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Research

# 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.

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## Events for 4 December 2017

### 'Hell, Heaven and Hope. A journey through life and the afterlife with Dante', Exhibition curated by Dr Annalisa Cipollone

9:00am to 11:55pm, Palace Green Library, Durham University

### IAS Fellow's Seminar - Studying the relationship between entropy and structure.

1:00pm to 2:00pm, IAS Seminar Room, Palace Green, Dr Andy Martin (University of Melbourne)

### Andrew Wade: The critical greedy server on the integers

2:00pm, cm221

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).

### Eric Hofmann: Modular Forms with Product Expansion and Geometric Liftings

4:00pm, CM221

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.

### Dr Hugh Houghton: The Rediscovered Fourth-Century Commentary on the Gospels by Fortunatianus of Aquileia

4:15pm, Seminar Room C (D/TH107), Dept. of Theology & Religion, Abbey House, DH1 3RS, Durham