Found at least 20 result(s)

01.01.1970 (Thursday)

NT' style='color:#f0ad4e'>NT 340' style='color:#f0ad4e'>London Number Theory Seminar: Manuel Hauke

regular seminar Manuel Hauke (University of York)

at:
01:00 - 01:00
KCL, Strand
room: K0.18
abstract:

Duffin-Schaeffer meets Littlewood and related topics

Khintchine's Theorem is one of the cornerstones in metric Diophantine approximation. The question of removing the monotonicity condition on the approximation function in Khintchine's Theorem led to the recently proved Duffin-Schaeffer conjecture. Gallagher showed an analogue of Khintchine's Theorem for multiplicative Diophantine approximation, again assuming monotonicity. In this talk, I will discuss my joint work with L. Frühwirth about a Duffin-Schaeffer version for Gallagher's Theorem. Furthermore, I will give a broader overview on various questions in metric Diophantine approximation and demonstrate the deep connection to analytic number theory that lies in the heart of the corresponding proofs.

Keywords:

01.01.1970 (Thursday)

NT' style='color:#f0ad4e'>NT 337' style='color:#f0ad4e'>Algebraic Number Theory Study Group: Lecture 1

regular seminar Netan Dogra (KCL)

at:
01:00 - 01:00
KCL, Strand
room: K0.18
abstract:

This term we will have a study group on the work of Dimitrov--Gao--Habegger and Kühne on uniformity in the Mordell conjecture. The first half of the schedule is meant to be an introduction to the area for non-specialists. In the second half, we will try to introduce some of the ideas from functional transcendence, dynamics and the moduli of abelian varieties which go into the proof.

The first talk will be an introduction to the history and statement of the results, with a vague hint at the methods of proof. A plan of the rest of the study group can be found here: https://sites.google.com/site/netandogra/seminars/uniform-mordell

Keywords:

Q: How many rational number solutions does a rational polynomial in two variables have?
A: Not many.

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102709' style='color:#f0ad4e'>Classical observables of General Relativity from scattering amplitudes

Regular Seminar Paolo di Vecchia (Stockholm U. and Nordita)

at:
01:00 - 01:00
KCL Strand
room: S0.12
abstract:

I will be using scattering amplitudes, instead of the Lagrangian of General Relativity (GR), to compute classical observables in GR. In the first part of the seminar I will consider the elastic scattering of two massive particles, describing two black holes, and I will show how to compute the eikonal up to two-loop order, corresponding to third Post-Minkowskian (3PM) order, that contains all the classical information. From it I will compute the first observable that is the classical deflection angle. In the second part of the seminar I will consider inelastic processes with the emission of soft gravitons. In this case the eikonal becomes an operator containing the creation and annihilation operators of the gravitons. The case of soft gravitons can be treated following the Bloch-Nordsieck approach and, in this case, I will be computing two other observables: the zero-frequency limit (ZFL) of the spectrum dE/d\omega of the emitted radiation and the angular momentum loss at 2PM and 3PM. I will consider also the case in which there are static modes localised at $\omega=0$. In the third part of the seminar I will be discussing soft theorems with one graviton emission, first briefly at tree level, and then at loop level following the paper by Weinberg from 1965. Assuming the eikonal resummation and that all infrared divergences in the case of gravity come only from one loop diagrams, I will compute the universal soft terms, corresponding to $\frac{1}{\omega}$, $\log \omega$ and $\omega \log^2 \omega$, first at the tree and one-loop level and then for the last two observables also at two-loop level. I will then use them to compute their contribution to the spectrum of emitted energy. Finally, if I have time left, I I will study the high energy limit. In particular, since the graviton is the massless particle with the highest spin, we expect universality at high energy. I will show that universality at high energy is satisfied both in the elastic and inelastic case, but this happens in the inelastic case in a very non trivial way. I will end with some conclusions and with a list of open problems.

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 336' style='color:#f0ad4e'>TBA

regular seminar Bruno Bertini (University of Nottingham)

at:
01:00 - 01:00
KCL, Strand
room: S4.23
abstract:

TBA

Keywords:

01.01.1970 (Thursday)

GE' style='color:#f0ad4e'>GE 328' style='color:#f0ad4e'>Homology stability for generalised Hurwitz spaces and asymptotic monopoles

regular seminar Ulrike Tillmann (University of Oxford)

at:
01:00 - 01:00
KCL, Strand
room: S4.29
abstract:

Configuration spaces have played an important role in mathematics and its applications. In particular, the question of how their topology changes as the cardinality of the underlying configuration changes has been studied for some fifty years and has attracted renewed attention in the last decade.

While classically additional information is associated "locally" to the points of the configuration, there are interesting examples when this additional information is "non-local". With Martin Palmer we have studied homology stability in some of these cases, including Hurwitz space and moduli spaces of asymptotic monopoles.

Keywords:

01.01.1970 (Thursday)

PR' style='color:#f0ad4e'>PR 325' style='color:#f0ad4e'>KCL Probability Seminar: First passage percolation on Erdos-Renyi graphs with general weights

regular seminar Seva Shneer (University of Edinburgh)

at:
01:00 - 01:00
KCL, Strand
room: S4.29
abstract:

We consider an Erdos-Renyi random graph on n nodes where the probability of an edge being present between any two nodes is equal to a/n with a > 1. Every edge is assigned a (non-negative) weight independently at random from a general distribution. For every path between two typical vertices we introduce its hop-count (which counts the number of edges on the path) and its total weight (which adds up the weights of all edges on the path). We prove a limit theorem for the joint distribution of the appropriately scaled hop-count and general weights. This theorem, in particular, provides a limiting result for hop-count and the total weight of the shortest path between two nodes. This is a joint work with Fraser Daly and Matthias Schulte.

Keywords: First passage percolation, Erdos-Renyi random graphs

01.01.1970 (Thursday)

DS' style='color:#f0ad4e'>DS 335' style='color:#f0ad4e'>Coexistence of conservative and dissipative dynamics and vortex mediated turbulence in laser physics

regular seminar Gian-Luca Oppo (University of Strathclyde)

at:
01:00 - 01:00
KCL, Strand
room: S4.23
abstract:

Vortices, turbulence, and rogue waves are typical phenomena of fluid dynamics. They can all be found, however, in simple models of lasers with optical injection. Almost 40 years ago we introduced a model of laser oscillations where, unexpectedly, conservative and dissipative dynamics coexist in the same phase space. When these laser models are extended to partial differential equations to include diffraction or dispersion, the underlying wave dynamics leads first to Turing patterns and then to regimes of defect-mediated turbulence where creation and annihilation of 2D vortices produce psychedelic spiral structures. In these regimes of spatio-temporal disorder, we observe the appearance of rogue waves corresponding to rare events, enormous peaks of light and heavily non-Gaussian probability density functions.

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 284' style='color:#f0ad4e'>TBA

journal club Simon Ekhammar (KCL)

at:
01:00 - 01:00
KCL, Strand
room: Norfolk Building 342N
abstract:

Keywords:

01.01.1970 (Thursday)

AN' style='color:#f0ad4e'>AN 330' style='color:#f0ad4e'>Invariance of Stochastic Integral

regular seminar Purba Das (KCL)

at:
01:00 - 01:00
KCL, Strand
room: S5.20
abstract:

We study the concept of quadratic variation of a continuous path along a sequence of partitions and its dependence with respect to the choice of the partition sequence to define invariance notion of stochastic integrals. We introduce the concept of quadratic roughness of a path along a partition sequence and show that for HÃlder-continuous paths satisfying this roughness condition, the quadratic variation along balanced partitions is invariant with respect to the choice of the partition sequence. Using these results we derive a formulation of the pathwise FÃllmer-Itô calculus which is invariant with respect to the partition sequence.

We further present several constructions of paths and processes with finite quadratic variation along a refining sequence of partitions, extending previous constructions to the non-uniform case. We study in particular the dependence of quadratic variation with respect to the sequence of partitions for these constructions. We identify a class of paths whose quadratic variation along a partition sequence is invariant under coarsening

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102702' style='color:#f0ad4e'>Lonti: Geodesics and Singularity Theorems in General Relativity (4/4)

Regular Seminar Sunil Mukhi (IISER, Pune)

at:
01:00 - 01:00
KCL Strand
room: LIMS
abstract:

These lectures will summarise mathematical aspects of classical General Relativity that are helpful in understanding current developments in the field. Lecture I will focus on Lorentzian-signature geometry, with an emphasis on causal structure. Some topological notions will also be introduced. In Lecture II we will go on to study the behaviour of geodesics in General Relativity and derive the famous Raychaudhuri equation. The null version of this equation, due to Sachs, will also be derived. Lecture III will focus on the "Hawking singularity theorem", namely that cosmological spacetimes with positive local Hubble constant are geodesically incomplete in the past under suitable conditions. In Lecture IV we will discuss the "Penrose singularity theorem" for black holes.

Keywords:

01.01.1970 (Thursday)

NT' style='color:#f0ad4e'>NT 332' style='color:#f0ad4e'>London Number Theory Seminar: Mohamed Tawfik

regular seminar Mohamed Tawfik (King's College London)

at:
01:00 - 01:00
KCL, Strand
room: K0.18
abstract:

We start by introducing Brauer-Manin obstructions to local-global principles over varieties. We then move to some of the known literature on Brauer-Manin obstructions for Kummer surfaces of products of elliptic curves. We finally present our work on some of the special cases where we calculate the Brauer group of a Kummer surface $X=Kum(E \times E')$ of a product of CM elliptic curves $E$ and $E'$, where $End(E)=End(E')=\mathbb{Z}[\zeta_3]$, and show that a non-trivial 5-torsion element of the transcendental Brauer group gives rise to Brauer Manin obstruction to weak approximation for $X$.

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102706' style='color:#f0ad4e'>On beta functions in the first-order sigma models

Regular Seminar Oleksandr Gamayun (LIMS, London)

at:
01:00 - 01:00
KCL Strand
room: S-3.18
abstract:

I will introduce a first-order formalism for two-dimensional sigma models with the Kähler target space. I will explain how to compute the metric beta function in this approach using the conformal perturbation methods. Comparing the answer with the standard geometric background field methods we observe certain anomalies, which we later resolve with supersymmetric completion. Based on 2312.01885 and 2307.04665.

Keywords:

01.01.1970 (Thursday)

GE' style='color:#f0ad4e'>GE 331' style='color:#f0ad4e'>Quiver varieties for the working geometer

regular seminar Dan Kaplan (University of Hasselt)

at:
01:00 - 01:00
KCL, Strand
room: S4.29
abstract:

This talk is divided into two related, yet self-contained sections. The first section is an elementary introduction to (Nakajima) quiver varieties, beginning with representations of quivers and emphasizing small examples. The second section shifts gears to symplectic resolutions of singularities, including the minimal resolutions of du Val singularities and the Springer resolution of the nilpotent cone of a Lie algebra.

The sections unite as we construct symplectic resolutions for quiver varieties by varying a stability parameter. In joint work with Travis Schedler, we leverage these symplectic resolutions to build resolutions for spaces that are (analytically) locally quiver varieties. The key idea here is to choose local resolutions at the most singular points and then demonstrate that certain compatible, monodromy-free choices extend and glue to a global resolution.

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102701' style='color:#f0ad4e'>Lonti: Geodesics and Singularity Theorems in General Relativity (3/4)

Regular Seminar Sunil Mukhi (IISER, Pune)

at:
01:00 - 01:00
KCL Strand
room: LIMS
abstract:

These lectures will summarise mathematical aspects of classical General Relativity that are helpful in understanding current developments in the field. Lecture I will focus on Lorentzian-signature geometry, with an emphasis on causal structure. Some topological notions will also be introduced. In Lecture II we will go on to study the behaviour of geodesics in General Relativity and derive the famous Raychaudhuri equation. The null version of this equation, due to Sachs, will also be derived. Lecture III will focus on the "Hawking singularity theorem", namely that cosmological spacetimes with positive local Hubble constant are geodesically incomplete in the past under suitable conditions. In Lecture IV we will discuss the "Penrose singularity theorem" for black holes.

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102700' style='color:#f0ad4e'>Lonti: Geodesics and Singularity Theorems in General Relativity (2/4)

Regular Seminar Sunil Mukhi (ICTS)

at:
01:00 - 01:00
KCL Strand
room: LIMS
abstract:

These lectures will summarise mathematical aspects of classical General Relativity that are helpful in understanding current developments in the field. Lecture I will focus on Lorentzian-signature geometry, with an emphasis on causal structure. Some topological notions will also be introduced. In Lecture II we will go on to study the behaviour of geodesics in General Relativity and derive the famous Raychaudhuri equation. The null version of this equation, due to Sachs, will also be derived. Lecture III will focus on the "Hawking singularity theorem", namely that cosmological spacetimes with positive local Hubble constant are geodesically incomplete in the past under suitable conditions. In Lecture IV we will discuss the "Penrose singularity theorem" for black holes.

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102699' style='color:#f0ad4e'>Lonti: Geodesics and Singularity Theorems in General Relativity (1/4)

Regular Seminar Sunil Mukhi (ICTS)

at:
01:00 - 01:00
KCL Strand
room: LIMS
abstract:

These lectures will summarise mathematical aspects of classical General Relativity that are helpful in understanding current developments in the field. Lecture I will focus on Lorentzian-signature geometry, with an emphasis on causal structure. Some topological notions will also be introduced. In Lecture II we will go on to study the behaviour of geodesics in General Relativity and derive the famous Raychaudhuri equation. The null version of this equation, due to Sachs, will also be derived. Lecture III will focus on the "Hawking singularity theorem", namely that cosmological spacetimes with positive local Hubble constant are geodesically incomplete in the past under suitable conditions. In Lecture IV we will discuss the "Penrose singularity theorem" for black holes.

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102703' style='color:#f0ad4e'>3d mirror symmetry with four supercharges

Regular Seminar Sergio Benvenuti (INFN, Trieste)

at:
01:00 - 01:00
KCL Strand
room: S0.12
abstract:

3d mirror symmetry for theories with eight supercharges is understood in terms of Hanany-Witten brane setups and plays an important role in many areas of supersymmetric qftââ¬â¢s. The generalization to theories with four supercharges, in the non-Abelian case, has been a long standing open problem. In this talk, based on work with Riccardo Comi and Sara Pasquetti, we focus on brane setups with NS and D5ââ¬â¢ branes, proposing that the related quiver gauge theories involve ââ¬Ëœimproved bifundamentalsââ¬â¢, that is strongly coupled SCFT's which are ancestors of the well known T[SU(N)] theories. Our proposal leads to 3d mirror dualities that can be exactly proven, reducing them to known Seiberg-like dualities. This gives strong support to the proposal. The simplest example is the duality between adjoint SQCD with F flavors, and a quiver with F-1 nodes and F-2 improved bifundamentals.

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 329' style='color:#f0ad4e'>Topological Data Analysis and Phase Transitions

regular seminar Jeffrey Giansiracusa (Durham University)

at:
01:00 - 01:00
KCL, Strand
room: K2.31
abstract:

Our speaker Prof. Jeffrey Giansiracusa (Durham University) is an expert on topological data analysis (TDA), a subject that combines insights from both pure mathematics and the applied sciences. There will be an introduction on TDA and persistent homology and TDA (Talk 1), and a research-oriented talk on applications on phase transitions (Talk 2). There will also be a crash-course on homology (Talk 0) by Dr. Peter Jossen. See https://kings-math-data-science.weebly.com/#TDA

Keywords: Mathematical Data Science

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 283' style='color:#f0ad4e'>TBA

journal club Vasileos Letsios (KCL)

at:
01:00 - 01:00
KCL, Strand
room: Norfolk Building 342N
abstract:

Keywords:

01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102694' style='color:#f0ad4e'>Euclidean Wormholes in Holography and their relation to Wilson Loops

Regular Seminar Olga Papadoulaki (Ecole Polytechnique)

at:
01:00 - 01:00
KCL Strand
room: S0.12
abstract:

Euclidean wormholes are exotic types of gravitational solutions that still challenge our physical intuition and understanding. After reviewing universal properties of asymptotically AdS wormhole solutions from a gravitational (bulk) point of view and the paradoxes they raise, I will describe some concrete (microscopic) field theoretic setups and models that exhibit such properties. These models can be reduced to matrix integrals and crucially involve correlated ("entangled") sums of representations of the boundary symmetry group. I will conclude with the realisation of such set-up in N=4 SYM/type IIB SUGRA.

Keywords: