Dr. Michael S. Turner, Professor, Kavli Institute for Cosmological Physics, University of Chicago. Presented Feb. 15, 2011

Our current cosmological model describes the evolution of the universe from a very early burst of accelerated expansion (known as inflation) a tiny fraction of a second after the beginning, through the assembly of galaxies and large-scale structure shaped by dark matter, to our present epoch where dark energy controls the ultimate fate of the universe. As successful as it is, this model rests upon three mysterious pillars: inflation, dark energy and particle dark matter. All three point to exciting and important new physics that have yet to be revealed and understood -- or possibly, to a fatal flaw in the paradigm.

The University of Arizona College of Science's Cosmic Origins lecture series is the story of the universe but it's also our story. Hear about origin of space and time, mass and energy, the atoms in our bodies, the compact objects where matter can end up, and the planets and moons where life may flourish. Modern cosmology includes insights and triumphs, but mysteries remain. Join the six speakers who will explore cosmology's historical and cultural backdrop to explain the discoveries that speak of our cosmic origins. http://cos.arizona.edu/cosmic/

Dr. Nima Arkani-Hamed (Perimeter Institute and Institute for Advanced Study) delivers the second lecture of the 2014/15 Perimeter Institute Public Lecture Series, in Waterloo, Ontario, Canada. Held at Perimeter Institute and webcast live worldwide on Nov. 6, 2014, Arkani-Hamed's lecture explores the exciting concepts of quantum mechanics and spacetime, and how our evolving understanding of their importance in fundamental physics will shape the field in the 21st Century.

The centuries-old tradition of folding two-dimensional paper into three-dimensional shapes is inspiring a scientific revolution. The rules of folding are at the heart of many natural phenomena, from how leaves blossom to how beetles fly. But now, engineers and designers are applying its principles to reshape the world around us—and even within us, designing new drugs, micro-robots, and future space missions. With this burgeoning field of origami-inspired-design, the question is: can the mathematics of origami be boiled down to one elegant algorithm—a fail-proof guidebook to make any object out of a flat surface, just by folding? And if so, what would that mean for the future of design? Explore the high-tech future of this age-old art as NOVA unfolds “The Origami Revolution.”

Machine Teaching: For many Machine Learning problems, labeled data is readily available. The algorithm is the bottleneck.

If machine learning is to discover knowledge, then machine teaching is to pass it on. Machine teaching is an inverse problem to machine learning. Given a learning algorithm and a target model, machine teaching finds an optimal (e.g. the smallest) training set. For example, consider a "student" who runs the Support Vector Machine learning algorithm. Imagine a teacher who wants to teach the student a specific target hyperplane in some feature space (never mind how the teacher got this hyperplane in the first place). The teacher constructs a training set D=(x1,y1) ... (xn, yn), where xi is a feature vector and yi a class label, to train the student. What is the smallest training set that will make the student learn the target hyperplane? It is not hard to see that n=2 is sufficient with the two training items straddling the target hyperplane.

Machine teaching mathematically formalizes this idea and generalizes it to many kinds of learning algorithms and teaching targets. Solving the machine teaching problem in general can be intricate and is an open mathematical question, though for a large family of learners the resulting bilevel optimization problem can be approximated.

Machine teaching can have impacts in education, where the "student" is really a human student, and the teacher certainly has a target model (i.e. the educational goal). If we are willing to assume a cognitive learning model of the student, we can use machine teaching to reverse-engineer the optimal training data -- which will be the optimal, personalized lesson for that student. We have shown feasibility in a preliminary cognitive study to teach categorization. Another application is in computer security where the "teacher" is an attacker and the learner is any intelligent system that adapts to inputs.

John Edmark's sculptures are both mesmerizing and mathematical. Using meticulously crafted platforms, patterns, and layers, Edmark's art explores the seemingly magical properties that are present in spiral geometries. In his most recent body of work, Edmark creates a series of animating “blooms” that endlessly unfold and animate as they spin beneath a strobe light.

Neil deGrasse Tyson and panelists discuss de-extinction in the 2017 Isaac Asimov Memorial Debate at the American Museum of Natural History. Biologists today have the knowledge, the tools, and the ability to influence the evolution of life on Earth. Do we have an obligation to bring back species that human activities may have rendered extinct? Does the technology exist to do so? Join Tyson and the panel for a lively debate about the merits and shortcomings of this provocative idea.

2017 Asimov Debate panelists are:

George Church Professor of Health Sciences and Technology, Harvard University and MIT

Hank Greely Director of the Center for Law and the Biosciences, Stanford University

Gregory Kaebnick Scholar, The Hastings Center; Editor, Hastings Center Report

Ross MacPhee Curator, Department of Mammalogy, Division of Vertebrate Zoology; Professor, Richard Gilder Graduate School

Beth Shapiro Professor of Ecology and Evolutionary Biology, University of California, Santa Cruz

From Jos Leys, Étienne Ghys and Aurélien Alvarez, the makers of Dimensions, comes CHAOS. It is a film about dynamical systems, the butterfly effect and chaos theory, intended for a wide audience.

How do you stack hundred-dimensional oranges? Learn about recent breakthroughs in our understanding of hyperspheres in the first episode of Infinite Series, a show that tackles the mysteries and the joy of mathematics. From Logic to Calculus, from Probability to Projective Geometry, Infinite Series both entertains and challenges its viewers to take their math game to the next level.

Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed truths about 8 and 24 dimensions that we don't even understand in 4 dimensions.

Emmy Noether made one the most significant discovery of the 20th century. As female Jewish intellectual in Nazi Germany, Emmy's had a special approach to life. Noether's Theorem ties the laws of nature -- from Newton's laws to thermodynamics to charge conservation -- directly to the geometry of space and time, the very fabric of reality. It is the basis for the standard model of particle physics, quantum electrodynamics, and grand unified theories including supersymmetry and superstrings. As usual in physics, it gets really interesting when the theorem is violated: answers to the origin of mass and the matter-antimatter asymmetry problems emerge when Noether's theorem is violated. Two things should bother you about Noether's Theorem: (1) how come so few people have heard of Emmy Noether? and (2) why isn't her theorem well known to lovers of science? With the help of a bunch of straw, Ransom Stephens solves these problems on June 16, 2010.

Will Detmold, professor at MIT and visitor at KITP's program Nuclear16, gave his "Chalk Talk" about understanding the dynamics of quarks and gluons using lattice QCD on August 21, 2016.

Google's DeepMind's founder Demis Hassabis lecturs about the future and capabilities of artificial intelligence. Hassabis was born to a Greek father and a Chinese mother and grew up in North London. A child prodigy in chess, Hassabis reached master standard at the age of 13 with an Elo rating of 2300 (at the time the second highest rated player in the world Under-14 after Judit Polgár who had a rating of 2335) and captained many of the England junior chess teams. He is a pioneering British artificial intelligence researcher, neuroscientist, computer game designer, entrepreneur, and world-class Go games player.

Currently, there are over 250 PhDs and 400 research scientists working on DeepMind’s unlimited funding projects with two main goals in mind. The first is to try and solve intelligence and figure out how the human brain became capable of taking over the planet. The second is use that intelligence to do everything else. If this latter point can be achieved, Google will soon become the most powerful entity on Earth.

And you may laugh, but thus is not some crazy far fetched idea either. These goals are for real, and the company is more than happy to talk freely with anyone about it. To get an even deeper understanding of what their plans involve why not check out a recent presentation given by Demis Hassabis, founder of DeepMind, who will talk you through their ideas.

You've probably heard about the recent news of the strange dimmings of Tabby's Star and the provoactive hypothesis of an alien megastructure (fi not check out http://bit.ly/TabbysStar). But could there be a natural explanation instead? Well two theoretical astrophycistss here at Columbia think so and here they briefly summarize some of the leading theories (although news ones are appearing almost every day!) and they think their own explanation is the best one so far.

At the heart of the Milky Way, there's a supermassive black hole that feeds off a spinning disk of hot gas, sucking up anything that ventures too close -- even light. We can't see it, but its event horizon casts a shadow, and an image of that shadow could help answer some important questions about the universe.

Scientists used to think that making such an image would require a telescope the size of Earth -- until Katie Bouman and a team of astronomers came up with a clever alternative. Katie explains how we can take a picture of the ultimate dark using the Event Horizon Telescope.

It is possible to turn a sphere inside out in 3-space with possible self-intersections but without creating any crease, a process often called sphere eversion (eversion means "to turn inside out").

Andreas Dewes explains why quantum computing is interesting, how it works and what you actually need to build a working quantum computer. He uses the superconducting two-qubit quantum processor which he built during his PhD thesis as an example to explain its basic building blocks. He shows how this processor can be used to achieve so-called quantum speed-up for a search algorithm that can be run on it. Finally, he gives a short overview of the current state of superconducting quantum computing and Google's recently announced effort to build a working quantum computer in cooperation with one of the leading research groups in this field.

Google recently announced that it is partnering up with John Martinis - one of the leading researchers on superconducting quantum computing - to build a working quantum processor. This announcement has sparked a lot of renewed interest in a topic that was mainly of academic interest before. So, if Google thinks it's worth the hassle to build quantum computers then there surely must be something about them after all?

In this video the Mathologer gives an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track way to pinpoint a transcendental number and to show that it is really transcendental. Also find out why there are a lot more transcendental numbers than numbers that we usually think of as numbers, and this despite the fact that it is super tough to show the transcendence of any number of interest such as pi or e. Also featuring an animated introduction to countable and uncountable infinities, Joseph Liouville's ocean of zeros constant, and much more.

Here is a link to one of Georg Cantor's first papers on his theory of infinite sets. Interestingly it deals with the construction of transcendental numbers!

Cantor, Georg (1874), "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen", Journal für die Reine und Angewandte Mathematik, 77: 258–262 http://gdz.sub.uni-goettingen.de/pdfc...

Here is the link to the free course on measure theory by my friend Marty Ross who I also like to thank for his help with finetuning this video: http://maths.org.au/index.php/2013/10... (it's the last collection of videos at the bottom of the linked page).

Thank you also very much to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.

Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to do calculations[1] and is closely related to, and may be regarded as a subclass of, quantum annealing. First, a (potentially complicated) Hamiltonian is found whose ground state describes the solution to the problem of interest. Next, a system with a simple Hamiltonian is prepared and initialized to the ground state. Finally, the simple Hamiltonian is adiabatically evolved to the desired complicated Hamiltonian. By the adiabatic theorem, the system remains in the ground state, so at the end the state of the system describes the solution to the problem. Adiabatic Quantum Computing has been shown to be polynomially equivalent to conventional quantum computing in the circuit model.[6] The time complexity for an adiabatic algorithm is the time taken to complete the adiabatic evolution which is dependent on the gap in the energy eigenvalues (spectral gap) of the Hamiltonian. Specifically, if the system is to be kept in the ground state, the energy gap between the ground H(t) state and the first excited state of {\displaystyle H(t)} provides an upper bound on the rate at which the t Hamiltonian can be evolved at time {\displaystyle t}.[7

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