SHORT COURSES
Quantifying Knowledge and Ignorance
It’s normal and natural to think that how much we know, individually and collectively, grows over time. What could seem more obvious and unremarkable than the claim that, for example, I know more now than I did when I was 10 years old? Or that I know more now about Edinburgh than I did when I first moved here in 2012? Yet when we think carefully about what it is for knowledge to grow, about what an amount of knowledge is, and about what it is for one amount of knowledge to be more or less than another, deep and interesting problems come to the surface. In this talk I will explore this issue, examining and arguing against a very natural approach to understanding the measure or extent of one’s knowledge. The goal will be to give a sense of the shape and character of the problem, but equally to reveal how an adequate understanding of the quantitative dimension of knowledge rests on central issues in contemporary philosophy. Materials · The Measure of Knowledge · Truth and Epistemic Value · The Proper Work of the Intellect
Nick Treanor
University of Edinburgh         A  
Transdisciplinary Mathematics
In this course we shall introduce some basic mathematical notions to build towards Hypergraph Theory in a way that reflects the core tenets of SEMF. We aim to: - illustrate the depth and disciplinary transversality of mathematical formalisms - dispel misconceptions about the difficulty or inaccessibility of mathematics - give some basic concepts and tools that are ready to use in practice - link basic mathematical notions with constellations of ideas in multiple fields - provide some starting point references for further study The course will be structure around the following thematic sections: Foundation (sets, multisets and tuples) Transformation (algebra) Connection (hypergraphs) Structure (category theory) Materials · Course Slides · Adjacency Slides
Carlos Zapata Carratalá
SEMF President Wolfram Research
            Gauge Symmetries and Standard Model
The Standard Model (SM) is the one which describes with the highest accuracy the behaviour and existence of most of the elementary particles that define our universe. This model incorporates quantum mechanics, gauge symmetry, group theory and special relativity; it also postulates a great number of experimentally found symmetries related to particle properties. In this brief course I will give an introduction to the main symmetries that SM is based on. We will start with abelian symmetries, such as the U(1) symmetry to give an explanation to the electromagnetic force. Then, we will see how non-abelian theories work, such as QCD described with the SU(3) symmetry. And finally, we will see that by breaking the Electroweak symmetry SU(2)L×U(1)Y the Higgs field gives mass to the elementary particles in the universe. All the above will be used to develop some of the different terms in the SM lagrangian to see how Particle Physics works. Materials · Course program
Brief Introduction to Functional Analysis
The importance of Functional Analysis in mathematics relies in the fact that it serves as a bridge between two of the main branches of study historically: analysis and linear algebra. While this is an abstract topic of study, and the terms and result are rather complex, many of the concepts are actually based in geometrical intuitions. In this course we will do a brief introduction to the basics of functional analysis from an intuitive approach, trying to visualize the actual meaning behind some of the basic concepts, such as metrics or norms, with some analogies to some real world entities. The course is not exclusively aimed at people with a high background in mathematics. We will attempt to cover the main ideas from topological, metric, normed and Banach spaces, without getting too much into the deep formal details.
Laws of Quantum Thermodynamics
Quantum thermodynamics arises when extending the laws and ideas from classical thermodynamics to the microscopical, i.e. quantum, regime. In this course, we will address the fundamentals of the theory focusing on the laws of quantum thermodynamics. We will also present the main practical applications of this theory, such as quantum thermal machines, and point out the main conceptual issues when dealing with quantities such as heat, work or entropy. It is convenient to know the fundamentals of classical thermodynamics and quantum theory to assist. Materials · Thermodynamics in the quantum regime.
TALKS
Learning in Plants: The Journey so Far, Challenges and Reflections
One of the exciting developments in the contemporary analysis of behaviour is the possibility of learning in plants. Whether plants can learn by habituation and/or by association has remained a persistent subject of inquiry, however, it still remains an unresolved question. What are the challenges to answering this puzzling question? Where do we stand as of now and how can we further facilitate the study of learning in plants? In this talk, I will reflect on these points with reference to my experience of trying to replicate pea plant learning experiments.
The Future of Computing with Brain-Inspired Silicon Circuits
In the past decades we have experienced an unprecedented technological revolution. Modern cell phones hold the same computational power as a desktop computer did just a few years ago. Machine learning algorithms have conquered problems believed to be near impossible to solve, beating chess and go champions, predicting the structure of proteins, generating art with astonishing aesthetics and even fooling experienced google engineers into being conscious. However, our current computer architectures rely on a single design from back in the 40’s that has not been updated since its conception. Even though computers have proven to be one the most successful technological discoveries of humankind, they are approaching a serious bottleneck. In the search for powerful future alternatives, a new computational paradigm is rising as a promising technology: neuromorphic computing. This field takes inspiration from the brain to build non-traditional silicon hardware that obey organisational principles of biological neural circuits. Neuromorphic engineers are already developing a new generation of intelligent and autonomous devices that can perform complex computations while, crucially, using extremely low power, as it is found in the brain. In this talk, I will provide a historic perspective of the foundations of the field, as well as its most recent developments and future challenges. Finally, I will talk about our current efforts to unravel key computational principles of biological brains that can be implemented into neuromorphic hardware, with the hope to enhance its computational power to unprecedented scales.
Saray Soldado Magraner
University of California, Los Angeles            
Evolution & Origin of Life
This talk will be three-folded: 1) Walkthrough to evolution: what we know so far?, 2) What is life?, and 3) The beginning of everything: experiments on abiogenesis and theories on the origin of life.
Brain Circuit Dynamics and Computation
The human brain contains an estimate of 100 billion (1011) neurons. Each one of them receives about a thousand direct connections from other neurons, amounting to a total of a trillion connections (1014). Information in the brain flows through this intricately connected neural network, giving rise to our sensations, desires and thoughts. Each instance of our perception emerges from the coordinated activity of thousands of neurons within this network, forming brain circuits that are in charge of performing specific functions or computations. To understand these computations it is paramount to characterize how the collective activity of large neural populations evolve over time. Dynamical systems theory has proven to be a very successful mathematical framework to understand this evolving brain activity, and its link to computation. Through this framework we have been able to uncover hidden computational motives in the complex activity patterns of neural populations. This has provided new insights into how brain circuits process information about the external world, giving rise to the plans and actions that allow us to navigate the complexity of our environments.
Complex Systems against the Anthropogenic Climate Change
Our planet is currently changing rapidly. The poles are melting, oceans biodiversity is vanishing due to plastic pollution, and deserts are advancing at an unstoppable rhythm. Since the origin of life, Earth has evolved due to the interactions between geology, climate, and the biosphere itself. In the past, the emergence of photosynthetic organisms (i.e. cyanobacteria) changed the composition and behavior of the entire planet. Thus, enabling biodiversity to flourish and cover the whole planet. However, since the dawn of humankind, we have altered the balance with our societies pushing the planet towards a new era largely altered by humans. Such changes could be promoting unavoidable and irreversible alterations, the so-called tipping points. These critical points where the systems change dramatically have been observed in many different systems, such as the infection spreading, clouds formation, or population dynamics. We are not only talking about an alternative from existence to extinction, but also from static behaviors to oscillations or even chaos. All this could seem to be very complicated problems to study or tackle, but thanks to complex systems science we have a chance. Complex systems have studied those complicated systems and shown that usually we can imitate those behaviors by means of small and more comprehensive systems (the minimal models). This does not mean that we can study the system from its smallest parts, but the opposite. Studying an isolated individual (such as an ant) makes it impossible to predict the global dynamics (such as the nest formation). We need to model the essential interactions between the agents to observe emergent phenomena at the scale of the system, where network science plays a crucial role. Another important outcome is the observation that many of the interesting features exhibited are universal. That is, they do not depend on the particularities of the system but arise from the fundamental mechanisms. In this talk, we will discuss some aspects of the current planetary state, how we have arrived at this point and how scientists are addressing this important subject using Complexity Systems science. The importance of these critical or tipping points and their ghosts (dynamical phenomena that warns us that current ecosystems may be not as healthy as they seem) will also be discussed. Last, but not least, we will talk about how modeling and studying these simple processes could give us a chance to revert or help to improve the current degradation tendency. Can we terraform Earth ecosystems from our knowledge about synthetic organisms?
Blai Vidiella Rocamora
Centre de Recerca Matemàtica
              Structural Thinking and Bungean Exact Philosophy
Bungean Exact Philosophy is the radical yet simple idea of doing philosophy in exact languages – that is, by expressing philosophical ideas in terms usually reserved to mathematicians and researchers alike. Far from an empty defense of some impractical standard, it is very much the description of a practice by the philosopher Mario Bunge, as is best exemplified by his monumental work Treatise of Basic Philosophy, where he works towards building a system for the foundation of philosophy. Specifically, “[t]he treatise encompasses what the author takes to be the nucleus of contemporary philosophy, namely semantics […], epistemology […], metaphysics […], and ethics […].” However, I'd argue an exact language is not up to Bunge's dream of an exact philosophy. Rather, we can improve upon it by using structural thinking, which leverages Category Theory and Logic to synthetize systems for formalizing concepts. My main example for this will be the paper Behavioral Mereology, by Brendan Fong, David Jaz Myers, and David I. Spivak. In this talk, I intend to summarize these two works and draw some speculations as to what an exact and structural philosophy could look like.
Orxata and Cyperus esculentus
In this talk we will give a broad perspective on the origins of one of the most iconic beverages from the mediterranean coast of Spain.
Carlos Zapata Carratalá
SEMF President Wolfram Research
            AI for Neutrino Astronomy
TBC.
Counterintuitive Mathematical Facts
In this talk we will discuss some mathematical results and examples that seem to go against intuitions.
Discrete Geometry
This talk will be a brief introduction to how one might cook up a "digital geometry" with the sole ingredients of graph theory. We'll consider edge-labeled graphs, with special attention paid to graphs that arise out of the actions of groups. The tour will continue through some topological aspects: what open sets on graphs look like, and the notion of continuous maps between graphs -- which take the form of path homomorphisms. The group structure of graph automorphisms will be exploited to give a discrete version of isometry. Lastly, we'll look at how one can construct fiber bundles of graphs, which brings with it a notion of homotopy.