The meeting will include a variety of topics, such as partial differential equations, curvature flows, spectral theory, index theory and non-commutative geometry. A guiding motivation at will be applications to topology, geometry and physics, and talks will highlight applications of analytic techniques to problems in these areas. This way, we aim to inspire research on new bridges between different areas of analysis, geometry, topology and physics, to foster collaboration between researchers in these fields, and to inspire the next generation of mathematicians.

TF — Dirac operators in differential geometry and global analysis. Conference in memory of Thomas Friedrich The purpose of this workshop is to bring together researchers from different areas in order to share different points of view and to make collaborations possible, with the ultimate aim that this will result in new connections and possibly unexpected breakthroughs. The Conference will discuss the issues of - infinite dimensional holomorphy, - topological tensor products, - Banach space theory, - operator theory, - topological algebra, - geometric and infinite dimensional topology.

The aim of the Workshop on Harmonic Analysis and Integral Geometry with Applications, Errachidia, October , is to bring researchers and professionals to discuss recent developments in both theoretical and applied mathematics, to create the knowledge exchange platform between mathematicians. The conference is broad-based that covers all branches of mathematical physics, Lie algebras and interdisciplinary researches. Functional and integral inequalities, Mathematical physics, Lie Algebras, Q-analogue. Workshop on birational geometry.

Event listing ID:. Western Algebraic Geometry Symposium. Algebraic Geometry Symposium. Louis, United States. Buildings, Varieties and Applications. This workshop, sponsored by AIM and the NSF, will be devoted to studying geometric realizations of Langlands functoriality via cycles on Shimura varieties.

Spintronics Meets Topology in Quantum Materials. This conference is intended to kickstart the program "Spin and Heat Transport in Quantum and Topological Materials" which combines the fields of spintronics, quantum magnetism, topological matter, and quantum criticality. It explores connections between the most recent experimental and theoretical progress in these areas, setting the stage for the program and establishing targets and key grand challenges.

Calculus, Differential Equations and Integration. Workshop on Higher Structures in Geometry and Physics. With an eye towards the use and need for higher structures, this workshop will bring together experts in algebraic geometry, symplectic geometry, and theoretical physics to focus on common areas interacting with HMS. Potential topics are Bershadsky--Cecotti--Ooguri--Vafa theory, shifted symplectic structures, higher Donaldson-Thomas invariants, and symplectic duality, in relation to HMS. Workshop on BPS states.

Recent progress in the study of BPS states in string theory and in supersymmetric field theories, as well as on the theory of topological recursion, gives hints towards profound connections with the exact WKB method from the mathematical study of differential equations with a large parameter, and the abelianisation of flat connections on Riemann surfaces. The goals of our workshop are to bring together some leading experts in the field to stimulate the interactions between these lines of research, and to introduce young researchers and PhD students to attractive topics of current research with a rich potential for further developments.

Supergeometry, supersymmetry and quantization. The conference will bring researchers across both the fields of mathematics and physics together in order to discuss recently developed topics, on-going work and speculative new ideas within supergeometry and its applications in physics. This event offers a unique opportunity to unite physicists and mathematicians who share a common interest in supermathematics. There will be enough time available for discussions between the participants and there will be a poster session.

Supermanifolds and their generalizations e. Algebraic geometry in Auckland. Winter Graduate School in Toric Topology. Two intensive mini-courses will be given over one week by experts on polyhedral products and toric topology. These are designed to give graduate students and early career researchers in nearby fields a better understanding of each subject by presenting multiple viewpoints from different lecturers, thus enabling the participants to better engage in the subsequent workshops and seminars. Geometry from the Quantum.

A complete understanding of quantum gravity, as it pertains to our universe, remains one of the biggest challenges in theoretical physics. As our observational constraints on the early universe and black hole physics improve, this theoretical challenge has become even more urgent. This conference aims to explore the latest developments in quantum gravity and string theory, ranging from ideas motivated from holographic dualities to new results developing the landscape of string theory vacua.

This three-day workshop is intended to bring together young and more experienced researchers working in the fields of symplectic geometry, contact geometry, and Floer theory. Mathematical Physics. East Asian Conference on Geometric Topology. Workshop — Low-dimensional Topology. French Computational Geometry Days. Numerical Analysis and Computational Mathematics. This Spring School will gather together PhD students and junior researchers who use category-theoretic ideas or techniques in their research. It will provide a forum to learn about important themes in contemporary category theory, both from experts and from each other.

Three invited speakers will each present a three-hour mini-course, accessible to non-specialists, introducing an area of active research. There will also be short talks contributed by PhD students and postdocs, and a poster session. The focus of the Spring School is on aspects of pure category theory as they interact with research in other areas of algebra, geometry, topology and logic.

Any "categorical thinker" - that is, any mathematician whose work makes use of categorical ideas - is welcome to participate. AIM Workshop: Mathematics of topological insulators. This workshop, sponsored by AIM, the Simons Foundation, and the NSF, will consider the role of topology in characterizing materials and in the prediction of their physical properties, particularly for two-dimensional material such as graphene. The focus will be on important mathematical questions at the interface of the analysis and topology in the context of the governing fundamental partial differential equations and other models.

Two such questions are the bulk edge correspondence and the existence and robustness of edge states in aperiodic settings. Shokurov's 70th Birthday. Spring Topology and Dynamical Systems Conferences are a long-running series of annual conferences focusing on several actively researched areas in topology and dynamical systems. Systems theory, Control and Automation. Workshop on Torus Actions in Topology. The workshop will introduce and explore new themes of research in toric topology. It will provide an opportunity for interaction between people who work on different aspects of torus actions, such as topological, combinatorial, symplectic and algebro-geometric.

Knots are fundamental objects of study in low dimensional topology and geometry, and the subject has seen tremendous progress in the recent years. The aim of this program is to familiarise and enthuse younger researchers in India about the latest advances in the subject with a particular emphasis on computational aspects of co homological, combinatorial and polynomial invariants of knots. The program will also discuss some important aspects of knot theory from physics point of view. The program will have two components, an advanced workshop 23 - 28 March followed by a discussion meeting 30 March - 03 April The advanced workshop will consist of mini courses on current aspects of knot theory by renowned experts.

These topics will cover some of the latest advances in the subject, and will also prepare the participants for the discussion meeting which will consist of talks by well-known researchers in the field. Knots, quandles, Khovanov Homology, Jones Polynomial. Arithmetic geometry, cycles, Hodge theory, regulators, periods and heights. Number Theory, Arithmetic. Periods, Motives and Differential equations: between Arithmetic and Geometry.

Real Algebraic Geometry. Facets of Real Algebraic Geometry. Quantum Topology and Geometry. Foundations and Perspectives of Anabelian Geometry. The workshop will review fundamental developments in several branches of anabelian geometry, as well as report on recent developments. Two mini-courses will be given by experts in Geometric Group Theory. These are designed to give graduate students and early career researchers a research level perspective on how and why Polyhedral Products appear in Geometric Group Theory, thereby enabling the participants to engage fully in the workshop that immediately follows.

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However, the interaction between toric topology and geometric group theory is largely unexplored. The purpose of this workshop is to significantly increase synergies between the two groups and establish a framework for approaching common problems and methods in a more global context. Group Theory. Index Theory and Complex Geometry. Interactions between people working in Index Theory and Complex Geometry are increasing.

More specifically, we shall seek to show that the world of qualitative structures, for example of colour and sound, or the commonsense world of coloured and sounding things, can be treated scientifically ontologically on its own terms, and that such a treatment can help us better to understand the structures both of physical reality and of cognition.

Matter in Philosophy of Physical Science.

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- Philosophy: A Very Short Introduction (Very Short Introductions);

Perception and the Mind, Misc in Philosophy of Mind. Perceptual Qualities in Philosophy of Mind. Symmetry in Physics in Philosophy of Physical Science. Chaos in Philosophy of Physical Science. History of Physics in Philosophy of Physical Science. Nonlinear Dynamics in Philosophy of Physical Science.

The fact that boundaries are ontologically dependent entities is agreed by Franz Brentano and Roderick Chisholm. This article studies both authors as a single metaphysical account about boundaries. The Brentano-Chisholm theory understands that boundaries and the objects to which they belong hold a mutual relationship of ontological dependence: the existence of a boundary depends upon a continuum of higher spatial dimensionality, but also is a conditio sine qua non for the existence of a continuum.

Although the view that ordinary material In modal terms, both are two kinds of de re ontological dependence that this article tries to distinguish. Roderick Chisholm in 20th Century Philosophy. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals.

Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions.

## Pitzer College: Topology Seminar

Analysis in Philosophy of Mathematics. General Relativity in Philosophy of Physical Science.

Geometry in Philosophy of Mathematics. Rosen's modelling relations constitute a conceptual schema for the understanding of the bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems used in this study refers to information structures constructed as algebraic rings of observable attributes of natural systems, in which the notion of observable signifies a physical attribute that, in principle, can be measured.

Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation in terms As an application, we construct a topological modelling schema of complex systems. The crucial distinguishing requirement between simple and complex systems in this schema is reflected with respect to their rings of observables by the property of global commutativity.

The global information structure representing the behaviour of a complex system is modelled functorially in terms of its spectrum functor. Complexity in Philosophy of Physical Science. Complexity in Biology in Philosophy of Biology. Systems Theory in Philosophy of Physical Science. We develop a general covariant categorical modeling theory of natural systems' behavior based on the fundamental functorial processes of representation and localization-globalization.

In the second part of this study we analyze the semantic bidirectional process of localization-globalization. The notion of a localization system of a complex information structure bears a dual role: Firstly, it determines the appropriate categorical environment of base reference contexts for considering the operational modeling of a complex system's behavior, and secondly, it specifies the global compatibility conditions A localization system acts on the global information structure of a complex system, partitions it into sorts, and eventually, forces the consistent sheaf-theoretic fibering of the latter over the base category of commutative reference contexts.

In this manner, the sheafification of the Spectrum functor of a complex information structure takes place by imposing on the uniform and homologous fibered structure of elements of the Spectrum presheaf the following two requirements of coherence in relation to the localization-globalization process: [i].

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Compatibility of information under restriction from the global to the local level, and [ii]. Compatibility of information under extension from the local to the global level. Correspondingly, the options of local and global receive a concrete mathematical meaning with respect to a suitable notion of topology categorical Grothendieck topology defined on the base category of commutative reference contexts.

Finally, the accurate functorial process modeling of a complex system's behavior, respecting the processes of representation and localization-globalization, is being effectuated by means of establishing a categorical dual equivalence between the category of complex information structures, and the topes of sheaves over the base category of partial or local information carriers, equipped with the categorical topology of epimorphosis families.

Remove from this list. We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras.

The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of Quantum Logic in Logic and Philosophy of Logic. Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events.

We study localization systems of quantum events' structures by means of Gtothendieck topologies on the base category of Boolean events' algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events' fibres over the base category of local Boolean frames. Relational Interpretations in Philosophy of Physical Science.

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and Aspects of the scheme semantics are discussed in relation to logic.

The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime. This volume develops a fundamentally different categorical framework for conceptualizing time and reality. In this new framework, time functions In singularities, by contrast, the opposite happens: Reality loses its local spacetime formation and reverts back to its primordial, pre-local shape — making the use of causality relations, Boolean logic and the dichotomization of subject and object obsolete in the process.

The mathematical approach is based on the logical and topological features of the Borromean Rings, and draws upon concepts and methods from algebraic and geometric topology — especially the theory of sheaves and links, group theory, logic and information theory in relation to the standard constructions employed in quantum mechanics and general relativity, shedding new light on the problems of their compatibility.

The intended audience includes physicists, mathematicians and philosophers with an interest in the conceptual and mathematical foundations of modern physics. Nonclassical Logics in Logic and Philosophy of Logic. Philosophy of Mathematics, Miscellaneous in Philosophy of Mathematics. All the typical global quantum mechanical observables are complex relative phases obtained by interference phenomena.

The origin of a geometric phase factor can be traced to the local phase invariance of the transition probability assignment in quantum mechanics. Beyond this invariance, transition probabilities also remain invariant under Most important, geometric phase factors distinguish between unitary and antiunitary transformations in terms of complex conjugation. These two types of invariance functions as an anchor point to investigate the role of loops and based loops in the state space of a quantum system as well as their links and interrelations. We show that arbitrary transition probabilities can be calculated using projective invariants of loops in the space of rays.

The case of the double slit experiment serves as a model for this purpose. We also represent the action of one-parameter unitary groups in terms of oppositely oriented-based loops at a fixed ray. In this context, we explain the relation among observables, local Boolean frames of projectors, and one-parameter unitary groups. Next, we exploit the non-commutative group structure of oriented-based loops in 3-d space and demonstrate that it carries the topological semantics of a Borromean link.

Finally, we prove that there exists a representation of this group structure in terms of one-parameter unitary groups that realizes the topological linking properties of the Borromean link. Human cognitive acts are directed towards entities of a wide range of different types. What follows is a new proposal for bringing order into this typological clutter. A categorial scheme for the objects of human cognition should be 1 critical and realistic.

Cognitive subjects are liable to error, even to systematic error of the sort that is manifested by believers in the Pantheon of Olympian gods. Thus not all putative object-directed acts should be recognized as having objects of their own. Broadly, the objects towards which human cognition is directed should be parts of reality in a sense that is at least consistent with the truths of natural science.

But such a scheme should also be 2 comprehensive: it should do justice to each sort of object on its own terms, and not attempt to eliminate objects of one sort in favour of objects of other, more favoured sorts. Linguistic and other forms of idealism, as well as Meinongian theories, which assign to each and every referring expression or intentional act an object tailored to fit, yield categorial schemes which fail to satisfy 1.

## First two-dimensional material that performs as both topological insulator and superconductor

Physicalistic and other forms of reductionism yield categorial schemes which fail to satisfy 2. What follows is a categorial scheme that is both critically realistic and comprehensive. Thus it enjoys some of the benefits of linguistic idealism and physicalism, without or so it is hoped the corresponding disadvantages of each. This paper attempts to explore a possibility to visualize the structure of time-consciousness in a knot shape. Philosophy of Consciousness in Philosophy of Mind.

Brouwer's views on the foundations of mathematics have inspired the study of intuitionistic logic, including the study of the intuitionistic propositional calculus and its extensions. The theory of these systems has become an independent branch of logic with connections to lattice theory, topology, modal logic and other areas. This paper aims to present a modern account of semantics for intuitionistic propositional systems.

The guiding idea is that of a hierarchy of semantics, organized by increasing generality: from the least general Kripke While the Kripke, topological, and algebraic semantics have been extensively studied, the Beth and Dragalin semantics have received less attention. We bring Beth and Dragalin semantics to the fore, relating them to the concept of a nucleus from pointfree topology, which provides a unifying perspective on the semantic hierarchy. Cohn and N.

## Topology Conference Announcements

Linguistics in Cognitive Sciences. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them. Analyticity and A Priority in Philosophy of Language. History: Philosophy of Mathematics in Philosophy of Mathematics. Intuitionism and Constructivism in Philosophy of Mathematics. Mathematical Psychologism in Philosophy of Mathematics. Mathematical Structuralism in Philosophy of Mathematics. The discrepancy between syntax and semantics is a painstaking issue that hinders a better comprehension of the underlying neuronal processes in the human brain.

Once established a correlation between a purely logical approach to the language and computable psychological activities, Starting from topological arguments, we suggest that the semantic properties of a proposition are processed in higher brain's functional dimensions than the syntactic ones.

In a fully reversible process, the syntactic elements embedded in Broca's area project into multiple scattered semantic cortical zones. The presence of higher functional dimensions gives rise to the increase in informational content that takes place in semantic expressions. Therefore, diverse features of human language and cognitive world can be assessed in terms of both the logic armor described by the Tractatus, and the neurocomputational techniques at hand. One of our motivations is to build a neuro-computational framework able to provide a feasible explanation for brain's semantic processing, in preparation for novel computers with nodes built into higher dimensions.

Knowledge of Language in Philosophy of Language. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. The two structures are seen to mirror each other in expressing the psychophysical phenomenological action But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution.

This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist yin-yang counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe.

The paper closes by considering the role of the analyst per se in the further evolution of the cosmos. Classical Chinese Philosophy in Asian Philosophy. Particle Physics in Philosophy of Physical Science. String Theory in Philosophy of Physical Science. Causal set theory and the theory of linear structures share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. Moreover, I show that all topological aspects of The value of this theory depends crucially on whether it is true that its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime.

On the one hand, my theorems support : the theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condition-justification and redundancy-justification.

To my knowledge, the latter two have not been identified before. I argue that these three kinds of justification are widespread After that, I first discuss the state of the art in the literature about the justification of definitions in the light of actual mathematical practice. To what in reality do the logically simple sentences with empirical content correspond?

Two extreme positions can be distinguished in this regard: 'Great Fact' theories, such as are defended by Davidson; and trope-theories, which see such sentences being made the simply by those events or states to which the relevant main verbs correspond. A position midway between these two extremes is defended, one according to which sentences of the given sort are made tme by what are called 'dependence structures', or Principles governing such dependence-structures are laid down, principles of an ontologically motivated sort which serve as basis for a topological semantics conceived as an altemative to standard set-theoretic approaches to semantics of the Tarskian sort.

These principles are then used to resolve certain puzzles generated by the semantically motivated theory of events put forward by Davidson. Donald Davidson in 20th Century Philosophy. Event-Based Semantics in Philosophy of Language. Events in Metaphysics.