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The University of Southampton
Joining the dots: from data to insight

Joining The Dots: Topology, Machine learning and Statistics Seminar - Holography, geometry and machine learning, Professor Marika Taylor (Southampton) Seminar

JTD Seminar
14:00 - 15:00
25 April 2018
Lecture Theatre D, Room 1009, Building 58, University of Southampton, Highfield Campus, SO17 1BJ

For more information regarding this seminar, please email Professor Jacek Brodzki at .

Event details

In the last twenty years there has been a paradigm shift in theoretical physics, comparable to those of general relativity and quantum mechanics at the beginning of the twentieth century. Einstein's theory of general relativity established a deep relationship between geometry and the gravitational force, while quantum theory underpins our understanding of atomic and electromagnetic forces. In the second half of the twentieth century physicists started to explore how these very different ways of understanding physical forces could be reconciled i.e. how would one describe quantum gravity? The answer that has emerged in the last two decades is surprising: gravity is believed to be equivalent to a quantum system without gravity in one less dimension. This conjectured equivalence is called holography.

Holography clearly has deep conceptual consequences - gravity in our three-dimensional world can be described in terms of a flatland world without gravity! However, holography also implies very precise relationships between distinct mathematical quantities, such as renormalized areas of minimal surfaces, Willmore functionals, modular invariants of finite groups and so on. After introducing the main concepts of holography, we will turn to mathematical relationships that are particularly relevant to the JTD programme. For example, holography allows us to extract from hyperbolic geometries data about (quantum) dynamical systems; topological data analysis techniques may be relevant to understanding better key features of the underlying dynamics implicit in this data. More generally, there is an ongoing programme of research linking hyperbolic geometries, tensor networks and machine learning. 

Speaker information

Professor Marika Taylor. University of Southampton

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