Found at least 20 result(s)

01.01.1970 (Thursday)

NT' style='color:#f0ad4e'>NT 184' style='color:#f0ad4e'>London Number Theory Seminar: Primes and squares with preassigned digits

regular seminar Cathy Swaenepoel (Institut de Mathématiques de Jussieu-Paris Rive Gauche)

at:
01:00 - 01:00
KCL, Strand
room: S3.30
abstract:

Bourgain (2015) estimated the number of prime numbers with a positive
proportion of preassigned digits in base 2. We first present a
generalization of this result to any base g at least 2. We then discuss
a more recent result for the set of squares, which may be seen as one
of the most interesting sets after primes. More precisely, for any
base g, we obtain an asymptotic formula for the number of
squares with a proportion c>0 of preassigned digits. Moreover we
provide explicit admissible values for c depending on g. Our
proof mainly follows the strategy developed by Bourgain for primes in
base 2, with new difficulties for squares. It is based on the circle
method and combines techniques from harmonic analysis together with
arithmetic properties of squares and bounds for quadratic Weyl sums.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102528' style='color:#f0ad4e'>Scalar QED in AdS

Regular Seminar Lorenzo Di Pietro (Trieste)

at:
01:00 - 01:00
KCL Strand
room: K0.16
abstract:

Based on 2306.05551 with Ankur and D. Carmi. Studying QFT in AdS allows to translate phenomena in massive QFT in the bulk to properties of the boundary conformal correlators. I will illustrate this in the example of a strongly coupled gauge theory, namely scalar QED in dimension D<4. The tool that I will use to compute is the large N expansion, where N is the number of flavors. I will show that the four-point function of the charged operator dual to the scalar electrons can be computed exactly in the coupling at leading order at large N, both in the Coulomb and in the Higgs phase, and explain its salient properties. Finally I will discuss an IR divergence present in integer dimension D=3 that signals the breaking of the AdS isometries due to a boundary running coupling.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102563' style='color:#f0ad4e'>Holographic description of code CFTs

Regular Seminar Anatoly Dymarsky (Kentucky)

at:
01:00 - 01:00
KCL Strand
room: K6.63
abstract:

Recently, a relation was introduced connecting codes of various types with the space of abelian (Narain) 2d CFTs. We extend this relation to provide holographic description of code CFTs in terms of abelian Chern-Simons theory in the bulk. For codes over the alphabet Z_p corresponding bulk theory is, schematically, U(1)_p times U(1)_{-p} where p stands for the level. Furthermore, CFT partition function averaged over all code theories for the codes of a given type is holographically given by the Chern-Simons partition function summed over all possible 3d geometries. This provides an explicit and controllable example of holographic correspondence where a finite ensemble of CFTs is dual to "topological/CS gravity" in the bulk. The parameter p controls the size of the ensemble and "how topological" the bulk theory is. Say, for p=1 any given Narain CFT is described holographically in terms of U(1)_1^n times U(1)_{-1}^n Chern-Simons, which does not distinguish between different 3d geometries (and hence can be evaluated on any of them). When p approaches infinity, the ensemble of code theories covers the whole Narain moduli space with the bulk theory becoming "U(1)-gravity" proposed by Maloney-Witten and Afkhami-Jeddi et al.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102527' style='color:#f0ad4e'>The partial Bondi gauge: Further enlarging the asymptotic structure of gravity

Regular Seminar Celine Zwikel (Perimeter)

at:
01:00 - 01:00
KCL Strand
room: K0.16
abstract:

I will introduce the partial Bondi gauge for 4-dimensional spacetimes. This gauge includes the usual Bondi gauge and Newman-Unti gauge and is designed to approach asymptotic boundaries along null rays. The new gauge is defined by three conditions on the metric (g_{rr}=0=g_{rA}) and relaxes the condition on the radial coordinate. I will discuss the solution space and asymptotic symmetries. Most importantly, by relaxing the gauge, we uncover new large symmetries that characterize asymptotically flat spacetimes.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102560' style='color:#f0ad4e'>Information loss, black holes, and algebras in time

Regular Seminar Nima Lashkari (Purdue)

at:
01:00 - 01:00
KCL Strand
room: K6.63
abstract:

A manifestation of the black hole information loss problem is that the two-point function of probe operators in an eternal AdS black hole decays exponentially fast in time, whereas, on the boundary, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity. In the thermodynamic limit of infinite entropy (infinite volume or large N), the operators that cluster in time are expected to form an algebra. We prove that this algebra is a unique and very special infinite dimensional algebra called the III_1 factor. This has implications for the emergence of a local bulk in holography.
An important example is \mathcal{N}=4 SYM, above the Hawking-Page phase transition. The clustering of the single trace operators implies that the algebra is a type III_1 factor. We prove a generalization of a conjecture of Leutheusser and Liu to arbitrary out-of-equilibrium states. We explicitly construct the C^*-algebra and von Neumann subalgebras associated with time bands and more generally, arbitrary open sets of the bulk spacetime in the strict N\to \infty limit. The emergence of time algebras is intimately tied to the second law of thermodynamics and the emergence of an arrow of time.

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01.01.1970 (Thursday)

NT' style='color:#f0ad4e'>NT 183' style='color:#f0ad4e'>London Number Theory Seminar: The valuative section conjecture and étale homotopy

regular seminar Jesse Pajwani (Imperial College London)

at:
01:00 - 01:00
KCL, Strand
room: S3.30
abstract:

The p-adic section conjecture is a long standing conjecture of Grothendieck about curves of high genus over p-adic fields, linking the p-adic points of a curve to sections of a short exact sequence of étale fundamental groups. A powerful way of interpreting the section conjecture is as a fixed point statement, and this interpretation makes the statement look like many other theorems in algebraic topology. For this talk, we'll first introduce the framing of the section conjecture as a fixed point statement, and then show this interpretation allows us to give an alternate proof of part of a result of Pop and Stix towards the section conjecture. This new proof generalises to other fields, and the new fields allow us to extend the original result to a larger class of varieties.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102526' style='color:#f0ad4e'>Quantum and Classical Eikonal Scattering

Regular Seminar Giulia Isabella (Geneva)

at:
01:00 - 01:00
KCL Strand
room: K0.16
abstract:

I will discuss the eikonal scattering of two gravitationally interacting bodies, showing that exponentiation of the scattering phase matrix is a direct consequence of the group contraction $SU(2) \rightarrow ISO(2)$, in the large angular momentum limit. The emergence of the classical limit is understood in terms of the continuous-spin representations admitted by $ISO(2)$. We will compare the competing classical and quantum corrections to the leading classical eikonal scattering in the transplanckian regime and discuss how observables are extracted from the scattering phase matrix.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 181' style='color:#f0ad4e'>Blackhole, Blackring transition

regular seminar Indranil Halder (Harvard)

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

We will discuss BPS objects in M theory compactified on a Calabi-Yau three fold X. From the microscopic point of view such degeneracies are encoded in the partition function of the topological strings on X through the Gopakumar-Vafa formula. For the first part of the talk, as an example we will focus on quintic, and discuss how Gopakumar-Vafa invariants can be calculated systematically from the knowledge of boundary condition on the moduli space together with holomorphic ambiguity equation and mirror symmetry. When the entropy thus obtained is plotted against the left moving angular momentum for fixed M2 brane charge, there is a clear transition point at a critical angular momentum. Comparison of the the curve with leading order results from supergravity in 5d shows a large deviation. We will explain the conceptual origin of such deviations using Ooguri-Strominger-Vafa conjecture in 4d string theory though 4d-5d lift. In particular we will observe that the curve is well approximated by the (suitably corrected) entropy of BMPV blackhole for smaller angular momentum and for larger angular momentum by the (suitably corrected) entropy of a particular EEMR blackring. We will show that these observations remain valid on a class of one parameter Calabi-Yau three folds.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102556' style='color:#f0ad4e'>Blackhole, Blackring transition

Regular Seminar Indranil Halder (Harvard)

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

We will discuss BPS objects in M theory compactified on a Calabi-Yau three fold X. From the microscopic point of view such degeneracies are encoded in the partition function of the topological strings on X through the Gopakumar-Vafa formula. For the first part of the talk, as an example we will focus on quintic, and discuss how Gopakumar-Vafa invariants can be calculated systematically from the knowledge of boundary condition on the moduli space together with holomorphic ambiguity equation and mirror symmetry. When the entropy thus obtained is plotted against the left moving angular momentum for fixed M2 brane charge, there is a clear transition point at a critical angular momentum. Comparison of the the curve with leading order results from supergravity in 5d shows a large deviation. We will explain the conceptual origin of such deviations using Ooguri-Strominger-Vafa conjecture in 4d string theory though 4d-5d lift. In particular we will observe that the curve is well approximated by the (suitably corrected) entropy of BMPV blackhole for smaller angular momentum and for larger angular momentum by the (suitably corrected) entropy of a particular EEMR blackring. We will show that these observations remain valid on a class of one parameter Calabi-Yau three folds.

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01.01.1970 (Thursday)

ST' style='color:#f0ad4e'>ST 182' style='color:#f0ad4e'>Non-Gaussian Lévy-driven SDEs for irregular time series and spatial applications

regular seminar Simon Godsill (University of Cambridge )

at:
01:00 - 01:00
KCL, Strand
room: Bush House (SE) 1.01
abstract:

In this talk I will describe state-space models based on point process theory and Lévy processes, allowing very flexible modelling of continuous time non-Gaussian behaviours subject to irregular discrete time observations. In contrast with most of the classical models which use Brownian motion assumptions, our approach is based on pure jump-driven Lévy processes driving stochastic diferential equations, leading to powerful models based on, for example, alpha-stable or Generalised hyperbolic processes (including Student-t, variance-gamma and normal-inverse Gaussian). We are able to construct a full state-space model (The `Levy state-space modelâ) driven by such continuous time processes, observed at discrete time, as well as deriving central limit style theorems that prove Gaussianity of certain series residual terms, and inference for these models can be carried out using highly efficient Rao-Blackwellised versions of particle filters and sequential Markov chain Monte Carlo. The models can find application tracking of agile objects such as birds or drones, in financial prediction and in analysis of vibrational data under non-Gaussian perturbation.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 180' style='color:#f0ad4e'>London Number Theory Seminar: Exceptional biases (in the distribution of irreducible polynomials over finite fields)

regular seminar Lucile Devin (Université du Littoral Côte d'Opale)

at:
01:00 - 01:00
KCL, Strand
room: S3.30
abstract:

Studying the secondary terms of the Prime Number Theorem in Arithmetic Progressions, Chebyshev claimed that there are more prime numbers congruent to 3 modulo 4 than to 1 modulo 4. This claim was later corrected by Littlewood, explained, and quantified by Rubinstein and Sarnak.
Pursuing the work of Cha, we investigate analogues to Chebyshev's bias in the setting of irreducible polynomials over finite fields. In particular, we observe exceptional behaviors occurring when the zeros of the involved L-functions are not linearly independent. More precisely, we will present instances of "complete bias" and "reversed bias", and explain why they occur with probability tending to 0, in the large q limit.

This is joint work with Bailleul, Keliher and Li

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01.01.1970 (Thursday)

NT' style='color:#f0ad4e'>NT 178' style='color:#f0ad4e'>London Heilbronn Colloquium: The Shimura-Taniyama-Weil conjecture and beyond

colloquium Chandrashekhar Khare (UCLA)

at:
01:00 - 01:00
KCL, Strand
room: K6.29
abstract:

The Shimura-Taniyama-Weil modularity conjecture asserts that all elliptic curves over Q arise as images of quotients of the Poincare upper half plane by congruence subgroups of the modular group SL2(Z). Wiles proved Fermat's Last Theorem by establishing the modularity of semistable elliptic curves over Q. Subsequent work of Breuil-Conrad-Diamond-Taylor established the modularity of elliptic curves over Q in full generality. My work with J-P. Wintenberger gave a proof of the generalized Shimura-Taniyama-Weil conjecture which asserts that all "odd, rank 2 motives over Q" are modular. This is a corollary of our proof of Serre's modularity conjecture.


Very little is known when one looks at the same question over finite extensions of Q. I will talk about the recent beautiful work of Ana Caraiani and James Newton which proves modularity of all elliptic curves over Q(i). An input into their proof is a result, proved in joint work with Patrick Allen and Jack Thorne, that proves the analog of Serre's conjecture for mod 3 representations that arise from elliptic curves over Q(i).

My talk will give a general introduction to this circle of ideas centred around the modularity conjecture for motives and Galois representations over number fields. We know only fragments of what is conjectured, but what little we know is already quite remarkable!

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01.01.1970 (Thursday)

01.01.1970 (Thursday)

NT' style='color:#f0ad4e'>NT 179' style='color:#f0ad4e'>London Number Theory Seminar: Quadratic Twists as Random Variables

regular seminar Ross Paterson (University of Bristol)

at:
01:00 - 01:00
KCL, Strand
room: S3.30
abstract:

If E/Q is an elliptic curve, and d is a squarefree integer, then the 2-torsion modules of E and its quadratic twist E_d are isomorphic. In particular their 2-Selmer groups can be made to lie in the same space. Poonen-Rains provide a heuristic model for the behaviour of these 2-Selmer groups individually, as E varies, but how independent are they? We'll present results in this direction.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102552' style='color:#f0ad4e'>Machine Learning and Flows for Lattice QCD

Regular Seminar Sebastien Racaniere (Deepmind)

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

Recently, there have been some very impressive advances in generative models for sound, text and images. In this talk, I will look into applications of generative models to Lattice QCD. The models I will consider are flows, which are families of diffeomorphisms transforming simple base distributions into complicated target distributions. Traditional ML flows are on vector spaces, which is different from our setup where we need to deal with products of SU(N). I will give details on how we built these flows, and explain how known symmetries of LQCD can be incorporated into them.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 162' style='color:#f0ad4e'>LonTI: Supersymmetry, complex geometry and the Hyperkähler quotient

regular seminar Ulf LindstrÃm (Uppsala and Middle East Tech. U.)

at:
01:00 - 01:00
KCL, Strand
room: LIMS, Royal Institution
abstract:

Ulf LindsrÃm, a Leverhulme visiting professor at Imperial College will discuss sigma models, which are maps from a domain to a target space T. The geometry of the target space is determined by the dimension of the domain and symmetries of the model. When it has isometries that can be gauged, the quotient space, i.e., the space of orbits under the isometries, supports a new sigma model. The target space geometry of the new model is the quotient of the T by the isometry group.

This is first described for a bosonic sigma model and it is pointed out that we need to understand supersymmetric sigma models, their isometries and gauging as well as the quotient in order to apply the scheme to models with extended supersymmetry. We then look at these issues. The final goal is to construct new hyperkähler geometries from hyperkähler geometries with isometries, so making sure that the quotient construction preserves the symmetries etc.

Please visit https://lonti.weebly.com/spring-2023-series.html for more information.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102534' style='color:#f0ad4e'>LonTI: Leverhulme Lectures on Supersymmetry, complex geometry and the hyperkahler quotient

Regular Seminar Ulf Lindstrom (Uppsala)

at:
01:00 - 01:00
KCL Strand
room: LIMS, Royal Institution
abstract:

Sigma models are maps from a domain to a target space T. The geometry of the target space is determined by the dimension of the domain and symmetries of the model. When it has isometries that can be gauged, the quotient space, i.e., the space of orbits under the isometries, supports a new sigma model. The target space geometry of the new model is the quotient of the T by the isometry group. This is first described for a bosonic sigma model and it is pointed out that we need to understand supersymmetric sigma models, their isometries and gauging as well as the quotient in order to apply the scheme to models with extended supersymmetry. We then look at these issues. The final goal is to construct new hyperkahler geometries from hyperkähler geometries with isometries, so making sure that the quotient construction preserves the symmetries etc. Ulf Lindstrom is Leverhulme Visiting Professor at Imperial College.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 174' style='color:#f0ad4e'>Higgs Workshop: TBA

regular seminar Bartomeu Fiol (Barcelona)

at:
01:00 - 01:00
KCL, Strand
room: K6.29
abstract:

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01.01.1970 (Thursday)

NT' style='color:#f0ad4e'>NT 175' style='color:#f0ad4e'>Internal number theory seminar

regular seminar Fred Diamond (King's College London)

at:
01:00 - 01:00
KCL, Strand
room: K4.31
abstract:

Title: Geometric Serre weight conjectures, Hasse invariants and \Theta-operators

Abstract: Serreâs conjecture, now a theorem of Khare and Wintenberger, states that every odd, irreducible representation Gal(K/Q) --> GL(2,F_p) arises from a modular form. Furthermore it prescribes the minimal weight (at least 2) and level (prime to p) of such a form. Iâll recall this, along with a more geometric variant due to Edixhoven involving modular forms of weight one, and the relation with certain âœweight-shiftingâ operators in characteristic p. Then Iâll discuss a generalization (joint with Sasaki) of the geometric variant and related weight-shifting phenomena in the context of Hilbert modular forms.

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01.01.1970 (Thursday)

TP' style='color:#f0ad4e'>TP 102543' style='color:#f0ad4e'>Higgs Workshop: Radiation from Matrices

Conference Bartomeu Fiol (Barcelona)

at:
01:00 - 01:00
KCL Strand
room: K6.29 Anatomy Theatre
abstract:

I give an overview of work characterizing radiation in generic four-dimensional conformal field theories. I argue that for theories with conformal scalars, the radiated energy is not positive definite and the radiated power is not Lorentz invariant. I then determine the coupling dependence of radiation, for N=2 superconformal field theories in the planar limit. This involves a purely combinatorial solution of certain matrix models, in terms of tree graphs.

If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

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