Prof. Timothy Gowers, Can interesting mathematics problems be solved systematically?

Speaker: Prof. Timothy Gowers (DPMMS)                                                                               Venue: Winstanley Lecture Theatre                                                                                                     Time: 26/01/2015 20:30, drinks from 20:15

Solving a mathematics problem that is not a routine exercise can often feel more like an art than a science. Different people attack problems in different ways, and ideas can appear to spring into one’s mind from nowhere. I shall argue that solving problems is a much more systematic process than it appears, and shall also try to explain why, if that is the case, it has the features that make us think that it isn’t. For the bulk of the talk, I shall attempt, with help from the audience, to solve an Olympiad-style problem that I have not seen before, and to do so systematically rather than by waiting for a clever idea to appear out of the blue. The attempt is not guaranteed to succeed, but I hope that it will be informative whether or not it does.

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Film Night: A Beautiful Mind (2001)

Venue: Winstanley Lecture Theatre                                                                                                     Time: 19/01/2015 20:30, drinks and snacks from 20:15

John Nash is on the brink of international acclaim when he becomes entangled in a mysterious conspiracy. Starring Russell Crowe.

 

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Lent 2015 Termcard

All talks are to be held in the Winstanley Lecture Theatre in Trinity College, and will begin at 8.30pm with port and juice from 8.15pm. With the exception of the film night, which is open to all, talks are members only; non-members may join at the door.

Monday, 19th January: Film Night:                                                                                    A Beautiful Mind (2001)

John Nash is on the brink of international acclaim when he becomes entangled in a mysterious conspiracy. Starring Russell Crowe.

Monday, 26th January: Prof. Sir Timothy Gowers (DPMMS):                                   Can interesting mathematics problems be solved systematically?

Solving a mathematics problem that is not a routine exercise can often feel more like an art than a science. Different people attack problems in different ways, and ideas can appear to spring into one’s mind from nowhere. I shall argue that solving problems is a much more systematic process than it appears, and shall also try to explain why, if that is the case, it has the features that make us think that it isn’t. For the bulk of the talk, I shall attempt, with help from the audience, to solve an Olympiad-style problem that I have not seen before, and to do so systematically rather than by waiting for a clever idea to appear out of the blue. The attempt is not guaranteed to succeed, but I hope that it will be informative whether or not it does.

Monday, 2nd February: Dr. Milan Vojnovic (Microsoft Research):                         How to divide prize money?

The question of how to split a prize purse between position prizes in a contest has a long and rich history going all the way back to the work by Galton (1902). The economists’ approach to this question is to assume that contestants strategically invest efforts aiming at selfishly maximizing their payoffs, which combine in some way the value of winning a prize and the cost of production. How should a contest owner split a prize purse with the goal of maximizing the expected total effort in an equilibrium? What if the goal is to maximize the expected maximum individual effort?

Monday, 9th February: Dr. Paul Birrell (MRC Biostatistics Unit):                           The Anatomy of an Influenza Pandemic

Monday, 16th February: Dr. Henry Wilton (DPMMS):                                                 The Banach-Tarski Paradox

The Banach-Tarski Paradox is the counter-intuitive fact that a sphere can be cut into finitely many pieces and reassembled into two copies of itself. Of course, you can’t do this in real life, but it’s more than just a curiosity. In fact, it’s the start of a beautiful mathematical story at the heart of modern group theory, geometry, logic and analysis. I’ll try to tell some of that story.

Sunday, 22nd February:                                                                                                             Symposium

Monday, 2nd March: Prof. Imre Leader/Dr. Thomas Forster (DPMMS):             This House believes that the continuum is not always a continuum.’

A debate.

Monday, 9th March: Dr. Eric Lauga (DAMTP):                                                               The mathematical life of microbes.

While we all know that fluid dynamics allows planes to fly and boats to sail, it is less known that it also plays a crucial role in many biological processes. Here we will illustrate a particular biological phenomenon which actively uses the presence of a flowing liquid, namely how small organisms such as bacteria and algae use hydrodynamic forces to self-propel.

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Call My Bluff

Come and celebrate Christmas with the TMS’s annual Call My Bluff event. Watch a Freshers’ Team take on a team drawn from the combined might of the rest of the university in a competition in which mathematical knowledge takes a second place to the ability to hold a good poker face. And if that is not reason enough to join us, there will be port.

Freshers’ Team: Ollie Sayeed, Anindya Sharma and Vikramaditya Giri

Non-Freshers’ Team: Adam P Goucher, Dan Safka and Levent Alpoge

Hosted By: Sam Tickle

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Dr. Nathanaël Berestycki, Emergence of Symmetry in Planar Probability

Speaker: Dr. Nathanaël Berestycki (Stats Lab)
Venue: Winstanley Lecture Theatre
Time: 24/11/2014 20:30, drinks from 20:15

I will describe several simple and natural random systems which exist on the two-dimensional infinite square grid. Often there is a “critical point” for these systems. At this point, it has been predicted for more than 30 years that these systems acquire an unexpected symmetry: invariance under conformal transformations of the complex plane.

I will explain what that means, discuss some examples, and try to convey a few ideas about remarkable progress which has taken place in the last 15 years to describe these objects rigorously, notably Schramm’s famous SLE random curves.

 

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Prof. Benjamin Allanach, Possible Hints for Supersymmetry at the Large Hadron Collider

Speaker: Prof. Benjamin Allanach (DAMTP)
Venue: Winstanley Lecture Theatre
Time: 17/11/2014 20:30, drinks from 20:15

The Large Hadron Collider is about to start operation again at a higher energy at the beginning of 2015. I shall introduce the machine, particle physics and the discovery of the Higgs boson. Standard theory predicts that the quantum fluctuations should make the Higgs boson much heavier than it is observed to be, but a speculative theory of particle physics (supersymmetry) explains why the quantum fluctuations are small. This theory predicts a host of new particles for the LHC to find. There were a few small anomalies in LHC data already that can be interpreted as the production of certain supersymmetric particles. Such interpretations are ready for further experimental testing next year.

 

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Dr. James Cranch, Which Real Numbers are Pleasant?

Speaker: Dr. James Cranch (University of Sheffield)
Venue: Winstanley Lecture Theatre
Time: 10/11/2014 20:30, drinks from 20:15

Every well-educated fresher has already been indoctrinated with the right answer to this question: reals are either algebraic or transcendental. Algebraic numbers are obviously fantastic. By contrast, the transcendental numbers are utterly hideous and deserve no attention whatsoever, with the two exceptions of pi and e (bless their little cotton socks). Contrary to this received opinion, I’ll explain why it should be a major goal of 21st-century mathematics to reclaim more of the reals for explicit use by mathematicians, and I’ll tell you about some difficult problems that need to be solved along the way.

 

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Dr. Daniel Baumann, The Quantum Origin of Structure in the Universe

Speaker: Dr. Daniel Baumann (DAMTP)
Venue: Winstanley Lecture Theatre
Time: 3/11/2014 20:30, drinks from 20:15

Quantum fluctuations in the vacuum play an important role in fundamental physics. In this talk, I will show that these fluctuations get stretched to cosmic scales if the early universe experienced a period of inflationary expansion. Using little more than the quantum mechanics of a simple harmonic oscillator, I will compute this effect and explain how it provides the primordial seeds for all structure in the universe. I will show how these predictions compare to recent observations of the cosmic microwave background. Finally, I will speculate about the physical cause for the inflationary expansion.

 

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Dr. Julia Gog, Embarrassing Diseases

Speaker: Dr. Julia Gog (DAMTP)
Venue: Winstanley Lecture Theatre
Time: 27/10/2014 20:30, drinks from 20:15

The use of mathematical systems for modelling the spread of infectious disease has been around for quite a while now. Mathematical biologists have developed a world of intricate models including things like distribution of household sizes, population flows such as commute to work, airline transportation networks, seasonal and climate factors and what everyone had for breakfast. So we know in glorious detail how a decent pandemic ought to spread, right? Thing is, no one told influenza what it was supposed to do.

 

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Dr. Perla Sousi, A Lost Man Will Reach Home, but a Lost Bird Will be Lost Forever

Speaker: Dr. Perla Sousi (Stats Lab)
Venue: Winstanley Lecture Theatre
Time: 20/10/2014 20:30, drinks from 20:15

Suppose you are lost while trying to get home. At every corner you decide to take a random direction independently of what you did previously. Will you ever get back home? The answer depends on which dimension you live in. What if you give a preference to roads you have used before. Does the answer change?

 

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