Jun 03 (Wed)
14:00 zoom A&CHongji Wei (Harvard): Light Rays as AdS_4 Soft Gluons and Gravitons
Soft symmetries in four-dimensional flat space are generated by infinite-dimensional algebras acting on scattering amplitudes. Using the conformal map between four-dimensional Minkowski space and AdS_4, we show that flat-space leading soft gluon generators map to light transforms of conserved color currents in CFT_3. The three-dimensional conformal descendants of these light-ray operators then generate the full nonabelian soft S-algebra. We similarly identify the light transform of the CFT_3 stress tensor, together with its conformal descendants, as the boundary realization of AdS_4 soft gravitons. Their commutators obey the recently discovered cosmological-constant-deformed \mathcal L_\Lambda w_{1+\infty} algebra, furnishing a universal soft graviton algebra in CFT_3.
Venue: zoom
Online: https://teams.microsoft.com/meet/335604449900654?p=pmuh8mA6eOhnzzNN1h
Jun 08 (Mon)
14:00 MCS0001 ASGDon 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
Click on title to see abstract.
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These events are hosted in and/or organised by members of the Department (follow links for details):
Jun 11 [CG93] 2026 Collingwood Lecture [Don Zagier]: The oldest and newest, the easiest and hardest maths problems
The saying is ascribed to Gauss that Mathematics is the queen of the sciences and number theory is the queen of Mathematics. If so, then the theory of Diophantine equations is surely the queen of number theory. It is named after the semi-mythical Diophantus, whose works were lost for almost 1500 years but were still revolutionary when they were rediscovered, and is concerned with the simplest-sounding problems imaginable: finding solutions in whole numbers or fractions of collections of polynomial equations. Some of the oldest of the problems in this field go back to Archimedes or even earlier, long before Diophantus, while new and equally difficult elementary problems are still being discovered today. The most famous problems in this domain -- Fermat's last theorem, the problem of congruent numbers, the representability of integers as sums of two perfect cubes, and many others -- have led to some of the deepest and most difficult developments in mathematics. The lecture will attempt to describe some of the most fascinating of these problems. The high point will be the theory of elliptic curves and the conjecture of Birch and Swinnerton-Dyer, one of the seven Clay Millennium Prize problems, which I will try to explain in the simplest form possible without betraying its essence.
Venue: CG93 at/from 14:00
Link: here
Click on series to expand.
Contact: arthur.lipstein@durham.ac.uk
Jun 03 14:00 Hongji Wei (Harvard): Light Rays as AdS_4 Soft Gluons and Gravitons
Soft symmetries in four-dimensional flat space are generated by infinite-dimensional algebras acting on scattering amplitudes. Using the conformal map between four-dimensional Minkowski space and AdS_4, we show that flat-space leading soft gluon generators map to light transforms of conserved color currents in CFT_3. The three-dimensional conformal descendants of these light-ray operators then generate the full nonabelian soft S-algebra. We similarly identify the light transform of the CFT_3 stress tensor, together with its conformal descendants, as the boundary realization of AdS_4 soft gravitons. Their commutators obey the recently discovered cosmological-constant-deformed \mathcal L_\Lambda w_{1+\infty} algebra, furnishing a universal soft graviton algebra in CFT_3.
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: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
