May 27 (Wed)
16:00 zoom A&CDenis Werth (Max Planck Institute): De Sitter Momentum Space
In this talk, I will construct a novel frequency-momentum space for de Sitter (dS) correlators from first principles. This construction follows directly from the decomposition into unitary irreducible representations (UIRs) of the spacetime isometry group. While the spatial momentum space is given by the standard Fourier transform, the frequency space arises from diagonalising the quadratic Casimir operator, leading to the Kontorovich-Lebedev-Fourier (KLF) transform. I will show that square-integrable functions decompose only along the principal series, whereas more general functions can receive discrete contributions from other UIRs. I will also derive the Feynman rules for in-in perturbation theory in KLF space, leading to the introduction of KLF-space correlators, which are simply related to late-time correlation functions through a general reduction formula. Throughout the talk, I will emphasise the analogy with harmonic analysis on the circle to provide intuition. This work is based on [ArXiv:2409.02072], [ArXiv:2601.15228] and [ArXiv:2604.15251].
Venue: zoom
Online: https://teams.microsoft.com/meet/377963401691370?p=kVYAvAANqtmuZoUvGv
Jun 01 (Mon)
14:00 MCS0001 PureDon Zagier (MPIM Bonn, ICTP Trieste): Modular forms, mock modular forms, and quantum modular forms
In this series of three talks I want to give an introduction into the wonderful world
of modular forms. These are special functions with huge symmetry groups that are
all-pervasive in modern mathematics and theoretical physics. It has even been
said -- indeed, I may have said it myself -- that "modular forms are everywhere". The
first lecture, on the many connections between modular forms and differential equations,
is meant for a general audience, including applied mathematicians and mathematical
physicists, while the two other talks will introduce more general types of modular
objects that have emerged in recent years in contexts ranging from the string theory
of black holes to the arithmetic properties of quantum invariants of knots. There will
be many examples in all the talks, and no prior knowledge will be assumed.
Venue: MCS0001
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Contact: arthur.lipstein@durham.ac.uk
May 27 16:00 Denis Werth (Max Planck Institute): De Sitter Momentum Space
In this talk, I will construct a novel frequency-momentum space for de Sitter (dS) correlators from first principles. This construction follows directly from the decomposition into unitary irreducible representations (UIRs) of the spacetime isometry group. While the spatial momentum space is given by the standard Fourier transform, the frequency space arises from diagonalising the quadratic Casimir operator, leading to the Kontorovich-Lebedev-Fourier (KLF) transform. I will show that square-integrable functions decompose only along the principal series, whereas more general functions can receive discrete contributions from other UIRs. I will also derive the Feynman rules for in-in perturbation theory in KLF space, leading to the introduction of KLF-space correlators, which are simply related to late-time correlation functions through a general reduction formula. Throughout the talk, I will emphasise the analogy with harmonic analysis on the circle to provide intuition. This work is based on [ArXiv:2409.02072], [ArXiv:2601.15228] and [ArXiv:2604.15251].
Venue: zoom
Usual Venue: MCS3070
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: herbert.gangl@durham.ac.uk
Jun 08 14:00 Don Zagier (MPIM Bonn, ICTP Trieste): Modular forms, mock modular forms, and quantum modular forms
In this series of three talks I want to give an introduction into the wonderful world
of modular forms. These are special functions with huge symmetry groups that are
all-pervasive in modern mathematics and theoretical physics. It has even been
said -- indeed, I may have said it myself -- that "modular forms are everywhere". The
first lecture, on the many connections between modular forms and differential equations,
is meant for a general audience, including applied mathematicians and mathematical
physicists, while the two other talks will introduce more general types of modular
objects that have emerged in recent years in contexts ranging from the string theory
of black holes to the arithmetic properties of quantum invariants of knots. There will
be many examples in all the talks, and no prior knowledge will be assumed.
Venue: MCS0001
Jun 15 14:00 Don Zagier (MPIM Bonn, ICTP Trieste): Modular forms, mock modular forms, and quantum modular forms
In this series of three talks I want to give an introduction into the wonderful world
of modular forms. These are special functions with huge symmetry groups that are
all-pervasive in modern mathematics and theoretical physics. It has even been
said -- indeed, I may have said it myself -- that "modular forms are everywhere". The
first lecture, on the many connections between modular forms and differential equations,
is meant for a general audience, including applied mathematicians and mathematical
physicists, while the two other talks will introduce more general types of modular
objects that have emerged in recent years in contexts ranging from the string theory
of black holes to the arithmetic properties of quantum invariants of knots. There will
be many examples in all the talks, and no prior knowledge will be assumed.
Venue: CLC202
Usual Venue: OC218
Contact: mohamed.anber@durham.ac.uk
For more information, see HERE.
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS3052
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: martin.p.kerin@durham.ac.uk
Jun 11 12:00 Zhang Rongkai (Osaka): Rigidity of the Borell-Brascamp-Lieb inequality
Optimal transport theory has been a powerful tool in
analysis on geometric spaces with curvature bounded since its
introduction into geometric analysis. In this talk, I will first briefly
introduce the application of the optimal transport theory on Riemannian
manifolds and show an interpolation inequality. I will then focus on the
recent work of mine, rigidity on curvature and measure of the
Borell-Brascamp-Lieb inequality on weighted Riemannian manifolds
satisfying the curvature dimension condition. I will also discuss the
Brunn-Minkowski inequality and its rigidity, as well as a few open
questions related.
Venue: MCS2068
Usual Venue: MCS2068
Contact: michael.r.magee@durham.ac.uk
Jun 01 14:00 Don Zagier (MPIM Bonn, ICTP Trieste): Modular forms, mock modular forms, and quantum modular forms
In this series of three talks I want to give an introduction into the wonderful world
of modular forms. These are special functions with huge symmetry groups that are
all-pervasive in modern mathematics and theoretical physics. It has even been
said -- indeed, I may have said it myself -- that "modular forms are everywhere". The
first lecture, on the many connections between modular forms and differential equations,
is meant for a general audience, including applied mathematicians and mathematical
physicists, while the two other talks will introduce more general types of modular
objects that have emerged in recent years in contexts ranging from the string theory
of black holes to the arithmetic properties of quantum invariants of knots. There will
be many examples in all the talks, and no prior knowledge will be assumed.
Venue: MCS0001
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
