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22 Jan 2008: Then thereare categories of spaces: the most familiar is Top, the category of topological spaces;but there are many other notions of space, for example [op, Sets], the category ofsimplicial sets

9 Sep 2002: The list does include allsimply-connected rank-one symmetric spaces except CP 2, OP 2 (the Cayley projectiveplane) and the obvious case S2.

29 Jul 2011: ON THE AUTOMORPHY OF l-ADIC GALOISREPRESENTATIONS WITH SMALL RESIDUAL. IMAGE. JACK THORNE. Abstract. We prove new automorphy lifting theorems for essen-tially conjugate self-dual Galois representations into GLn. Existingtheorems require that the

20 Dec 2018: Coding and Cryptography. T. W. Körner. December 20, 2018. Transmitting messages is an important practical problem. Coding theoryincludes the study of compression codes which enable us to send messagescheaply and error correcting codes which ensure

16 Mar 2016: A 2-adic automorphy lifting theorem for unitary groups over CM. fields. Jack A. Thorne. March 16, 2016. Abstract. We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitarytype, over imaginary CM fields. We

11 Jul 2015: The goals of Chapter 2 are to frame bqo theory from the ‘Simpsonian’ perspectiveintroduced in [18] and to prove (using Simpson’s topological definition) that certain op-erations preserve bqoness

10 Mar 2020: Remark 5.30. Consider the closure of the class of finite groups and abelian groups under the op-erations of Proposition 5.20; this is called the class of elementary amenable

8 Jun 2020: ii) We have a functor op : Cat Cat, with the identity operation on morphisms. ... C [C, Set] Y1 [C, Set]op [C, Set] [C,Set](,) Set,. where Cop Y [C, Set] is the Yoneda embedding, given by A 7 C (A,).

1 Feb 2023: Geometric inverse problems. with emphasis on two dimensions. Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann. iii. To our families and all who have supported us. This material has been published by Cambridge University Press & Assessment

13 Aug 2008: Thus RC (CR)op, and the categories are opposites of one another.