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###### UCL Undergraduate Maths Colloquium added an event.

Join us this week for a returning face, friend of the colloquium, Aryan!!

Abstract: Representation Theory is one of the most popular lines of research in current day Mathematics. In

this talk we will discuss the the Representation Theory of Artinian Rings (the easier part of Rep Theory). We

will first start by defining modules and consider their correspondence to vector spaces. We will then discuss...

the philosophy behind Representation Theory and the importance of Indecomposable modules. In more exact

terms, we will introduce ACC, DCC conditions on rings and modules, give a proof of the Krull-Schmidt

theorem and conclude the talk by a review of Idempotent theory and how one creates a ’Basic Algebra’ to

study the representation theory of an Artinian Algebra. Only previous knowledge of linear algebra and rings

is assumed, although the Commutative Algebra course would be helpful.

As always, biscuits provided.

###### UCL Undergraduate Maths Colloquium shared their event.

The Hidden Topology of Singularities.

Join us for this weeks talk, presented by LSGNT PhD student Emily Maw!

Abstract:I will talk about singularities, and how we can understand them via their so-called vanishing cycles. This topic beautifully illustrates how symplectic topology links algebraic geometry to low-dimensional topology. We will meet some basic examples, and hopefully get to “pinwheels”, which are what I am studying! The talk will be highly nontechnical and and invo...lve lots of pictures, so should be accessible to all.

As always, biscuits provided!

##### UCL Undergraduate Maths Colloquium added an event.

The Hidden Topology of Singularities.

Join us for this weeks talk, presented by LSGNT PhD student Emily Maw!

Abstract:I will talk about singularities, and how we can understand them via their so-called vanishing cycles. This topic beautifully illustrates how symplectic topology links algebraic geometry to low-dimensional topology. We will meet some basic examples, and hopefully get to “pinwheels”, which are what I am studying! The talk will be highly nontechnical and and invo...lve lots of pictures, so should be accessible to all.

As always, biscuits provided!

Our friends in the physics department are having an event! Please check it out.

##### UCL Undergraduate Maths Colloquium shared their event.

This Thursdays talk will be on the topic of Algebraic K-Theory, presented by Antoine!

Abstract: Algebraic K-theory, in its first steps, is concerned with the notion of modules, sort of hyped-up vector space. It is a rich and deep branch of algebra with connections to Topology (Serre-Swan theorem), Representation theory, Algebraic Number theory (Rims theorem) and even open problems (Bass-Quillen conjecture)! As with everything in algebra, notation and abstractness are always a... big initial barrier. In this talk, I will attempt to clarify some elementary (but not obvious!) notions such as rings, modules, and group rings. Then, the objective will be to present a non-empty subset of the set of powerful theorems in Algebraic K-theory, and get a grasp on some of the intuition behind them. For a smoother ride, I recommend you read back on what vector spaces, groups and fields are. Everything else should be self-contained! The following will probably come up: Rings, modules, fibre squares (pullback construction), Quillen-Suslin theorem, Milnors theorem, Rims theorem, ideal class groups, Serre-Swan theorem.

As always, biscuits provided.

##### UCL Undergraduate Maths Colloquium added an event.

This Thursdays talk will be on the topic of Algebraic K-Theory, presented by Antoine!

Abstract: Algebraic K-theory, in its first steps, is concerned with the notion of modules, sort of hyped-up vector space. It is a rich and deep branch of algebra with connections to Topology (Serre-Swan theorem), Representation theory, Algebraic Number theory (Rims theorem) and even open problems (Bass-Quillen conjecture)! As with everything in algebra, notation and abstractness are always a... big initial barrier. In this talk, I will attempt to clarify some elementary (but not obvious!) notions such as rings, modules, and group rings. Then, the objective will be to present a non-empty subset of the set of powerful theorems in Algebraic K-theory, and get a grasp on some of the intuition behind them. For a smoother ride, I recommend you read back on what vector spaces, groups and fields are. Everything else should be self-contained! The following will probably come up: Rings, modules, fibre squares (pullback construction), Quillen-Suslin theorem, Milnors theorem, Rims theorem, ideal class groups, Serre-Swan theorem.

As always, biscuits provided.

##### UCL Undergraduate Maths Colloquium shared their event.

Join us for our next talk in room 707.

This weeks colloquium is presented by Lukas, on the topic of Galois connections between syntax and semantics!

Abstract: Galois connections are simple relationships between monotone functions and have a surprisingly rich...

theory. First, we will look at partially ordered sets (posets) before defining Galois connections, giving some

familiar examples and proving a few theorems about them. Then we will lay out the very basics of model

theory, a branch of logic, in order to be able to define a surprising Galois connection between the sentences

and the structures of a formal language – somewhat informally, between syntax and semantics. To this we will

apply the theory just developed, drawing some interesting conclusions.

As always biscuits provided.

##### UCL Undergraduate Maths Colloquium added an event.

Join us for our next talk in room 707.

This weeks colloquium is presented by Lukas, on the topic of Galois connections between syntax and semantics!

Abstract: Galois connections are simple relationships between monotone functions and have a surprisingly rich...

theory. First, we will look at partially ordered sets (posets) before defining Galois connections, giving some

familiar examples and proving a few theorems about them. Then we will lay out the very basics of model

theory, a branch of logic, in order to be able to define a surprising Galois connection between the sentences

and the structures of a formal language – somewhat informally, between syntax and semantics. To this we will

apply the theory just developed, drawing some interesting conclusions.

As always biscuits provided.

##### UCL Undergraduate Maths Colloquium updated their cover photo.

##### UCL Undergraduate Maths Colloquium shared their event.

NEW YEAR NEW ROOM NEW TIME: Thursdays at 1600 room 707.

It’s the sequel to the talk we have all been waiting for; Yll will bring us ever closer to the cutting edge of physics: Quantum Field Theory.

Please note our new room! 707 in the math dept.

Abstract: Quantum Field Theory is by far one of the most elegant and beautiful theories of modern

Mathematical Physics. The idea of replacing localised particles by all permeating potential fields and

reinterpreting what it means to be a dynamical system with these new ideas opened up a real Pandora’s box

to those first pioneers.

In this talk I will continue my introduction to a spectrum of interesting Mathematics; applying the basic ideas

to a couple of physical limiting cases and then recovering some even deeper and more powerful maths from the

results. I will then connect these ideas with the theory of bundles through what are known as Gauge theories.

So, Maths, Physics and ultra cool Maths. It’ll be the second part of an adventure that you don’t want to miss.

(Don’t worry if you missed the first one!)

As always, biscuits provided.

##### UCL Undergraduate Maths Colloquium added an event.

It’s the sequel to the talk we have all been waiting for; Yll will bring us ever closer to the cutting edge of physics: Quantum Field Theory.

Please note our new room! 707 in the math dept.

Abstract: Quantum Field Theory is by far one of the most elegant and beautiful theories of modern

Mathematical Physics. The idea of replacing localised particles by all permeating potential fields and...

reinterpreting what it means to be a dynamical system with these new ideas opened up a real Pandora’s box

to those first pioneers.

In this talk I will continue my introduction to a spectrum of interesting Mathematics; applying the basic ideas

to a couple of physical limiting cases and then recovering some even deeper and more powerful maths from the

results. I will then connect these ideas with the theory of bundles through what are known as Gauge theories.

So, Maths, Physics and ultra cool Maths. It’ll be the second part of an adventure that you don’t want to miss.

(Don’t worry if you missed the first one!)

As always, biscuits provided.

##### UCL Undergraduate Maths Colloquium shared their event.

Join us for a talk all about teapots! Presented by fluids expert Josh!

As always, biscuits provided.

Abstract: Everyone has experienced the frustration of pouring their favourite beverage and having it dribble over the pouring edge and getting everywhere. This phenomenon has been described mathematically, notably, by Professor Vanden-Broeck of UCL. In this talk, I will provide a small introduction into the wonderful world of teapots and how they pour. I will explain how Professor Vanden-Broeck contributed to this area, and the only exact solution and how it works.

##### UCL Undergraduate Maths Colloquium added an event.

Join us for a talk all about teapots! Presented by fluids expert Josh!

As always, biscuits provided.

Abstract: Everyone has experienced the frustration of pouring their favourite beverage and having it dribble over the pouring edge and getting everywhere. This phenomenon has been described mathematically, notably, by Professor Vanden-Broeck of UCL. In this talk, I will provide a small introduction into the wonderful world of teapots and how they pour. I will explain how Professor Vanden-Broeck contributed to this area, and the only exact solution and how it works.

##### UCL Undergraduate Maths Colloquium shared their event.

After seeing Yohance’s talk on integration methods, it’s about time we saw which Integrals cannot be solved! As so, this weeks talk is entitled Impossible Indefinite Integrals, presented by Antoine de Saint Germain

Abstract: Have you ever wondered why integration felt so much more complicated than differentiation? Is it just that were not smart enough, that we havent yet found the all-powerful theorem which could solve any indefinite integration problem? It turns out, like so... often in mathematics, that things seem hard because they are fundamentally hard, or in this case, impossible. In this talk, we will aim to show that many elementary functions do not have antiderivatives that we can express using other elementary functions. Explicitly, we will try to explain and prove the key theorem, and then go on to some applications. Very much like the proof that e and π are irrational, I believe this result is of interest to anyone who likes mathematics for its own sake.

As always, biscuits provided.

##### UCL Undergraduate Maths Colloquium added an event.

After seeing Yohance’s talk on integration methods, it’s about time we saw which Integrals cannot be solved! As so, this weeks talk is entitled Impossible Indefinite Integrals, presented by Antoine de Saint Germain

Abstract: Have you ever wondered why integration felt so much more complicated than differentiation? Is it just that were not smart enough, that we havent yet found the all-powerful theorem which could solve any indefinite integration problem? It turns out, like s...o often in mathematics, that things seem hard because they are fundamentally hard, or in this case, impossible. In this talk, we will aim to show that many elementary functions do not have antiderivatives that we can express using other elementary functions. Explicitly, we will try to explain and prove the key theorem, and then go on to some applications. Very much like the proof that e and π are irrational, I believe this result is of interest to anyone who likes mathematics for its own sake.

As always, biscuits provided.

After tomorrow’s talk, we will be joined by chalkdust to discuss writing for them. Yet another great reason to be there!

##### UCL Undergraduate Maths Colloquium added an event.

Join us for our first talk by a first year, Prime Numbers and their uses, presented by Axel!

Afterwards, we will be joined by members of the chalkdust team to discuss writing articles for their fantastic magazine.

As always, biscuits provided.

... Abstract: If I were to give you a number, say 57, how does one go about determining its primality? What if, this time, I gave you a 200 digit number? In this talk, I will build on Fermats Little Theorem to derive the Miller-Rabin probabilistic test for primes, a surprisingly simple and effective way to determine if a number is

prime. I will then take a look at practical applications of large primes in public key cryptography.