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Machine Learning for Scent - Digitalize Smell and Make it Searchable

MIT Introduction to Deep Learning 6.S191: Lecture 10
*New 2020 Edition*
Machine Learning for Scent
Lecturer: Alex Wiltschko (Google Brain)
January 2020

For all lectures, slides, and lab materials: http://introtodeeplearning.com

Lecture Outline
0:00 - Introduction
2:55 - Digitizing smell
4:28 - The sense of smell
10:11 - Problem setup
12:58 - Molecule fragrance dataset
16:00 - Baseline algorithms
18:14 - Graph neural networks
21:25 - Molecules to graphs
23:03 - Predicting odor descriptors
25:19 - The odor embedding space
27:58 - Molecular neighbors
30:04 - Generalization
32:34 - Explaining/interpreting predictions
36:49 - Summary and future work

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David Silver - Deep Reinforcement Learning from AlphaGo to AlphaStar

Recently, self-learning systems have achieved remarkable success in several challenging problems for artificial intelligence, by combining reinforcement learnng with deep neural networks. In this talk, I describe the ideas and algorithms that led to AlphaGo: the first program to defeat a human champion in the game of Go; AlphaZero: which learned, from scratch, to also defeat the world computer champions in chess and shogi; and AlphaStar: the first program to defeat a human champion in the real-time strategy game of StarCraft.

 

Bio: David Silver is a principal research scientist at DeepMind and a professor at University College London. David's work focuses on artificially intelligent agents based on reinforcement learning. David co-led the project that combined deep learning and reinforcement learning to play Atari games directly from pixels (Nature 2015). He also led the AlphaGo project, culminating in the first program to defeat a top professional player in the full-size game of Go (Nature 2016), and the AlphaZero project, which learned by itself to defeat the world's strongest chess, shogi and Go programs (Nature 2017, Science 2018). Most recently, he co-led the AlphaStar project, which led to the world's first grandmaster level StarCraft player (Nature 2019). His work has been recognised by the Marvin Minsky award, Mensa Foundation Prize, and Royal Academy of Engineering Silver Medal.

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Dark Matter Hunt With Quantum Computer Parts

When it comes to dark matter, it might be time to leave WIMPS behind, as there’s a new candidate that’s been pulling ahead of its competitors in recent months: axions. Welcome to the new era of dark matter hunting.

For decades, physicists have embarked on a quest to understand what exactly dark matter—a mysterious substance that makes up most of the mass in the universe—is. They’ve searched high and low for hypothetical WIMPs, Weakly Interacting Massive Particles, but now the journey might be taking a new experimental turn toward another potential dark matter contender: axions.

Scientists have built an advanced instrument with parts from a quantum computer that’s sensitive enough to listen for the signal of a dark matter particle. The Axion Dark Matter Experiment (ADMX) at the University of Washington is the world's first dark matter experiment that's hunting specifically for axions.

So when it comes to the hunt for dark matter: Why are WIMPS looking less likely, why are axions the new leading candidate, and how do physicists plan to set out to find this new hypothetical particle that may or may not exist? Find out in this Focal Point.

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30 Lectures on Discrete Mathematical Structures (from Sets to Cryptography)

Lecture Notes

Section 1: Sets and counting.

  • Lecture 1.1: Basic set theory. [YouTube (60:20) | Slides]
  • Lecture 1.2: Inclusion-exclusion. [YouTube (36:42) | Slides]
  • Lecture 1.3: Permutations and combinations. [YouTube (41:41) | Slides]
  • Lecture 1.4: Binomial and multinomial coefficients. [YouTube (38:43) | Slides]
  • Lecture 1.5: Multisets and multichoosing. [YouTube (47:04) Slides]
  • Lecture 1.6: Combinatorial proofs. [YouTube (47:51) | Slides]

Section 2: Logic.

  • Lecture 2.1: Propositions and logical operators. [YouTube (42:31) | Slides]
  • Lecture 2.2: Tautology and contradiction. [YouTube (26:51) | Slides]
  • Lecture 2.3: Equivalence and implication. [YouTube (42:59) | Slides]
  • Lecture 2.4: Axiomatic systems. [YouTube (32:03) | Slides]
  • Lecture 2.5: Proofs in propositional calculus. [YouTube (36:50) | Slides]
  • Lecture 2.6: Proofs over a universe. [YouTube (37:45) | Slides]
  • Lecture 2.7: Quantifiers. [YouTube (40:04) | Slides]
  • Lecture 2.8: Set-theoretic proofs. [YouTube (47:30) | Slides]
  • Lecture 2.9: Russell's paradox and the halting problem. [YouTube (41:26) | Slides]

Section 3: Basic number theory.

  • Lecture 3.1: The pigeonhole principle. [YouTube (34:41) | Slides]
  • Lecture 3.2: Parity, and proving existential statements. [YouTube (27:13) | Slides]
  • Lecture 3.3: Proving universal statements. [YouTube (31:00) | Slides]
  • Lecture 3.4: Divisibility and primes. YouTube (29:45) | Slides]
  • Lecture 3.5: Rational and irrational numbers. [YouTube (31:44) | Slides]
  • Lecture 3.6: Quotient, remainder, ceiling and floor. [YouTube (31:42) | Slides
  • Lecture 3.7: The Euclidean algorithm. [YouTube (41:24) | Slides]

Section 4: Relations and functions.

  • Lecture 4.1: Binary relations on a set. [YouTube (41:30) | Slides]
  • Lecture 4.2: Equivalence relations and equivalence classes. [YouTube (52:14) | Slides]
  • Lecture 4.3: Partially ordered sets. [YouTube (49:55) | Slides]
  • Lecture 4.4: Functions. [YouTube (58:17) | Slides]
  • Lecture 4.5: Cardinalities and infinite sets. [YouTube (57:09) | Slides]

Section 5: Cyptography.

  • Lecture 5.1: Symmetric cryptographic ciphers. [YouTube (34:15) | Slides]
  • Lecture 5.2: Public-key cryptosystems and RSA. [YouTube (44:09) | Slides]
  • Lecture 5.3: Why RSA works. [YouTube (40:38) | Slides]
  • Lecture 5.4: The Diffie-Hellman key exchange.
  • Lecture 5.5: Error-correcting codes.
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Pearlfish: Seeking shelter up a sea cucumber's rear end cavity

Some pearlfish info:

  • One or sometimes two pearlfish animals (male and female when that is the case) will live in a single host sea cucumber.
  • Pearlfish live in the cloaca but can also live in the actual body cavity (i.e., coelom) and what's called the respiratory tree-a bunch of tubular branches that comes off the cloaca (in the diagram above in blue). Sea cucumbers use this structure to extract oxygen.
  • Pearlfish seek out the cloacal opening of the host and then work their way INTO the anus sometimes head first or sometimes tail first, working themselves backwards into the anus of the sea cucumber. This latter tail first method is used 80% of the time.
  • Larger pearlfish are found in larger host sea cucumbers.
  • Only SOME species of pearlfish are commensals in certain species of sea cucumbers. Some are free living and others are not.
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The Promise of Category Theory to Understand Open Systems and Possibly Our Place in the Universe

Based on the Mathematical Universe Hypothesis, the emerging reality is that we live in a relational reality. What does that mean? It means that the properties of the biosphere around us stem not from properties of its ultimate building blocks, but from the relations among these building blocks. While the position of category theory as a foundational language in applied mathematics and mathematical modeling is still in its infancy and a rather unexplored path, it is crucial to understand how it can help us understand the complex problems facing humanity.

 

The systems and structures we look at in the universe are self-organized at several different levels. Moreover, we live in a relational reality where self-organization is an obvious principle which is embedded in our description of the universe. This means that the properties of the world around us stem not from properties of its ultimate building blocks or individual units, but from the relations among these building blocks and units. That brings us to an important question: Is category theory a tool to understand the relationships? Moreover, how does category theory explain the relational reality of the contested commons of cyberspace, aquaspace, geospace, and space (CAGS)?

 

Category theory has already shown promise by providing an abstract framework for modeling processes to apply to science, engineering, and the contested commons of the human ecosystem. It is vital to explore how can we further apply category theory to the problems we are trying to solve today (security issues to surveillance issues, environmental issues to economics issues, automation issue to social issues and more).? How will category theory help us understand the complex issues facing the future of humanity?

 

Category Theory Applications

From assisting us in understanding how patterns of innovation rise to how patterns of destruction develop, category theory has the potential to be a powerful language or conceptual framework on which we can formulate our collective future. By keeping category theory as a reference model, we are more able to see the common components of a family of structures of any given kind that will finally help us understand how constructive and destructive structures and behavior are interrelated and integrated.

 

Now, processes are universal, but we don’t look at our human ecosystem in the form of processes. Should we? Since in nature, a causal law takes the form that, similarly to actions by an individual, specific processes tie causes and effects together, we most certainly should.

 

Prof. (Dr.) John Carlos Baez expands on this notion in Risk Roundup: “In any system, we are dealing with on Earth, it is always very fundamentally an open system — its constantly being affected in unpredictable ways by the outside world and it is also affecting the outside world in unpredictable ways.”

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Beyond Lithium-Ion Materials and Cells for Electrochemical Energy Storage

Ever since the development of lithium-ion batteries the spirit of invention has mainly lead to an evolution of existing materials. With the focus on olivine and Nickel- and cobalt based materials the energy densities, power densities and ageing mechanisms could be investigated over the years and support the understanding of the underlying mechanisms of electrochemical energy storage and conversion.

With increasing numbers of cells being used in the world the need of a post Lithium-Ion technology emerges due to a limited availability of highly pristine nickel and cobalt and increasing need for recycling, environmental protection and overall energy efficiency. Nevertheless there is still an ongoing and very promising approach for e. g. novel stoichiometries of NMC materials, olivine materials, and nickel-rich materials with can significantly increase the energy density. But due to some limitation in the field of raw materials availability, accessibility, and sustainability, low-cobalt or cobalt-free materials are of very high interest, too. For example LMR (LNMO) can be an ideal candidate. Due to the very high reactivity and potential (i. e. 4.5 V) these materials require highly stable electrolytes.

Finally, lithium-sulphur can lead to a highly recyclable, environmentally friendly system. Having a silicon-based anode (greater than 85 % Si) included both volumetric and gravimetric energy density can mean an interesting alternative to metal-oxide based materials.

With the increased energy density, safety becomes a more and more important aspect in thermodynamic and kinetic investigations of these materials. This aspect can lead to the development of non-flammable electrolytes or solid state cells.

Solid state cells are a very different but highly promising approach. Having a solid-solid interphase between electroactive materials and electrolyte the chemicals mechanisms significantly change to solid state chemistry rather than solid-organic interphases chemistry.

All types of novel chemistries exhibit very different chemical mechanisms which require specific synthetically work, e. g. with the support of numerical simulation, for electrolytes, additives, binders, carbon materials, and even the surfaces of the electro-active materials itself. Understanding these mechanisms is essential to further improve the life-time, efficiency, and hence, the sustainability of any kind of energy storage and conversion, but batteries in particular.

Bio: Andreas Hintennach; MD, PhD, Daimler AG, Mercedes-Benz, Group Research, Germany.

Andreas Hintennach is a chemist and medical doctor. He received his PhD in electrochemistry from the ETH Zurich and Paul Scherrer Institute (Switzerland) in 2010. After a postdoc stay at MIT in the field of lithium-air and catalysis 2010-11 he joined the research department of Mercedes-Benz (Daimler AG). His present focus in the field of electrochemistry is fundamental research on next generation electrical energy storage and conversion materials and systems, sustainability and toxicology

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NASA speakers at Google: "Roving and Drilling in 'Mars on Earth'" — 36 Talks at Google

The Atacama Rover Astrobiology Drilling Studies (ARADS) project recently completed a second field season in the Atacama Desert (Chile) testing a mobile robot equipped with a 1 meter drill and three life detection instruments. The goal of ARADS is to develop a new concept for a future rover mission to search for evidence of life on Mars. Such a mission would be radically different from both past and current Mars missions. This talk will introduce ARADS, roving life-detection, and results from testing in Chile.

Dr. Brian Glass leads the Deployable Automation Technologies (DAT) group at NASA Ames. Since joining Ames in 1987, Brian has been involved with (and led) many projects in adaptive controls, automated drilling, air traffic optimization, robotics, instrument automation, and vehicle and complex system health monitoring. Brian is the principal investigator for both the Life-Detection Mars-analog Project (LMAP) and the ARADS project, and has been called “NASA’s drilling guy” on occasion. Brian received his S.B. from MIT, his M.S. from Stanford, and his Ph.D. from Georgia Tech.

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Why do colliding blocks compute pi?

More 3Blue1Brown videos here

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The Secret Behind 5G Technology

5G networks are the next generation of mobile internet connectivity, offering faster speeds and more reliable connections on smartphones and other devices than ever before.

Combining cutting-edge network technology and the very latest research, 5G should offer connections that are multitudes faster than current connections, with average download speeds of around 1GBps expected to soon be the norm.

The networks will help power a huge rise in Internet of Things technology, providing the infrastructure needed to carry huge amounts of data, allowing for a smarter and more connected world.

With development well underway and testbeds already live across the world, 5G networks are expected to launch across the world by 2020, working alongside existing 3G and 4G technology to provide speedier connections that stay online no matter where you are.
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Kip Thorne - Is Time Travel Possible?

Some scientists take time travel seriously. Should you? What does time travel reveal about the nature of space and time? What about the laws of physics under extreme conditions? And don't forget those 'Grandfather Paradoxes', where a time traveler kills his own ancestor.

 

Click here to watch more interviews with Kip Thorne

http://bit.ly/2FdX0M0

 

Click here to watch more interviews on is time travel possible http://bit.ly/2JpQrbK

 

Click here to buy episodes or complete seasons of Closer To Truth http://bit.ly/1LUPlQS

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Einstein's Unfinished Revolution: Quantum Physics Seems Incomplete

Einstein's Unfinished Revolution: Quantum Physics Seems Incomplete | Science-Videos | Scoop.it

Quantum physics is the golden child of modern science. It is the basis of our understanding of atoms, radiation, and so much else – from elementary particles and basic forces to the behavior of materials.But for a century it has also been the problem child of  science: it has been plagued by intense disagreements among its inventors, strange paradoxes, and implications that seem like the stuff of fantasy. Whether it’s Schrödinger’s cat – a creature that is simultaneously dead and alive – or a belief that the world does not exist independently of our observations of it, quantum theory challenges our fundamental assumptions about reality.

 

In a special webcast talk based on his latest book, Einstein’s Unfinished Revolution, Perimeter’s Lee Smolin will argue that the problems that have bedeviled quantum physics since its inception are unsolved and unsolvable for the simple reason that the theory is incomplete. There is more to quantum physics waiting to be discovered.

 

Smolin will take the audience on a journey through the basics of quantum physics, introducing the stories of the experiments and figures that have transformed our understanding of the universe.

Smolin is one of Perimeter’s founding faculty members. He has made major contributions to the quantum theory of gravity in particular, though his work spans many areas of theoretical physics.

 

Including Einstein’s Unfinished Revolution, Smolin has authored or co-authored six books exploring philosophical issues raised by contemporary physics. He is a Fellow of the American Physical Society and the Royal Society of Canada.

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Shape oscillation of a levitated drop in an acoustic field

A `star drop' refers to the patterns created when a drop, flattened by some force, is excited into shape mode oscillations. These patterns are perhaps best understood as the two dimensional analog to the more common three dimensional shape mode oscillations. In this fluid dynamics video an ultrasonic standing wave was used to levitate a liquid drop. The drop was then flattened into a disk by increasing the field strength. This flattened drop was then excited to create star drop patterns by exciting the drop at its resonance frequency. Different oscillatory modes were induced by varying the drop radius, fluid properties, and frequency at which the field strength was modulated.

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CES 2020: An Hour with Amnon - Autonomous Vehicles Powered by Mobileye

Watch Prof. Amnon Shashua's annual CES address highlighting the progress and purpose of Mobileye's drive to full autonomy. He showcased new sensing technologies that culminate into a 23 minute drive on the congested streets of Jerusalem that is the basis for Mobileye's MaaS service. Shashua showcased the uninterrupted drive as an example of transparency he feels the industry should provide to get to full autonomy.

Watch the full unedited AV drive video here: https://www.youtube.com/watch?v=hCWL0XF_f8Y

About Mobileye:
Mobileye's advanced driver assistance systems (ADAS) technology is deployed in more than 50 million vehicles today and is integrated into hundreds of new car models from the world's major automakers including Audi, BMW, FCA, Ford, General Motors, Honda, Hyundai, Kia, Nissan, Volkswagen, and more. Mobileye began with the vision of reducing vehicle collisions and resulting injuries and fatalities. Today, Mobileye makes one of the most advanced collision avoidance systems on the market, while working toward autonomous driving and the coming autonomous mobility-as-a-service (MaaS) revolution in road safety.

Mobileye® 8 Connect™ - Driven by Safety: https://www.youtube.com/watch?v=VbX0hJqOqSo

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Learn Through Videos: Mathematics - Introduction to Number Theory

Learn Through Videos: Mathematics - Introduction to Number Theory | Science-Videos | Scoop.it

Introduction to Number Theory consists of twenty-four lectures taught by Professor Edward B. Burger, exploring the world of numbers. Throughout the lectures, Professor Burger explains all the fundamentals of number theory exploring the many different types of numbers: natural numbers, prime numbers, integers, irrational numbers, algebraic numbers, imaginary numbers, transcendental numbers. And also Professor Burger shows how number theory is applied to modern technology such as credit card encryption. 

 

Lecture 01 - Number Theory and Mathematical Research

Lecture 02 - Natural Numbers and Their Personalities

Lecture 03 - Triangular Numbers and Their Progressions

Lecture 04 - Geometric Progressions, Exponential Growth

Lecture 05 - Recurrence Sequences

Lecture 06 - The Binet Formula and the Towers of Hanoi

Lecture 07 - The Classical Theory of Prime Numbers

Lecture 08 - Euler's Product Formula and Divisibility

Lecture 09 - The Prime Number Theorem and Riemann

Lecture 10 - Division Algorithm and Modular Arithmetic

Lecture 11 - Cryptography and Fermat's Little Theorem

Lecture 12 - The RSA Encryption Scheme

Lecture 13 - Fermat's Method of Ascent

Lecture 14 - Fermat's Last Theorem

Lecture 15 - Factorization and Algebraic Number Theory

Lecture 16 - Pythagorean Triples

Lecture 17 - An Introduction to Algebraic Geometry

Lecture 18 - The Complex Structure of Elliptic Curves

Lecture 19 - The Abundance of Irrational Numbers

Lecture 20 - Transcending the Algebraic Numbers

Lecture 21 - Diophantine Approximation

Lecture 22 - Writing Real Numbers as Continued Fractions

Lecture 23 - Applications Involving Continued Fractions

Lecture 24 - A Journey's End and the Journey Ahead

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100 Million Exoplanets By 2050? How Will We Get There? - YouTube

Is there any hope for us to draw a plausible picture of the future of exoplanet research? Here we extrapolate from the first 25 years of exoplanet discovery into the year 2050. If the power law for the cumulative exoplanet count continues, then almost 100,000,000 exoplanets would be known by 2050. Although this number sounds ridiculously large, we find that the power law could plausibly continue until at least as far as 2030, when Gaia and WFIRST will have discovered on the order of 100,000 exoplanets. After an early era of radial velocity detection, we are now in the transit era, which might be followed by a transit & astrometry era dominated by the WFIRST and Gaia missions. And then? Maybe more is not better. A small and informal survey among astronomers at the “Exoplanet Vision 2050” workshop in Budapest suggests that astrobiological topics might influence the future of exoplanet research.

 

References:

https://arxiv.org/pdf/1911.12114.pdf https://www.investopedia.com/terms/m/... http://exoplanet.eu/catalog/51_peg_b/ https://sci.esa.int/web/plato/-/42276... https://www.eso.org/sci/facilities/eelt/ https://www.jpl.nasa.gov/habex/ https://ui.adsabs.harvard.edu/abs/201... https://sci.esa.int/web/gaia/-/58788-... https://arxiv.org/pdf/1707.01348.pdf

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Lethal Autonomous Weapons

Stuart Russell received his B.A. with first-class honours in physics from Oxford University in 1982 and his Ph.D. in computer science from Stanford in 1986. He then joined the faculty of the University of California at Berkeley, where he is Professor (and formerly Chair) of Electrical Engineering and Computer Sciences and holder of the Smith-Zadeh Chair in Engineering. He is also an Adjunct Professor of Neurological Surgery at UC San Francisco and Vice-Chair of the World Economic Forum's Council on AI and Robotics. He has published over 150 papers on a wide range of topics in artificial intelligence including machine learning, probabilistic reasoning, knowledge representation, planning, real-time decision making, multitarget tracking, computer vision, computational physiology, and global seismic monitoring. His books include "The Use of Knowledge in Analogy and Induction", "Do the Right Thing: Studies in Limited Rationality" (with Eric Wefald), and "Artificial Intelligence: A Modern Approach" (with Peter Norvig).

 

Abstract: Autonomous weapons systems select and engage targets without human intervention; they become lethal when those targets include humans. LAWS might include, for example, armed quadcopters that can search for and eliminate enemy combatants in a city, but do not include cruise missiles or remotely piloted drones for which humans make all targeting decisions. The artificial intelligence (AI) and robotics communities face an important ethical decision: whether to support or oppose the development of lethal autonomous weapons systems (LAWS). The UN has held three major meetings in Geneva under the auspices of the Convention on Certain Conventional Weapons, or CCW, to discuss the possibility of a treaty banning autonomous weapons. There is at present broad agreement on the need for "meaningful human control" over selection of targets and decisions to apply deadly force. Much work remains to be done on refining the necessary definitions and identifying exactly what should or should not be included in any proposed treaty.

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Expanded Euler's Formula for the Quaternions

In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex number exponentials.

 

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Vector and Matrix Algebra Tutorial: 46 Video Lectures

Vector and Matrix Algebra Tutorial

 

This tutorial from Santa Fe Institute's Complexity Explorer introduces students to essential ideas related to vectors and matrices.  These mathematical structures form the foundations for many key topics in complex systems, such as dynamical systems, stochastic processes, and network science.  The prerequisite for this tutorial is knowledge of high-school algebra.  The content of the tutorial is built, in a self-contained fashion, starting with basic notions of real numbers and elementary set theory.

 

Ideas of vectors and vector operations are developed next, in an intuitive way, by appealing, simultaneously to their algebraic and geometric underpinnings. Next, the tutorial explores matrices and vector spaces, determininants and eigenvalues with, again, an eye toward understanding the intuitive geometric and algrebraic connections that tie these notions together. Finally, the tutorial concludes with a survey of applications of matrix algebra, including diagnolization, recursion, geometric transformations, differential operators and Markov Chains.

 

Importantly, the content and emphasis of this material differs significantly from a standard university course in linear algebra.  Instead of solving and analyzing systems of linear equations of the form Ax=b, as is conventional from the perspective of linear algebra, students will instead be exposed to the fundamental ideas of matrix algebra in a less restrictive and more conceptually-integrated way. At the conclusion of this tutorial, students will be equipped with a core understanding of the breadth and power of matrix algebra as an essential tool for complex systems research. 

For more information and a complete list of courses and tutorials, visit www.complexityexplorer.org

Nur Hanan's curator insight, October 1, 2021 9:03 AM
Ringkaan : 
 Artikel ini berisi tentang tutorial melalui video yang menjelaskan topik vektor dan matriks yang sangat diperlukan sebagai alat analisis pada cabang-cabang ilmu lainnya seperti sistem dinamis, proses stokastik, dan ilmu jaringan.

 Manfaat konten artikel bagi saya :
 Artikel ini bisa menambah keluasan pengetahuan saya tentang vektor dan matriks  , bisa saya bagikan ke mahasiswa yang saya ajar untuk yang mengambil  mata kuliah yang terdapat topik vektor dan matriks
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Memory, Modularity, and the Theory of Deep Learnability

Why does deep learning work well for some applications and not for others? Do we need major architectural changes in deep learning to solve complex problems like natural language understanding and logic? Does memory and modular organization play an important role, and if so, how do we store complex concepts in memory? We will try to get a conceptual understanding of these questions by studying learning problems arising from synthetic mathematical function classes such as the learnability of polynomials, shallow teacher networks, and possible cryptographic hardness of learning deeper teacher networks. Finally we will present nascent ideas about how we should model memory and evolve a modular view of deep learning for higher level cognitive functions.

About the Speaker: Rina Panigrahy is a Research Scientist at Google specializing in applied and theoretical algorithms in areas such as deep learning, high dimensional search, hashing, sketching, streaming, prediction and graph analysis with engineering and research impact covering over 75 publications and 50 patents. His Masters thesis work at MIT was used in founding Akamai Technologies. He has held research and engineering positions at Microsoft(principal researcher) and Cisco Systems. He obtained his Ph.D. in Algorithms from Stanford, and did his undergrad from IIT Mumbai after securing the top rank at the IIT-JEE entrance examination all over India. He is a recipient of a Gold medal at the International Math Olympiad and a winner of several best paper awards.Click here to edit the content

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University of Arizona - Distinguished Outreach Faculty - 102 Lectures

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A Ripple, a Flash and a Bang: The Story of Two Neutron Stars

Recently, astronomers and physicists around the world turned their eyes and "ears" towards an incredible event in the night sky. For the first time, we detected the collision of two neutron stars using both traditional telescopes and a gravitational wave detector called LIGO/Virgo. This event triggered a so-called "kilonova" - an event so powerful that it forged gold weighing half as much as Jupiter. Peter Blanchard and Ashley Villar will help unravel the mystery behind gravity waves, neutron stars, and this exciting event.

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Split Octonions and the Rolling Ball (by Prof. Dr. John Baez - University of California Riverside)

Understanding exceptional Lie groups as the symmetry groups of more familiar objects is a fascinating challenge. The compact form of the smallest exceptional Lie group, G2, is the symmetry group of an 8-dimensional non-associative algebra called the octonions. However, another form of this group arises as symmetries of a simple problem in classical mechanics! The space of configurations of a ball rolling on another ball without slipping or twisting defines a manifold where the tangent space of each point is equipped with a 2-dimensional subspace describing the allowed infinitesimal motions. Under certain special conditions, the split real form of G2 acts as symmetries. We can understand this using the quaternions together with an 8-dimensional algebra called the 'split octonions'. The rolling ball picture makes the geometry associated to G2 quite vivid. This is joint work with James Dolan and John Huerta, with animations created by Geoffrey Dixon.

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The Quantum Origins of Gravity [by Leonard Susskind, 2019]

It is often said that general relativity and quantum mechanics are separate subjects that don’t fit together comfortably. There is a tension, even a contradiction between them—or so one often hears. Prof. Susskind takes an exception to this view. He thinks that exactly the opposite is true. It may be too strong to say that gravity and quantum mechanics are exactly the same thing, but people who are paying attention, may already sense that the two are inseparable, and that neither makes sense without the other.

 

Two things make him think that this idea is valid. The first is ER=EPR, the equivalence between quantum entanglement and spatial connectivity. In its strongest form ER=EPR holds not only for black holes but for any entangled systems—even empty space. One may say that the most basic property of space—its connectivity—is due to the most quantum property of quantum mechanics: entanglement.

 

The second has to do with the dynamics of space, in particular its tendency to expand. One sees this in cosmology, but also behind the horizons of black holes. The expansion is thought to be connected with the tendency of quantum states to become increasingly computationally complex: a “second law of quantum complexity.” If one pushes these ideas to their logical limits, quantum entanglement of any kind implies the existence of hidden Einstein-Rosen bridges which have a strong tendency to grow, even in situations which one naively would think have nothing to do with gravity.

 

To summarize this viewpoint in a short slogan: Wherever there is quantum mechanics, there is also gravity. The lecture took place in the Oskar Klein Auditorium, AlbaNova, Stockholm on January 29, 2019.

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Illustrated Math: The Klein Quartic

In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientation-preserving automorphisms, and 336 automorphisms if orientation may be reversed. As such, the Klein quartic is the Hurwitz surface of lowest possible genus; see Hurwitz's automorphisms theorem. Its (orientation-preserving) automorphism group is isomorphic to PSL(2, 7), the second-smallest non-abelian simple group. The quartic was first described in (Klein 1878b).

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