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The Fox and Hedgehog seminars, established in 2023, aims to forge closer ties between mathematicians and physicists. The target audience of this series of pedagogical blackboard talks are PhD students, although any and all interested staff and students are always welcome to attend.
In an article in the New York Review of Books, Freeman Dyson writes,
“Great scientists come in two varieties, which Isaiah Berlin, quoting the seventh-century-BC poet Archilochus, called foxes and hedgehogs. Foxes know many tricks, hedgehogs only one. Foxes are interested in everything, and move easily from one problem to another. Hedgehogs are interested only in a few problems which they consider fundamental, and stick with the same problems for years or decades... Science needs both hedgehogs and foxes for its healthy growth, hedgehogs to dig deep into the nature of things, foxes to explore the complicated details of our marvelous universe.”
Every two weeks, we invite a member of our community to give a pedagogical blackboard talk aimed at a broad audience of PhD students from mathematics, mathematical physics, and theoretical physics. Every speaker will be asked to answer the following:
- What is one big problem/idea in your field, and why is it interesting/motivating to you?
- How did you first encounter this problem/idea? How did you come to approach it, and how has your thinking and methodology developed along the way?
- Are you a Fox or a Hedgehog?
The seminar will alternate among our different physical locations, always available online. For in-person participants, the seminar will be followed by refreshments and a half-hour informal discussion, starting with “a day in the life” of the speaker.
Come along to these seminars and find out which type of scientist you are!


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More to be announced soon...
The University of Glasgow
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To be announced
Higgs Centre Seminar Room, JCMB
This event is a Event.
More to be announced soon...
The University of Glasgow
This event is a Event.
More to be announced soon
This event is a Event.
To be announced
Higgs Centre Seminar Room, JCMB
This event is a Event.
More to be announced soon....
The University of Glasgow
This event is a Event.
More to be announced soon...
This event is a Event.
To be announced
Higgs Centre Seminar Room, JCMB
This event is a Event.
To be announced
7 George Square, Room S.1
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I will explain the mathematical formulation of this tantalising question, will give a bit of an overview of what is known about it, and will tell you what Aurel Page and I recently contributed to the area. In the spirit of the seminar, I will explain how I, as a ...
The University of Glasgow
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In 1995, James Dolan and I formulated a series of “hypotheses” about topology and higher categories, before the theory of higher categories was sufficiently developed to make these into precisely stated conjectures. In 2009 Jacob Lurie reformulated one of these using infinity-categories, called it the “cobordism hypothesis”, and gave a ...
Higgs Centre Seminar Room, JCMB
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I will give a general overview of our current understanding of the symmetries of renormalization group fixed points in quantum field theory and why they are interesting, including scale, conformal and Weyl invariance. I will describe the distinction between these symmetries, as well as what is generally known about when ...
50 George Square, Edinburgh
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Tannaka duality was developed in the late 1930’s in order to reconstruct a complex Lie group from its category of representations. Its generalisation, more often simply called “reconstruction theory,” has now become a fundamental part of representation theory — in particular, representation theory of categories and higher categories. It was ...
Higgs Centre Seminar Room, JCMB
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Black holes are singular solutions of Einstein's equations. It turns out that they also satisfy thermodynamic laws if we identify some of their geometric properties with thermodynamic property. This thermodynamic nature indicates that black holes are probably a macroscopic manifestation of a collection of large number of microstates. Now ...
Higgs Centre Seminar Room, JCMB
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To be announced
Higgs Centre Seminar Room, JCMB
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Physical theories typically rely on a perturbative formulation where the relevant quantities are computed order by order in a small coupling parameter. However, even if the challenge of accessing higher orders can be overcome, the resulting series is divergent, highlighting the shortcoming of the formulation and understanding of the theory ...
Higgs Centre Seminar Room, JCMB
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Perturbative quantum field theory (QFT) provides an extremely powerful framework for making predictions in particle physics. However, working out these predictions beyond leading order requires evaluating increasingly complicated integrals over the (unobserved) momentum flowing through virtual loops. At one loop, these integrals are under good control and can be evaluated ...
Higgs Centre Seminar Room, JCMB
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I find a 'good formula' to be very inspirational for research: understanding where surprising and powerful formulae in mathematics and physics come from —and why they exist —can be a gateway to finding other such formulae, or cast light on a set of ideas that can take you in exciting ...
Higgs Centre Seminar Room, JCMB
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Let me celebrate the end of the term by offering you a 30-minute crash summary of the course on kinetic theory for self-gravitating systems which I have just finished teaching. Mathematically speaking, self-gravitating systems and plasmas are very much alike - and we will discuss why and how. In the last ...
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Classical/Quantum information and computation provide a transversal perspective on many aspects of science, including gravitational physics. We shall take a bird’s-eye view on a survey of topics where these disciplines attempt to feed insights into each other, extending the well-known relations within thermodynamics.
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I'll talk a bit about why you may (and should) be interested in quantum groups, and how cluster algebras help study them. Perhaps, some integrable systems will also make their way into this talk (they often do).
Higgs Centre Seminar Room, JCMB
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Category theory and representation theory are branches of mathematics concerned with very general collections of objects and how to transform – i.e. exhibit symmetries – between them. There is a recent upsurge of interest from the physics community in the role of categorical representation theory to capture the topological symmetries of ...
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Category theorists love pointing at some important concept from
another branch of mathematics or science and saying "it's just a ...",
where the rest of the sentence will involve some word like "universal",
"functor" or "adjoint". This can be clarifying for both the subject at
hand and its relationship with ...
Higgs Centre Seminar Room, JCMB
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At early times, the universe was an almost perfectly uniform plasma of elementary particles in almost perfect thermal equilibrium. Then, at a later point, it "came alive" (at least in one region, on Earth) – it began evolving and learning about itself, first unconsciously and later deliberately. How did that transition ...
Higgs Centre Seminar Room, JCMB
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QFT is a beautiful yet mysterious framework, in which it is unfortunately rather hard to obtain exact results. In talks by Anton and Matthew we have seen some of the exciting new tools to make new numerical predictions in strongly-interacting regimes. In particular, Anton introduced resummation techniques for divergent perturbation ...
Higgs Centre Seminar Room, JCMB
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Quantum groups are deformations of universal enveloping algebras of Lie algebras. But where do these deformations come from? I'll discuss a compelling addition to the possible ways to answer this question, coming from adding equivariant parameters to cohomological Hall algebras. I won't assume that you know what these ...
Higgs Centre Seminar Room, JCMB
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Scattering amplitudes are an important observable in quantum field theory. However, in certain quantum field theories (such as quantum chromodynamics or QCD) it can be very challenging to reliably predict scattering amplitudes of low-energy bound states. In this talk, I will explain how progress has been made by deriving mathematical ...
Higgs Centre Seminar Room, JCMB
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Quantum field theory (QFT) forms the backbone of our conceptual understanding of most physical systems, yet our ability to use this framework to make quantitative predictions is largely limited to systems which are weakly-interacting or have large amounts of symmetry, leaving a significant gap in our understanding of the physical ...
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Freeman Dyson also compared frogs and birds: "Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. ... Frogs live in the mud below and see only the flowers that grow nearby.” In this dichotomy I am definitely a frog. This talk will be ...
Higgs Centre Seminar Room, JCMB
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Perturbation theory (expanding interesting quantities in a power series of some small parameter) is a physicist’s go-to tool for solving pretty much anything. It’s enormously useful. Mathematically, there is a huge body of literature on the summation, convergence, and resummation of possibly divergent series. In this talk I ...
Higgs Centre Seminar Room, JCMB
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