Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|November 2017||January 2018|
Events for 4 December 2017
'Hell, Heaven and Hope. A journey through life and the afterlife with Dante', Exhibition curated by Dr Annalisa Cipollone
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Each site of the one-dimensional integer lattice hosts a queue with arrival rate $\lambda$. A single server, starting at the origin, serves its current queue at rate $\mu$ until that queue is empty, and then moves to the longest neighbouring queue. In the critical case $\lambda = \mu$, we show that the server returns to every site infinitely often. We also give an iterated logarithm result for the server's position. In the talk I will try to explain the main ingredients in the analysis: (i) the times between successive queues being emptied exhibit doubly exponential growth, (ii) the probability that the server changes its direction is asymptotically equal to 1/4, and (iii) a martingale construction that facilitates the proofs. This is joint work with James Cruise (Heriot-Watt).
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When dealing with modular forms, one of the first examples encountered is the discriminant function, the (essentially unique) cusp form of weight 12, which, moreover has an infinite product expansion.
After a brief introduction on modular forms, I want to focus on this example and describe how, by a relationship discovered by R. E. Borcherds in the mid 1990s, the discriminant function can be viewed as the‘lifting’ of another well-known modular form, the Jacobi theta function.
In fact, Borcherds’ construction is much more general: It relates modular forms, which transform under the elliptic modular group, to modular functions for indefinite orthogonal groups. The background for this lies in the theory of theta-liftings.
I will sketch this briefly, and indicate how Borcherds’ lift can be extended to a geometric lifting. Further, I will describe its relationship to another, more intrinsically geometric lifting, which was constructed by Kudla and Millson.
Finally, one can study these liftings in a different setting: replacing orthogonal groups with unitary groups. This is my main area of research. At the end of the talk, I want to say a few words about that, too, and about my joint research project with Jens Funke here in Durham.
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Dr Hugh Houghton: The Rediscovered Fourth-Century Commentary on the Gospels by Fortunatianus of Aquileia
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Fluid dynamics is a very old subject, with thousands of papers being written on it every year. Landau and his contemporaries compiled the underlying principles of fluid dynamics into a coherent framework of hydrodynamics, and until very recently, most of the following work was on the application of their ideas in the real world. But with the introduction of the fluid/gravity correspondence in 2008, fluid dynamics regained the attention of fundamental physicists. This has lead to many new insights and developments in our understanding of fluids over the past decade. In this talk, I will try to forget everything we already know about fluids from our daily lives, and develop them from a fundamental perspective of quantum field theories. Hopefully, this will allow the audience to better appreciate some of the recent advancements in hydrodynamics. The talk is going to be extremely basic and hand-wavy, but if time permits, I will comment towards the end on how my work fits into this bigger picture.
Contact Daniel Martin
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