# Mathematics Postgraduate Seminar Series - 2015

## Seminars in 2015, Semester 1

Thursday March 5

Adrianne Jenner (Sydney University)

Mathematical model of cancer treatments using oncolytic viruses and immunotherapy.

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Thursday March 12

Joachim Worthington (Sydney University)

Some steady states solutions of the Euler equations on a toroidal domain and their stability.

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Thursday March 19

Andrew Swan (Sydney University)

Introduction to Random Matrix Theory.

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Friday March 27

Alex Casella (Sydney University)

3-manifolds and hyperbolic geometry.

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Thursday April 3

Patrick Eades (Sydney University)

Free Lie Algebras and the Symmetric Group.

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Friday April 17

Christopher Ryba (Sydney University)

A connection between formal power series for solutions to ODEs and the combinatorics of rooted trees.

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Friday April 24

Montek Gill (Sydney University)

Computing the universal cover and fundamental group of triangulated 3-manifolds.

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Thursday April 30

Christopher Thornett (Sydney University)

Forms and Semigroups: Modern Methods for Evolution Equations

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Thursday May 7

Marcus Webb (Cambridge University)

An Introduction to Geometric Integration via Runge-Kutta Methods

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Thursday May 14

Sean Carnaffan (Sydney University)

Anomalous diffusion processes

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Thursday May 21

Ishraq Uddin (Sydney University)

A gentle introduction to topological quantum computation

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Thursday May 28

Kamil Bulinski (Sydney University)

Ergodic Plunnecke inequalities

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## Seminars in 2015, Semester 2

Wednesday August 5

James Diaz (Sydney University)

Morse Theory and Morse Homology: Critical Points

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Wednesday August 12

Robert Haraway (Boston College)

Binary quadratic forms after Conway and Eindhoven

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Wednesday August 18

Christopher Ryba (Sydney University)

An Introduction to Representation Theory

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Wednesday August 26

Makoto Suwama (Sydney University)

The ideal class group: An introduction to algebraic number theory

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Wednesday September 2 - Social Event

Wednesday September 9 - Fourth Year Joint Talk

Abraham Ng (Sydney University) & Hao Guo (Sydney University)

Proof of the Fundamental Gap Conjecture & Witten's Deformation and the Morse Inequalities

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Wednesday September 16 - Fourth Year Joint Talk

Joshua Ciappara (Sydney University) & Dominic Tate (Sydney University)

Categorification of Quantum sl_2 & Teichmuller space on surfaces

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Wednesday September 23

Danya Rose (Sydney University)

Geometric phase and periodic orbits in the equal-mass, planar three-body problem with vanishing angular momentum

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Wednesday September 30 - Mid-Semester Break

Wednesday October 7 - Mid-Semester Break

Wednesday October 14

Alex Casella (Sydney University)

A baby step towards (linear) Lie Groups and Lie Algebras for non--experts

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a) Basic definitions;

b) The exponential map and its properties;

c) Von Neumann and Cartan Theorem;

The talk is based on the book: "Notes on differential geometry and Lie Groups - Jean Gallier"Wednesday October 21

Sasha Fish (Sydney University)

A (mega)-brief introduction to Ergodic Theory

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a) Ergodic theorems;

b) Normal numbers in [0,1], and their connection to Birkhoff ergodic theorem;

c) Poincare recurrence;

d) Multiple recurrence and non-standard ergodic averages;

e) Szemeredi theorem on arbitrary long arithmetic progressions in sets of positive density.

Wednesday October 28

Alexander Kerschl (Sydney University)

Introduction to cellular algebras and their representation theory

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