# Next Week

Here is a selection of seminars that might be of interest to string theorists in Oxford:

On Monday, October 29, at 14:15 in L4, a seminar in
the Geometry and Analysis series:

Kobi Kremnitzer (Oxford)

Differentiable chiral and factorisation algebras

*The Beilinson-Drinfeld Grassmannian, which classifies a G-bundle trivialised away from a finite set of points on a curve, is one of the basic objects in the geometric Langlands programme. Similar construction in higher dimensions in the algebraic and analytic settings are not very interesting because of Hartogs' theorem. In this talk I will discuss a differentiable version. I will also explain a theory of D-modules on differentiable spaces and use it to define differentiable chiral and factorisation algebras. By linearising the Grassmannian we get examples of differentiable chiral algebras. This is joint work with Dennis Borisov.*

**Further information:**
On Tuesday, October 30, at 11:30 in Fisher Room, DWB, a seminar in
the Cosmology series:

Matthew Lewandoski (Institut de physique theorique, Universite Paris Saclay)

TBC

On Tuesday, October 30, at 12:00 in L4, a seminar in
the Relativity series:

Dr Wolfgang Wieland (Perimeter Institute)

Loop Quantum Gravity and the Continuum

*One of the main open problems in loop quantum gravity is to reconcile the fundamental quantum discreteness of space with general relativity in the continuum. In this talk, I present recent progress regarding this issue: I will explain, in particular, how the discrete spectra of geometric observables that we find in loop gravity can be understood from a conventional Fock quantisation of gravitational edge modes on a null surface boundary. On a technical level, these boundary modes are found by considering a quasi-local Hamiltonian analysis, where general relativity is treated as a Hamiltonian system in domains with inner null boundaries. The presence of such null boundaries requires then additional boundary terms in the action. Using Ashtekar’s original SL(2,C) self-dual variables, I will explain that the natural such boundary term is nothing but a kinetic term for a spinor (defining the null flag of the boundary) and a spinor-valued two-form, which are both intrinsic to the boundary. The simplest observable on the boundary phase space is the cross sectional area two-form, which generates dilatations of the boundary spinors. In quantum theory, the corresponding area operator turns into the difference of two number operators. The area spectrum is discrete without ever introducing spin networks or triangulations of space. I will also comment on a similar construction in three euclidean spacetime dimensions, where the discreteness of length follows from the quantisation of gravitational edge modes on a one-dimensional cross section of the boundary. The talk is based on my recent papers: arXiv:1804.08643 and arXiv:1706.00479.*

**Further information:**
On Tuesday, October 30, at 15:45 in L4, a seminar in
the Algebraic Geometry series:

Chunyi Li (University of Warwick)

Bogomolov type inequality for Fano varieties with Picard number 1

*I will talk about some basic facts about slope stable sheaves and the Bogomolov inequality. New techniques from stability conditions will imply new stronger bounds on Chern characters of stable sheaves on some special varieties, including Fano varieties, quintic threefolds and etc. I will discuss the progress in this direction and some related open problems.*

**Further information:**
On Thursday, November 1, at 12:45 in L6, a seminar in
the Strings Junior series:

Hadleigh Frost

Supermanifolds and super Lie groups

On Thursday, November 1, at 13:00 in Simpkins Lee Seminar Room, a seminar in
the Dalitz Seminar in Fundamental Physics series:

James Unwin (Illinois)

TBC

On Thursday, November 1, at 16:00 in L6, a seminar in
the Number Theory series:

Daniel Gulotta (Oxford University)

Shimura varieties at level Gamma_1(p^{\infty}) and Galois representations

*Let F be a totally real or CM number field. Scholze has constructed Galois representations associated with torsion classes in the cohomology of locally symmetric spaces for GL_n(F). We show that the nilpotent ideal appearing in Scholze's construction can be removed when F splits completely at the relevant prime. As a key component of the proof, we show that the compactly supported cohomology of certain unitary and symplectic Shimura varieties with level Gamma_1(p^{\infty}) vanishes above the middle degree. This is joint work with Ana Caraiani, Chi-Yun Hsu, Christian Johansson, Lucia Mocz, Emanuel Reinecke, and Sheng-Chi Shih.*

**Further information:**
On Thursday, November 1, at 16:15 in Simpkins Lee Seminar Room, a seminar in
the Theoretical Particle Physics series:

Steve Abel (Durham)

Asymptotically safe Standard Model

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**Further information:**
On Friday, November 2, at 15:30 in Martin Wood Lecture Theatre, a seminar in
the Colloquia Series Seminars series:

Prof Jonathan Gregory (Host Tim Palmer) (University of Reading/Met Office)

Sea level change in the Anthropocene

On Friday, November 2, at 16:00 in L1, a seminar in
the Math Colloquium series:

Jon Keating (University of Bristol)

Characteristic Polynomials of Random Unitary Matrices, Partition Sums, and Painlevé V

*The moments of characteristic polynomials play a central role in Random Matrix Theory. They appear in many applications, ranging from quantum mechanics to number theory. The mixed moments of the characteristic polynomials of random unitary matrices, i.e. the joint moments of the polynomials and their derivatives, can be expressed recursively in terms of combinatorial sums involving partitions. However, these combinatorial sums are not easy to compute, and so this does not give an effective method for calculating the mixed moments in general. I shall describe an alternative evaluation of the mixed moments, in terms of solutions of the Painlevé V differential equation, that facilitates their computation and asymptotic analysis.*

**Further information:**