We will discuss some classification results for Hermitian non-Kähler gravitational instantons. There are three main results: (1) Non-existence of certain Hermitian non-Kähler ALE gravitational instantons. (2) Complete classification for Hermitian non-Kähler ALF/AF gravitational instantons. (3) Non-existence of Hermitian non-Kähler gravitational instantons under suitable curvature decay condition, when there is more collapsing at infinity (ALG, ALH, etc.). These are achieved by a thorough analysis of the collapsing geometry at infinity and compactifications.
A criptografia, a arte e ciência de proteger a comunicação, passou por transformações significativas desde sua origem. Este seminário explora a evolução histórica das técnicas criptográficas, desde cifras antigas até algoritmos modernos, e examina o seu papel crucial na proteção das informações num mundo cada vez mais digital. Iremos abordar os principais esquemas usados ao longo dos tempos, desde o RSA às curvas elípticas e esquemas pós-quânticos. Gostavas de perceber o quão vasto é o mundo da criptografia? Queres comunicar secretamente com os teus amigos? Este é o seminário para ti!
Quantum topologists are used to thinking about traces in the framework of pivotal tensor categories and thus in a two-dimensional context to which a two-dimensional graphical calculus can be associated. We explain that traces are already naturally defined for twisted endomorphisms of linear categories, i.e. in a one-dimensional context. The endomorphisms are twisted by the Nakayama functor which, for a module category over a monoidal category, is a twisted module functor and hence an inherently three-dimensional object. This naturally leads to a three-dimensional graphical calculus. This calculus also has applications to Turaev–Viro topological field theories with defects.
In this talk we will discuss a collection of convolution inequalities for real valued functions on the hypercube, motivated by combinatorial applications.
We develop a general theory of 1-, 2-, and 3-dimensional "orbifold completion", to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. This can be viewed as the "oriented version" of condensation completion. We give a basic introduction to TQFTs and their orbifolds, and discuss applications which include defect TQFTs for state sum models, Reshethikin-Turaev and Crane-Yetter theory. This is joint work with Lukas Müller.
In this talk, we propose a new approach to solving the Buckley-Leverett System, which is to consider a compressible approximation model characterized by a stiff pressure law. Passing to the incompressible limit, the compressible model gives rise to a Hele-Shaw type free boundary limit of Buckley-Leverett System, and it is shown the existence of a weak solution of it.
The local information of a 2d rational conformal field theory (RCFT) is encoded in a vertex operator algebra, whose modules constitute a modular fusion category C. The collection of global observables of the theory is given by conformal blocks and carries actions of mapping class groups, which is described mathematically by a modular functor that assigns the Drinfeld center Z(C) to a circle. The string-net construction, which first appeared in the study of topological phases of matter, not only provides such a modular functor but also supplies a graphical construction of correlators. A generalization of the string-net construction takes a pivotal bicategory as input. When such a bicategory is taken to be C (considered as a bicategory with one object), it recovers the modular functor of conformal blocks. On the other hand, the modular functor associated with the Morita bicategory of separable symmetric Frobenius algebras internal to C classifies stratified worldsheets up to "categorical symmetries". In this talk we explain, using the framework of double categories, that RCFT correlators exhibit an equivalence between these two modular functors. This is in fact a consequence of the functoriality of the string-net construction: the lax biadjunction between a pivotal bicategory and its orbifold completion induces an equivalence between their string-net modular functors.
We study transitions from chaotic to integrable Hamiltonians in the double scaled SYK and $p$-spin systems. The dynamics of our models is described by chord diagrams with two species. We begin by developing a path integral formalism of coarse graining chord diagrams with a single species of chords, which has the same equations of motion as the bi-local Liouville action, yet appears otherwise to be different and in particular well defined. We then develop a similar formalism for two types of chords, allowing us to study different types of deformations of double scaled SYK and in particular a deformation by an integrable Hamiltonian. The system has two distinct thermodynamic phases: one is continuously connected to the chaotic SYK Hamiltonian, the other is continuously connected to the integrable Hamiltonian, separated at low temperature by a first order phase transition.
In recent years, there has been a growing number of applications of stable homotopy theory to condensed matter physics, many of which stem from a conjecture of Kitaev that gapped invertible phases of matter should be classified by the homotopy groups of a spectrum. This gives rise to a mathematical modeling question: how do we model quantum systems in such a way that this result can be better understood, perhaps even proved? In this talk, I will discuss some aspects of this modeling problem. This is based on joint work with Mike Hermele, Juan Moreno, Markus Pflaum, Marvin Qi and Daniel Spiegel, David Stephen, Xueda Wen.
Nonstandard analysis (NSA), founded by Abraham Robinson in the 1960’s, was to a great extent inspired by Leibniz’s ideas and intuitions towards the use of infinitesimal and infinitely large quantities. One of the greatest features of NSA is that, by allowing a correct formulation of infinitesimals, one is now able to reason using orders of magnitude. This means that one can give precise meaning, and reason formally, about otherwise vague terms such as "small" or "large". Recently, accounts of vagueness relying on NSA were introduced [2, 8, 4]. In particular, and unlike other accounts of vagueness, the so-called nonstandard primitivist account [4, 5] embraces transitivity for marginal differences (i.e. "small" differences), but not for large differences in a soritical series. Nonstandard primitivism also seems to be particularly adequate to deal with the ship of Theseus paradox [3, 6] and may also shed some light in doxastic reasoning by considering infinitesimal probabilities and associating them to infinitesimal credences [1, 7]. We aim at assessing the relative merits of nonstandard primitivism and to show some lines of future research regarding the connections between NSA and philosophy. (This is joint work with Bruno Jacinto) [1] Benci, Vieri and Horsten, Leon and Wenmackers, Sylvia. Infinitesimal Probabili- ties. The British Journal for the Philosophy of Science, 69 (2): 509–552, 2018. doi: 10.1093/bjps/axw013 [2] Walter Dean. Strict finitism, feasibility, and the sorites. Review of Symbolic Logic, 11 (2):295–346, 2018. doi: 10.1017/S1755020318000163. [3] Bruno Dinis. Equality and near-equality in a nonstandard world. Log. Log. Philos., 32 (1):105–118, 2023. ISSN 1425-3305,2300-9802. [4] Bruno Dinis and Bruno Jacinto. A theory of marginal and large difference. Erkenntnis, 2023. [5] Bruno Dinis and Bruno Jacinto. Marginality scales for gradable objects. (preprint), 2023. [6] Bruno Dinis and Bruno Jacinto. Counterparts as Near-equals. (preprint), 2024. [7] Kenny Easwaran. Regularity and Hyperreal Credences. Philosophical Review, 123 (1):1- 41, 2014. [8] Yair Itzhaki. Qualitative versus quantitative representation: a non-standard analysis of the sorites paradox. Linguistics and Philosophy, 44:1013–1044, 2021. URL https: //doi.org/10.1007/s10988-020-09306-7.
I will present some models in ecology and epidemiology using a transport equation approach, so called structured models. The first models are of predator-prey type and include a variable hunger structure. They take the form of nonlocal transport equations coupled to ODEs. Then, we use a similar approach in an epidemiological model including disease awareness and variable susceptibility. We show well-posedness results, asymptotic behavior, and numerical simulations. This is joint work with C. Rebelo, A. Margheri, and P. Lafargeas.
