Quantum Mathematics and Computation
|
Fri, 20/01/2012 10:30 |
Bob Coecke (Oxford) |
Quantum Mathematics and Computation  |
Room 051, Department of Computer Science |
|
We will demonstrate the following. Category theory, usually conceived as some very abstract form of metamathematics, is present everywhere around us. Explicitly, we show how it provides a kindergarten version of quantum theory, an how it will help Google to understand sentences rather than words. Some references are: -[light] BC (2010) "Quantum picturalism". Contemporary Physics 51, 59-83. arXiv:0908.1787 |
|||
|
Fri, 27/01/2012 11:00 |
André Henriques (Utrecht) |
Quantum Mathematics and Computation |
Comlab |
|
Introductory talk on topological quantum field theories (TQFTs) and the cobordism hypothesis, focusing on the conceptual issues involved. The lecture will take place this Friday at 11am in Lecture Theatre A of the Department of Computer Science |
|||
|
Fri, 03/02/2012 10:30 |
Samson Abramsky (Oxford) |
Quantum Mathematics and Computation |
Comlab |
|
The seminar will take place in Lecture Theatre A, Department of Computer Science. ------------------- Contextuality and non-locality are features of quantum mechanics which stand in sharp contrast to the realistic picture underlying classical physics. We shall describe a unified geometric perspective on these notions in terms of *obstructions to the existence of global sections*. This allows general results and structural notions to be uncovered, with quantum mechanics appearing as a special case. The natural language to use here is that of sheaves and presheaves; and cohomological obstructions can be defined which witness contextuality in a number of salient examples. |
|||
|
Fri, 17/02/2012 10:30 |
Kobi Kremnizer (Oxford) |
Quantum Mathematics and Computation |
Comlab |
| Algebraic theories, locally presentable categories and their application to type theories. The seminar will take place in Lecture Theatre A of the Department of Computer Science. | |||
|
Fri, 24/02/2012 14:00 |
Kobi Kremnizer (Oxford) |
Quantum Mathematics and Computation |
Comlab |
|
In recent years, surprising connections between type theory and homotopy theory have been discovered. In this talk I will recall the notions of intensional type theories and identity types. I will describe "infinity groupoids", formal algebraic models of topological spaces, and explain how identity types carry the structure of an infinity groupoid. I will finish by discussing categorical semantics of intensional type theories. The talk will take place in Lecture Theatre B, at the Department of Computer Science. |
|||
