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From UCL Undergrad Maths Colloquium
UCL Undergrad Maths Colloquium
Winter 2012 Organizers: Ignas Vysniauskas - About The Colloquium
The UCL Undergrad Maths Colloquium meets weekly (Tuesdays, 5pm at UCL Maths Dept. Room 505) during term to discuss and share interesting mathematical topics outside of (or complimentary to) our normal lecture courses. Each week an undergraduate gives a talk on a mathematical subject or problem, e.g. p-adic numbers, noncommutative geometry, applied mathematics, et cetera. Additionally, the Colloquium arranges weekly study group sessions in a variety of topics.
Upcoming events
 March 20th Hamiltonian Mechanics and ChaosSpeakers: Hannah Roland (RHUL 3rd Year) Abstract: Dynamical systems have always been interesting to study, as understanding them can help us predict future events. This talk will introduce the notion of Hamiltonian mechanics and the associated canonical transformations used to define dynamical systems. We will then quickly cover symplectic matrices and, using their properties, analyse phase flow and prove Liouville's theorem. Finally, we will discuss the impact of a small change in the initial configuration of a dynamical system and see how this finding relates to chaos theory. |
The Colloquium is open to all and the talks should be accessible to anyone with a first years' undergraduate background in mathematics and/or a willingness to learn. We hope to encourage all current undergrads (regardless of their mathematical background) to attend and/or give talks.
Study Groups
- Structure and Interpretation of Computer Programs Winter 2012
- Is there a subject you'd like to study contact Matthew.
Previous study groups:
Updates and Info
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Winter 2012 Colloquium
Jan 10th
The Hidden Life of Vector Spaces. Matthew Eric Bassett (UCL/QMUL)
We'll take an innocent vector space and see how, by considering it
with its dual, we can develop it into a new structure with rich
algebraic (or maybe even quantum) properties. This modified vector
space has ties to knots, braids, and even the Field with One Element
.
Jan 17th
Visualisng fractals. Jack Maizels (UCL)
Fractals are irregular shapes and surfaces that cannot be described using Euclidean geometry, produced by repeating geometric patterns at ever smaller scales. They make up some of the most iconic images in Mathematics and demonstrate infinite complexity created by simple rules. In this talk, we will look at defining fractals, first through simple examples such as the Sierpinski triangle, Koch snowflake and Cantor set, then through the more complex Julia sets and the Mandelbrot set. The talk will delivered using computer slides, allowing a great level of visual detail as well as an intuitive explanation of the mathematics, using animations.
Jan 24th
Let's count! Enumerative combinatorics. Hang Hao Chuien (UCL 2nd year)
Combinatorics is the art of counting things. In Mathematics, the study of finite or countable discrete structures has widespread applications ranging from number theory to geometry. Counting methods not only give rise to many useful and important combinatorial results, but the methods themselves can be applied directly to solving problems in many fields. In this talk we will explore the widely used idea in counting methods of looking at a problem from different angles and use it to solve many seemingly complicated problems.
Jan 31th
Cohomology of Finite Groups. Catherine Yao (UCL 4th year)
Group Cohomology is a powerful tool with applications in Algebraic Topology, Algebraic Number Theory as well as a vast number of other areas of mathematics. It is a general method of studying a group $G$, by associating to it a sequence of abelian groups, $H^n$. We shall explore some functorial properties of cohomology and use some familiar techniques from algebraic topology to explicitly compute it for some examples of finite groups.
Feb 7th
Algorithmic Entropy And The Limits Of Mathematics. Patrick Millwood (UCL 2nd year)
Is a picture worth a thousand words? In the 1960s a group of mathematicians and computer scientists began a quest to find out. Mixing ideas from the work of Gödel and Turing with an approach inspired by the newly invented computer, they sought to uncover the mathematical DNA that makes up data, objects and theorems. By examining the minimum information inherent in any piece of data they developed new insights into computability and incompleteness, and began to brush against the limits of mathematical reasoning. If you can describe a picture in 999 words or less, or want to find out how, come and hear their story.
Feb 14th
Reading week, no colloquium
Feb 21th
Prime k-tuples and small gaps between primes. Alexandre Peyrot (UCL 4th year)
The Twin Prime Conjecture is one of the most famous open problems in number theory. It is believed that there exist infinitely many primes p such that p + 2 is also a prime. We will discuss tools in analytic number theory to tackle problems relating to the distribution of primes and small gaps between primes. We will stumble upon the Hardy-Littlewood conjecture and the Riemann hypothesis on the way, and discuss a powerful method in analytic number theory known as Sieve theory.
Feb 28th
4th year project presentation session. Sharon Narh, Delia Mihalache, Nadine Amersi (UCL 4th years)
In this seminar three UCL 4th year students will present their MSci projects. Sharon Narh is going to talk about Non-commutative Unique Factorisation Domains. Delia Mihalache will introduce us to Nevanlinna Theory which is an interesting topic in Complex Analysis exploring meromorphic functions. Finally, former Colloquium leader Nadine Amersi will present her project on The Noncommutative Geometry of Conway's Game of Life. Come along to get inspired and to find out what kind of mathematics is cooking inside of the MSci projects!
Mar 6th
The Fluid Dynamics of Chocolate Fountains. Adam Townsend (UCL 4th year)
What do chocolate fountains have in common with teapots? Why don't they fall straight? How did I get the department to buy me one, and then why did the UCL postmaster refuse to deliver it? Discover what maths we can find in this most delectable of studies: how exactly do you go about modelling chocolate? In 45 minutes I'll show you that behind this tasty project lies a fascinating introduction to a world of non-Newtonian fluids. This will be a talk filled with demonstrations: we'll play with cornflour, we'll pour a cup of tea and, of course, the fountain will be there. All welcome; marshmallows will be provided.
Mar 13th
Special: Full day of maths talks!
Mar 20th
Hamiltonian Mechanics and Chaos. Hannah Roland (RHUL 3rd Year)
Dynamical systems have always been interesting to study, as understanding them can help us predict future events. This talk will introduce the notion of Hamiltonian mechanics and the associated canonical transformations used to define dynamical systems. We will then quickly cover symplectic matrices and, using their properties, analyse phase flow and prove Liouville's theorem. Finally, we will discuss the impact of a small change in the initial configuration of a dynamical system and see how this finding relates to chaos theory.
Past Colloquia
Founded Jan 2010 by Matthew Eric Bassett and Acyr Locatelli.
