of these ideas, with emphasis on the dynamical aspects.

• Public Lecture: Monday 23 Sept, 18:00 (EST time);
  Lecture Theatre 358, Physiology Building 63, University of Queensland, St Lucia.
  How to stack oranges in three dimensions, 24 dimensions, and beyond

Abstract: How can we pack balls as tightly as possible? In other words: to squeeze as many balls as possible into a limited space, what's the best way of arranging the balls? It’s not hard to guess what the answer should be — but it’s very hard to be sure that it really is the answer! I'll tell the interesting story of this problem, going back to the astronomer Kepler, and ending almost four hundred years later with Thomas Hales. I will then talk about stacking 24-dimensional oranges: what this means, how it relates to the Voyager spacecraft, and the many things we don’t know beyond this.

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Colloquium: Wednesday 25 Sept, 11:00 (WA time, 13:00 EST);
  AGR room, Science Library, University of Western Australia.
  The Cohen-Lenstra heuristics: from arithmetic to topology and back again

Abstract: I will discuss some models of what a “random abelian group” is, and some conjectures (the Cohen–Lenstra heuristics of the title) about how they show up in number theory. I'll then discuss the function field setting and a proof of these heuristics, with Ellenberg and Westerland. The proof is an example of a link between analytic number theory and certain classes of results in algebraic topology (“homological stability”).

• Public Lecture: Wednesday 25 Sept, 18:00 (WA time, 20:00 EST);
  Club Theatre Auditorium, University of Western Australia.
  Two centuries of prime numbers

Abstract: Surprisingly, there have been fundamental new discoveries about prime numbers in the last decade, most recently by Yitang Zhang a few months ago. I’ll survey some of our understanding of prime numbers in a nontechnical fashion, starting with the “music of the primes” — the strange oscillations between regions where primes are more common and more scarce — and concluding with a discussion of Zhang‘s discovery: prime numbers must occasionally come very close to one another.

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Public Lecture: Thursday 26 Sept, 18:00 (SA time, 18:30 EST);
  Horace Lamb Lecture Theatre, University of Adelaide.
  How to stack oranges in three dimensions, 24 dimensions, and beyond

Abstract: How can we pack balls as tightly as possible? In other words: to squeeze as many balls as possible into a limited space, what's the best way of arranging the balls? It’s not hard to guess what the answer should be — but it’s very hard to be sure that it really is the answer! I'll tell the interesting story of this problem, going back to the astronomer Kepler, and ending almost four hundred years later with Thomas Hales. I will then talk about stacking 24-dimensional oranges: what this means, how it relates to the Voyager spacecraft, and the many things we don’t know beyond this.

• Colloquium: Friday 27 Sept, 15:00 (SA time, 15:30 EST);
  Horace Lamb Lecture Theatre, University of Adelaide.
  Dynamics and the geometry of numbers

Abstract: It was understood by Minkowski that one could prove interesting results in number theory by considering the geometry of lattices in \mathbb{R}ⁿ. (A lattice is simply a grid of points.) This technique is called the “geometry of numbers.” We now understand much more about analysis and dynamics on the space of all lattices, and this has led to a deeper understanding of classical questions. I will review some of these ideas, with emphasis on the dynamical aspects.

AMSI/AustMS AGR National Seminar
The University of New South Wales

Fibonacci Numbers and Linear Algebra

Speaker: Prof Claus Ringel (University of Bielefeld, Germany)
Date & Time: 3:00 pm, Friday 27 September 2013
Access Grid Venue: University of NSW.

Abstract

The famous Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, ... have attracted a lot of interest in and outside of mathematics. They play an important role in applications in biology, but also in computer science and other areas. The lecture will draw the attention to questions in linear algebra which lead to Fibonacci numbers: we will give a categorical interpretation of some well-known combinatorial identities, but also exhibit new partition formulas.

We will consider triples of matrices (with entries in some field k) of the same shape, or, equivalently, triples of linear transformations say from V to W, where V, W are fixed vector spaces over k. Such triples are called 3-Kronecker modules. Trying to classify them, it turns out that certain 3-Kronecker modules play an exceptional role: we call these modules Fibonacci modules, since the dimension of the vector spaces involved are Fibonacci numbers. Given suitable 3-Kronecker modules, there is a corresponding linear representation of the 3-regular tree. In particular, this happens for the Fibonacci modules and it displays the Fibonacci numbers by integral functions on the tree. In this way we obtain the new partition formulas. Here is the display for the Fibonacci numbers 8 and 21:

The basic information can be arranged in two triangles, they are quite similar to the Pascal triangle of the binomial coefficients, but in contrast to the additivity rule for the Pascal triangle, we now deal with additivity along hooks. There are intriguing relations between the two triangles. These relations correspond to certain exact sequences involving Fibonacci modules, but they can be verified also recursively.

The lecture is based on joint investigations with Philipp Fahr.

Seminar Convenor: Maaike Wienk (agr@amsi.org.au)
AGR Support: Tim Salmon (tim@unsw.edu.au)

How to participate in this seminar

1. Book your nearest Access Grid room and ensure technical support is available throughout the seminar. Please notify the technical support people that connection time is 1.00pm AEST, for a 2.00pm AEST start of the presentation; and
2. Contact Maaike Wienk with a cc to Tim Salmon at the University of New South Wales (email addresses as above) one week in advance at the latest.

This information will also be available shortly on the AMSI website

Venue: Sancta Sophia College, 8 Missenden Rd, Camperdown

• Steering Committee: 6–8pm Saturday 28 September in the Carslaw Building, Univ. of Sydney
• Editors' Committee: 9:15am Sunday 29 September in the McDonald Room, Sancta Sophia College
• AMPAI meeting: 11am Sunday 29 September in the McDonald Room, Sancta Sophia College

• AustMS AGM: Wednesday 2nd October, University of Sydney

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Public Lecture: Monday 30 September, 19:00 EST;
  Eastern Avenue Auditorium, University of Sydney.
  Two centuries of prime numbers

Abstract: Surprisingly, there have been fundamental new discoveries about prime numbers in the last decade, most recently by Yitang Zhang a few months ago. I’ll survey some of our understanding of prime numbers in a nontechnical fashion, starting with the "music of the primes" — the strange oscillations between regions where primes are more common and more scarce — and concluding with a discussion of Zhang’s discovery: prime numbers must occasionally come very close to one another.

• AustMS Plenary Lecture (AM): Tuesday 1 Oct, ??:00 EST;
  Eastern Avenue Auditorium, University of Sydney.
  TBA

Public Lecture — Early-Career Lecturer, AustMS Annual Meeting

Speaker: A/Prof Sommer Gentry (US Naval Academy)
Date & Time: Monday 30 September, 19:00 EST
Venue: Eastern Avenue Auditorium, University of Sydney
Title: Faster, Safer, Healthier: Adventures in Operations Research

Abstract: While mathematical advances of all sorts have impacted our world for the better, operations research is a branch of mathematics that is expressly focused on applying advanced analytical methods to help make better decisions. Operations researchers have eased traffic jams by closing selected streets, and gotten packages to you more quickly by planning U.P.S. routes with fewer left turns. Operations researchers have shown which personal decisions are the leading causes of death, and planned maintenance schedules to minimize bridge collapses. I use operations research to get more people a kidney transplant, and to make sure liver transplants are allocated fairly to people who live in different places across the United States.

The mathematical tools of operations research, like using random numbers to simulate a range of outcomes when some data are unknown, or finding clever algorithms that shortcut the need to try every possible decision in order to find the best one, can be recycled and used to solve other practical problems. In this talk, I will describe some of my O.R. forays into far-flung fields, and tell my favorite stories about O.R.

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

• Colloquium: Friday 3 Oct, 14:00 EST;
  G001 Red Centre, University of NSW.
  The Cohen-Lenstra heuristics: from arithmetic to topology and back again

Biography

Abstract

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Colloquium: Monday 11 Oct, 13:30 EST;
  AGR room, University of Wollongong.
  Torsion in the homology of arithmetic groups

Abstract: Take a Bianchi group — e.g, invertible 2\times 2 matrices with entries in the Gaussian integers — and abelianize it. The result is often a very large torsion group. I will discuss this phenomenon and how it relates to number theory.

• Public Lecture: Monday 11 Oct, 17:00 EST;
  venue TBA, University of Wollongong.
  How to stack oranges in three dimensions, 24 dimensions, and beyond

Abstract: How can we pack balls as tightly as possible? In other words: to squeeze as many balls as possible into a limited space, what's the best way of arranging the balls? It’s not hard to guess what the answer should be — but it’s very hard to be sure that it really is the answer! I'll tell the interesting story of this problem, going back to the astronomer Kepler, and ending almost four hundred years later with Thomas Hales. I will then talk about stacking 24-dimensional oranges: what this means, how it relates to the Voyager spacecraft, and the many things we don’t know beyond this.

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Colloquium: Monday 7 Oct, 14:00 EST;
  room 345 Bldg 28, Monash University.
  Dynamics and the geometry of numbers

Abstract: It was understood by Minkowski that one could prove interesting results in number theory by considering the geometry of lattices in \mathbb{R}ⁿ. (A lattice is simply a grid of points.) This technique is called the “geometry of numbers.” We now understand much more about analysis and dynamics on the space of all lattices, and this has led to a deeper understanding of classical questions. I will review some of these ideas, with emphasis on the dynamical aspects.

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Colloquium: Tuesday 8 Oct, 11:00 EST;
  AGR room, University of Newcastle.
  Dynamics and the geometry of numbers

Abstract: It was understood by Minkowski that one could prove interesting results in number theory by considering the geometry of lattices in \mathbb{R}ⁿ. (A lattice is simply a grid of points.) This technique is called the “geometry of numbers.” We now understand much more about analysis and dynamics on the space of all lattices, and this has led to a deeper understanding of classical questions. I will review some of these ideas, with emphasis on the dynamical aspects.

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Colloquium: Wednesday 9 Oct, 15:00 EST;
  Room G35 Mathematics Department, Australian National University.
  The Cohen-Lenstra heuristics: from arithmetic to topology and back again

Abstract: I will discuss some models of what a “random abelian group” is, and some conjectures (the Cohen–Lenstra heuristics of the title) about how they show up in number theory. I'll then discuss the function field setting and a proof of these heuristics, with Ellenberg and Westerland. The proof is an example of a link between analytic number theory and certain classes of results in algebraic topology ("homological stability").

This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Colloquium: Thursday 10 Oct, 12:30 EST;
  Russell Love Theatre, University of Melbourne.
  From spherical harmonics to spherical varieties: harmonic analysis on homogeneous spaces and the Langlands program

Abstract: Spherical harmonics are eigenfunctions of the Laplacian on the sphere; they are also closely related to understanding how the group of rotations decomposes the space of L² functions on the sphere. We can ask similar questions replacing the sphere by other “highly symmetric” spaces — in particular, G/H where G and H are Lie groups. I will explain some of the work on this question and how it is related to the Langlands program.

• Public Lecture: Thursday 10 Oct, 18:00 EST;
  Michell Theatre, University of Melbourne.
  How to stack oranges in three dimensions, 24 dimensions, and beyond

Abstract: How can we pack balls as tightly as possible? In other words: to squeeze as many balls as possible into a limited space, what's the best way of arranging the balls? It’s not hard to guess what the answer should be — but it’s very hard to be sure that it really is the answer! I'll tell the interesting story of this problem, going back to the astronomer Kepler, and ending almost four hundred years later with Thomas Hales. I will then talk about stacking 24-dimensional oranges: what this means, how it relates to the Voyager spacecraft, and the many things we don’t know beyond this.