Tue, 17 May 2022

14:00 - 15:20
L3

Collider Physics and the Light-ray OPE

Murat Kologlu
(Oxford University)
Abstract

Detectors in collider experiments are modeled by light-ray operators in Quantum Field Theory. For example, energy detectors are certain null integrals of the stress-energy tensor, localized at an angle on the celestial sphere, where they collect quanta that escape in their direction. In this talk, I will discuss a series of work developing a nonperturbative, convergent operator product expansion (OPE) for light-ray operators in Conformal Field Theories (CFTs). Objects appearing in the expansion are more general light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula. An important application is to event shapes in collider physics, which correspond to correlation functions of light-ray operators within the state created by the incoming particles. I will discuss some applications of the light-ray OPE in CFT, and mention some extensions to QCD which make contact with measurements at the LHC. Talk based primarily on [1905.01311] and [2010.04726].

Fri, 18 Mar 2022
16:00
L6

Plaquette-dimer liquid with emergent fracton

Yizhi You
(Oxford University)
Further Information

The speaker will be in-person. It is also possible to join virtually via zoom.

Abstract

We consider close-packed tiling models of geometric objects -- a mixture of hardcore dimers and plaquettes -- as a generalisation of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be covered by either a dimer on a z-link or a plaquettein the x-y plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fracton-type `higher-rank electrostatics', which can exhibit a plaquette-dimer liquid and an ordered phase. We analyse this theory in detail, using height representations and T-duality to demonstrate that the concomitant phase transition occurs due to the proliferation of dipoles formed by defect pairs. The resultant critical theory can be considered as a fracton version of the Kosterlitz-Thouless transition. A significant new element is its UV-IR mixing, where the low energy behavior of the liquid phase and the transition out of it is dominated by local (short-wavelength) fluctuations, rendering the critical phenomenon beyond the renormalization group paradigm.

Mon, 09 May 2022
14:15
L5

Conformally Invariant Energies of Curves and Surfaces

Alexis Michelat
(Oxford University)
Abstract

The integral of mean curvature squared is a conformal invariant of surfaces reintroduced by Willmore in 1965 whose study exercised a tremendous influence on geometric analysis and most notably on minimal surfaces in the last years.


On the other hand, the Loewner energy is a conformal invariant of planar curves introduced by Yilin Wang in 2015 which is notably linked to SLE processes and the Weil-Petersson class of (universal) Teichmüller theory.


In this presentation, after a brief historical introduction, we will discuss some recent developments linking the Willmore energy to the Loewner energy and mention several open problems.


Joint work with Yilin Wang (MIT/MSRI)

Wed, 09 Mar 2022

14:00 - 15:00
Virtual

G_2 instantons in twisted M-theory

Jihwan Oh
(Oxford University)
Abstract

I will discuss a string theory way to study G_2 instanton moduli space and explain how to compute the instanton partition function for a certain G_2 manifold. An important insight comes from the twisted M-theory on the G_2 manifold. Building on the example, I will explain a possibility to extend the story to a large set of conjectural G_2 manifolds and a possible connection to 4d N=1 SCFT via geometric engineering. This talk is based on https://arxiv.org/abs/2109.01110 and a series of works in progress with Michele Del Zotto and Yehao Zhou.

 

 

Tue, 08 Mar 2022

13:00 - 18:00
L2

International Women’s Day

Various
(Oxford University)
Further Information

Please join us to celebrate International Women’s Day on Tuesday the 8th of March.

To address this year’s theme - Break the Bias - we will be hosting two sessions in Lecture Theatre 2:

1-2.30pm - How Women Rise in Professional Services, a focus on gender equality from the perspective of Professional Services Staff

2.45-5pm  - A screening of 'Picture A Scientist' and panel discussion

5pm – Drinks reception

Please sign up here.

Thu, 27 Jan 2022

12:00 - 13:00
L6

Regularity results for Legendre-Hadamard elliptic systems

Christopher Irving
(Oxford University)
Abstract

I will discuss the regularity of solutions to quasilinear systems satisfying a Legendre-Hadamard ellipticity condition. For such systems it is known that weak solutions may which fail to be C^1 in any neighbourhood, so we cannot expect a general regularity theory. However if we assume an a-priori regularity condition of the solutions we can rule out such counterexamples. Focusing on solutions to Euler-Lagrange systems, I will present an improved regularity results for solutions whose gradient satisfies a suitable BMO / VMO condition. Ideas behind the proof will be presented in the interior case, and global consequences will also be discussed.

Mon, 07 Mar 2022

16:30 - 17:30
Virtual

Nonlinear wave equations, the weak null condition, and radiation fields

Joseph Keir
(Oxford University)
Abstract

Nonlinear wave equations are ubiquitous in physics, and in three spatial dimensions they can exhibit a wide range of interesting behaviour even in the small data regime, ranging from dispersion and scattering on the one hand, through to finite-time blowup on the other. The type of behaviour exhibited depends on the kinds of nonlinearities present in the equations. In this talk I will explore the boundary between "good" nonlinearities (leading to dispersion similar to the linear waves) and "bad" nonlinearities (leading to finite-time blowup). In particular, I will give an overview of a proof of global existence (for small initial data) for a wide class of nonlinear wave equations, including some which almost fail to exist globally, but in which the singularity in some sense takes an infinite time to form. I will also show how to construct other examples of nonlinear wave equations whose solutions exhibit very unusual asymptotic behaviour, while still admitting global small data solutions.

Thu, 17 Feb 2022

15:00 - 16:00
C2

Torsion points on varieties and the Pila-Zannier method - TALK POSTPONED UNTIL WEEK 5

Francesco Ballini
(Oxford University)
Abstract
In 2008 Pila and Zannier used a Theorem coming from Logic, proven by Pila and Wilkie, to give a new proof of the Manin-Mumford Conjecture, creating a new, powerful way to prove Theorems in Diophantine Geometry. The Pila-Wilkie Theorem gives an upper bound on the number of rational points on analytic varieties which are not algebraic; this bound usually contradicts a Galois-theoretic bound obtained by arithmetic considerations. We show how this technique can be applied to the following problem of Lang: given an irreducible polynomial f(x,y) in C[x,y], if for infinitely many pairs of roots of unity (a,b) we have f(a,b)=0, then f(x,y) is either of the form x^my^n-c or x^m-cy^n for c a root of unity.
Thu, 27 Jan 2022

15:00 - 16:00
Virtual

Ricci curvature lower bounds for metric measure spaces.

Dimitri Navarro
(Oxford University)
Abstract
In the '80s, Gromov proved that sequences of Riemannian manifold with a lower bound on the Ricci curvature and an upper bound on the dimension are precompact in the measured Gromov--Hausdorff topology (mGH for short). Since then, much attention has been given to the limits of such sequences, called Ricci limit spaces. A way to study these limits is to introduce a synthetic definition of Ricci curvature lower bounds and dimension upper bounds. A synthetic definition should not rely on an underlying smooth structure and should be stable when passing to the limit in the mGH topology. In this talk, I will briefly introduce CD spaces, which are a generalization of Ricci limit spaces.
Wed, 02 Mar 2022

14:00 - 16:00
Virtual

Topics on Nonlinear Hyperbolic PDEs

Gui-Qiang G. Chen
(Oxford University)
Further Information

Dates/ Times (GMT): 2pm – 4pm Wednesdays 9th, 16th, 23rd Feb, and 2nd March

Course Length: 8 hrs total (4 x 2 hrs)

Abstract

Aimed: An introduction to the nonlinear theory of hyperbolic PDEs, as well as its close connections with the other areas of mathematics and wide range of applications in the sciences.

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