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Research Fellows Directory

Lotte Hollands

Dr Lotte Hollands

Research Fellow

Organisation

Heriot-Watt University

Research summary

Theoretical physics studies the elementary particles and elementary forces that govern our world. The language in which it is formulated is mathematics. In the past this has led to a fruitful collaboration between theoretical physics and pure mathematics. The seminal work of Newton in mechanics would not have been possible without the simultaneous invention of differential calculus, and Einstein's general relativity is intimately tied to the development of differential geometry.

My research centers around the interaction between theoretical physics and mathematics in a framework called string theory. String theory is a geometrical attempt to combine quantum theory and Einstein's general relativity into a unified theory of quantum gravity. In my fellowship I study simplified models of the strong force (the force that holds quarks together to form protons and neutrons). These models have an additional symmetry called supersymmetry. This additional symmetry makes it possible to study the strong force in regimes that are very hard to reach using conventional methods. By embedding such models in string theory it is furthermore possible to find a deeper understanding of these models through a geometric perspective.

A large class of models has an alternative description in terms of a two-dimensional surface. For instance, the surface of a doughnut corresponds to a particular well-studied model. The shape of the doughnut (whether it is thin and large or rather thick and small) describes the strength of the strong force in this model. Intricate geometrical objects that can be associated to the surface encode fundamental characteristics of the model. For instance, it turns out that its particle spectrum is encoded in certain graphs on the surface. In my work I study such graphs, and unreveal symmetries of physically very relevant, yet rather mysterious, models. This brings us a little step closer towards understanding the strong force in nature.

Grants awarded

Exploring mathematics using string theory: instantons, vortices and knots

Scheme: Dorothy Hodgkin Fellowship

Dates: Apr 2013 - Feb 2019

Value: £376,142.39