Found at least 20 result(s)
regular seminar Marius Tiba (King's)
at: 01:00 - 01:00 KCL, Strand room: S5.20 abstract: | The Brunn-Minkowski inequality is a fundamental geometric inequality, closely related to the isoperimetric inequality. It states that for (open) sets $A$ and $B$ in $\mathbb{R}^d$, we have $|A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}$. Here $A+B=\{a+b: a \in A, b \in B\}$. Equality holds if and only if $A$ and $B$ are convex and homothetic sets (one is a dilation of the other) in $\mathbb{R}^d$. The stability of the Brunn-Minkowski inequality is the principle that if we are close to equality, then A and B must be close to being convex and homothetic. We prove a sharp stability result for the Brunn-Minkowski inequality, establishing the exact dependency between the two notions of closeness, thus concluding a long line of research on this problem. This is joint work with Alessio Figalli and Peter van Hintum. Keywords: |
Regular Seminar Lucia Cordova (CERN)
at: 01:00 - 01:00 KCL Strand room: K3.11 abstract: | We demonstrate that crossing symmetry of S-matrices can be violated in theories with non-invertible symmetries. Focusing on integrable flows to gapped phases in two dimensions, we show that S-matrices derived previously from the bootstrap approach are incompatible with non-invertible symmetries along the flow. We present consistent alternatives, which however violate crossing symmetry and obey modified rules dictated by fusion categories. We also show how these modified crossing rules can be used to constrain the space of amplitudes with a given categorical symmetry.
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regular seminar Peter Latham (UCL)
at: 01:00 - 01:00 KCL, Strand room: S5.20 abstract: | Most modern deep networks are overparameterized: the number of training
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regular seminar Bruno Klingler (Humboldt University of Berlin)
at: 01:00 - 01:00 KCL, Strand room: abstract: | Given a quasi projective family S of complex algebraic varieties, its Hodge locus is the locus of points of S where the corresponding fiber admits exceptional Hodge classes (conjecturally: exceptional algebraic cycles). In this talk I will survey the many recent advances in our understanding of such loci, both geometrically and arithmetically, as well as the remaining open questions. Keywords: |
regular seminar Cécile Mailler (University of Bath)
at: 01:00 - 01:00 KCL, Strand room: S3.32 abstract: | In this joint work with Jakob Björnberg, Peter Mörters and Daniel Ueltschi, we introduce a disordered version of the CRP in which tables have different weights (or fitnesses). When a new customer enters the restaurant, they choose to open a new table with probability proportional to a parameter $\theta$, or they sit at an occupied table with probability proportional to the weight of this table times the number of customers already sitting at this table. We show that, in this model, in probability, a proportion converging to one of all customers sit at the largest table. We also show that this is not true almost surely, but prove instead that, almost surely, a proportion converging to one of all customers sit at one of the two largest tables. Keywords: Chinese restaurant processes |
Regular Seminar Ana-Maria Raclariu (King's College London)
at: 01:00 - 01:00 KCL Strand room: LIMS abstract: | These lectures will review recent developments surrounding the infrared sector of gravity in (3+1)-dimensional asymptotically flat spacetimes (AFS). In the first part of the course we will introduce soft theorems which govern the low-energy scattering of massless particles such as photons and gravitons. We will explain how these are related to classical observables known as memory effects and discuss their application to computing infrared-finite collider observables and gravitational waveforms. In the second part, we will introduce the notion of asymptotic or large-gauge symmetries and use it to derive the infinite-dimensional asymptotic symmetry algebra of (3+1)-dimensional AFS, also known as the BMS algebra. We will show that the conservation laws associated with these symmetries are equivalent to the Weinberg soft graviton theorem. Time-permitting, we will discuss some implications of these ideas for non-AdS holography. Keywords: |
journal club Pannell William (KCL)
at: 01:00 - 01:00 KCL, Strand room: Norfolk Building 342N abstract: | Fuzzy sphere regularization has proven to be a useful tool for deriving CFT data in a number of theories, most notably the 3d Ising model. Previous studies of these fuzzy sphere models relied explicitly upon matching with data known from other methods such as the conformal bootstrap, and were thus limited to already well-studied theories. Following two recent articles 2409.02998 and 2409.08257 I will detail how it is possible to explore the emergence of conformality within the constraints of the fuzzy sphere models themselves by explicitly realizing the generators of the conformal algebra as fuzzy sphere operators, and discuss their results for fuzzy sphere Ising model.
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regular seminar Cillian Doherty (Cambridge)
at: 01:00 - 01:00 KCL, Strand room: S5.20 abstract: | A compact subset $K$ of the complex plane is said to be $W^{1,p}$ removable if any continuous real-valued function $f$ on $\mathbb{C}$ which is in the Sobolev space $W^{1,p}(\mathbb{C} \setminus K)$ is automatically also in the Sobolev space $W^{1,p}(\mathbb{C})$. This property is true for all values of $p$ for points and line segments, but false for sets with non-empty interior, and in general there is no simple condition to determine whether a given set is removable or not. In certain cases, there is a link between removability and how “rough†the set $K$ is. In particular, if $K$ is the graph of a function, it is known that its Hölder continuity is related to its removability. We will present new results on the removability of the graph of a one-dimensional Brownian motion on an interval and show that it is almost surely not $W^{1,p}$ removable for finite $p$, but is removable for $p = \infty$. This talk is based on joint work with Jason Miller. Keywords: |
Regular Seminar Edward Mazenc (ETH)
at: 01:00 - 01:00 KCL Strand room: K3.11 abstract: | How are bulk strings related to boundary Feynman diagrams? I will give an overview of my work with Rajesh Gopakumar on deriving the closed string dual to the simplest possible gauge theory, a Hermitian matrix integral. Working in the conventional 't Hooft limit, we extract topological string theories which replace the minimal string away from the double-scaling limit. We show how to exactly reconstruct both the closed string worldsheet and its embedding into the emergent target space, purely from the matrix Feynman diagrams. I'll close by embedding our results in the broader context of AdS/CFT. Keywords: |
regular seminar Manuel Santos Gutierrez (Weizmann Institute of Science)
at: 01:00 - 01:00 KCL, Strand room: S5.20 abstract: | Linear response theory aims at predicting the mean properties of a dynamical system subject to external perturbations. It is first order approximation that relates the natural variability of the system with its ability to mitigate small disturbances. To this end, the eigenvalues of the Fokker-Planck operator associated with the unperturbed system provide the asymptotic rates at which the system attains a new and, possibly, non-equilibrium steady-state. When such operators, however, are non-selfadjoint, the dynamics become more sensitive, and the relaxation rates do not explain the transient behavior of the system. In this talk, we discuss the role of non-selfadjointness in deriving fluctuation-response relations for stochastic and chaotic systems. Keywords: |
regular seminar Stephen Lynch (KCL)
at: 01:00 - 01:00 KCL, Strand room: S4.29 abstract: | Mean curvature flow moves a hypersurface in Euclidean space with velocity equal to its mean curvature vector. This evolution is described by a nonlinear weakly parabolic system. Variationally, it is a formal gradient flow for the volume functional. Solutions to mean curvature flow exhibit a huge variety of different kinds of singularities. For solutions which move monotonically (have nowhere vanishing mean curvature), however, these singularities exhibit enough structure so that they might eventually be completely classified. We will discuss the now essentially complete picture for surfaces in R^3 developed over the last 40 years, and then explore the dramatically more complicated setting of 3-dimensional hypersurfaces in R^4. Keywords: |
regular seminar Rajeeva Karandikar (Chennai Mathematical Institute)
at: 01:00 - 01:00 KCL, Strand room: S3.32 abstract: | We will discuss Stochastic Approximation for Banach Valued observation sequences. First part of the talk we will consider Banach space satisfies appropriate geometric conditions. In the second half, we will consider Banach spaces that do not even satisfy Radon-Nikodym (such as L1[0,1] or C[0,1]) and in this case, we prove validity of stochastic approximation under suitable conditions on the error sequence. Keywords: |
regular seminar Rodrigo dos Santos Targino (Getulio Vargas Foundation (FGV))
at: 01:00 - 01:00 KCL, Strand room: S2.38 abstract: | In order to assess the financial condition of a pension fund, one needs to take into account the mortality forecast so the longevity risk is considered in a consistent way on future cash flows. Usually, the forecast of mortality rates is performed with national or country population data. Even in the presence of basis risk when applying it for pension funds sub-populations (selected populations), for most of the countries this may not be a meaningful problem. However, for countries with relevant social inequalities and a heterogeneous population, national mortality rates may be quite different and more severe than the ones observed in selected sub-populations. In this paper, we use Gaussian processes in a spatial covariance framework applied to sub-population frameworks such that reference populations are used. The applications are performed with a time series of a Brazilian small pension fund population along with the annual country mortality table and also with the use of a public non-periodic insurance industry mortality table. Our aim is to coherently forecast longevity scenarios for the pension fund population. Joint work with Eduardo F. L. de Melo (FGV) and Michael Ludkovski (UCSB). Keywords: |
colloquium Rupert Frank (LMU)
at: 01:00 - 01:00 KCL, Strand room: Bush House (SE) 1.05 abstract: | The coherent state transform, under various names, appears in many fields of mathematics and physics. It is associated with representations of a group. In this talk we are concerned with the problem of minimizing the entropy of the coherent state transform and we explain how complex analysis can be used to achieve this in certain settings. We discuss various open questions.
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regular seminar Dmytro Karvatskyi (Institute of Mathematics of NAS of Ukraine and the University of St. Andrews)
at: 01:00 - 01:00 KCL, Strand room: S5.20 abstract: | For a convergent positive series, we study the properties of the set of all possible subsums. It is well known that the aforementioned set, up to homeomorphism, is either a finite union of closed intervals, Cantor set, or M-Cantorval. The last case is quite complex and understudied. Formally, M-Cantorval is a perfect set on the real line, which is the closure of its interior, and the endpoint of any nontrivial component of this set are accumulation points of trivial components. Our focus lies in identifying the necessary conditions for the set of subsums to be a Cantorval and investigating its structure. Keywords: |
Regular Seminar Silvia Nagy (Durham U.)
at: 01:00 - 01:00 KCL Strand room: K3.11 abstract: | It is by now well understood how leading soft theorems follow as Ward identities of asymptotic symmetries defined at null infinity. For subleading infrared effects the connection is more subtle, but it turns out that this can be formalised, to all orders in the energy expansion, by adapting the Stuckelberg procedure to construct an extended radiative phase space at null infinity. I will exemplify this with Yang-Mills theory, showing the construction of the extended phase space, as well as the charges corresponding to the subleading soft theorems at all orders. These turn out to satisfy simple recursion relations, and organise themselves into infinite dimensional algebras in certain subsectors. Keywords: |
regular seminar Andrey Pilipenko (Kyiv Polytechnic Institute)
at: 01:00 - 01:00 KCL, Strand room: S3.32 abstract: | The Skorokhod reflection was used in 1961 to create a reflected diffusion on the half-line. Later, it was used for processes with jumps such as reflected Lévy processes. Like a Brownian motion, which is a weak limit of random walks, reflected processes on the half-line serve as weak limits of random walks with switching regimes at zero: one regime away from zero, the other around zero. We develop a general theory of this regime change and prove convergence to a function with generalized reflection. Our results are deterministic and can be applied to a wide class of stochastic processes. Applications include storage processes, heavy traffic limits, diffusion on a half-line with a combination of continuous reflection, jump exit, and a delay at 0. Keywords: |
regular seminar Anita Behme (TU Dresden)
at: 01:00 - 01:00 KCL, Strand room: S4.29 abstract: | According to Siegmund (1976) two Markov processes $X,Y$ on $\textbb{R}_+$ are dual, if for all $t,x,y\geq 0$
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regular seminar Ziluo Zhang (Wenzhou Institute, UCAS)
at: 01:00 - 01:00 KCL, Strand room: S4.23 abstract: | In this talk, we will present a field theoretic approach to capture the motion of an isolated Active Brownian Particle (ABP) [1]. We further add dry friction into the ABP model. Using the field theory approach, we calculate the effective diffusion coefficient in the presence of both wet and dry frictions in a perturbative way via the Green-Kubo relation [2]. We further compare the analytical result with the numerical simulation.
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regular seminar Shigeyuki Komura (Wenzhou Institute, UCAS)
at: 01:00 - 01:00 KCL, Strand room: S4.23 abstract: | The concept of odd elasticity is useful to characterize non-reciprocality in active systems such as micromachines and microswimmers. As an example, we first introduce a model for a thermally driven microswimmer in which three spheres are connected by two springs with odd elasticity. Using Onsager’s variational principle, we derive dynamical equations for a nonequilibrium active system with odd elasticity. We further investigate the emergence of odd elasticity in an elastic microswimmer model by using a reinforcement learning method.
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