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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 29 January 2018

### '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

### Christina Goldschmidt: Critical random graphs with i.i.d. random degrees having power-law tails

12:00am, CM221

Consider a graph with label set $\{1,2, \ldots,n\}$ chosen uniformly at random from those such that vertex i has degree $D_i$, where $D_1, D_2, \ldots, D_n$ are i.i.d. strictly positive random variables. The condition for criticality (i.e. the threshold for the emergence of a giant component) in this setting is $E[D^2] = 2 E[D]$, and we assume additionally that $P(D = k) \sim c k^{-(\alpha + 2)}$ as $k$ tends to infinity, for some $\alpha \in (1,2)$. In this situation, it turns out that the largest components have sizes on the order of $n^{\alpha/(\alpha+1)}$. Building on earlier work of Adrien Joseph, we show that the components have scaling limits which can be related to a forest of stable trees (\`a la Duquesne-Le Gall-Le Jan) via an absolute continuity relation. This gives a natural generalisation of the scaling limit for the Erd\H{o}s-Renyi random graph which I obtained in collaboration with Louigi Addario-Berry and Nicolas Broutin a few years ago (extending results of Aldous), and complements recent work on random graph scaling limits of various authors including Bhamidi, Broutin, Duquesne, van der Hofstad, van Leeuwaarden, Riordan, Sen, M. Wang and X. Wang.

This is joint work in progress with Guillaume Conchon-Kerjan (Paris 7).

### TBA: Durham Debate in Religion & Society (Postgraduate Research Seminar 6)

11:30am, Seminar Room C (D/TH107), Dept. of Theology & Religion, Abbey House, DH1 3RS, Durham

### IAS Fellows' Seminar - Is philosophy necessary for all thinking and speaking?

1:00pm to 2:00pm, Seminar Room, Institute of Advanced Study, Professor Vasilis Politis (Trinity College, Dublin)

### Prof. Helen Bond: Characterisation in Mark's bios: where the narrative critics missed their way

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