Anders Mörtberg: Yet Another Cartesian Cubical Type Theory yacctt
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: I will discuss recent work on developing a Cartesian cubical type theory inspired by the computational semantics of Computational Higher Type Theory of Angiuli et. al. Th
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Univalent Foundations of Mathematics - Vladimir Voevodsky
Univalent Foundations of Mathematics - Vladimir Voevodsky Institute for Advanced Study December 10, 2010 The correspondence between homotopy types and higher categorical analogs of groupoids which was first conjectured by Alexander Grothendieck naturally leads to a view of mathematics wh
From playlist Mathematics
Thorsten Altenkirch - 1/2 Towards a Syntax for Cubical Type Theory
One of the key problems of Homotopy Type Theory is that it introduces axioms such as extensionality and univalence for which there is no known computational interpretation. We propose to overcome this by introducing a Type Theory where a heterogenous equality is defined recursively and equ
From playlist T2-2014 : Semantics of proofs and certified mathematics
Computing with Univalence - Daniel Licata
Daniel Licata Carnegie Mellon University; Member, School of Mathematics September 28, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Univalent Foundations Seminar - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine
(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des
From playlist Mathematics
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
The Quest for the Ultimate Theory
Thirty-five years ago string theory took physics by storm, promising the coveted unified theory of nature’s forces that Einstein valiantly sought but never found. In the intervening decades, string theory has brought a collection of mind-boggling possibilities into the lexicon of mainstrea
From playlist Science Shorts and Explainers
Key Radio Unification Steps Before 1980 and Some Related Recent Radio Observations by A. Readhead
Extragalactic Relativistic Jets: Cause and Effect PROGRAM LINK: www.icts.res.in/program/ERG2015 DATES: Monday 12 Oct, 2015 - Tuesday 20 Oct, 2015 VENUE: Ramanujan Lecture Hall, ICTS Bangalore DESCRIPTION : Active Galactic Nuclei (AGN) are the luminous centers of galaxies that are belie
From playlist Extragalactic Relativistic Jets: Cause and Effect
Loose Ends: String Theory and the Quest for the Ultimate Theory
Thirty-five years ago string theory took physics by storm, promising the coveted unified theory of nature’s forces that Einstein valiantly sought but never found. In the intervening decades, string theory has brought a collection of mind-boggling possibilities into the lexicon of mainstrea
From playlist Watch Our Most Popular Programs
Do we need a Theory of Everything?
I get constantly asked if I could please comment on other people’s theories of everything. That could be Garrett Lisi’s E8 theory or Eric Weinstein’s geometric unity or Stephen Wolfram’s idea that the universe is but a big graph, and so on. First I explain what physicists mean by a theory
From playlist Physics
Beyond Einstein: In Search of the Ultimate Explanation
Albert Einstein spent his last thirty years unsuccessfully searching for a ‘unified theory’ — a single master principle to describe everything in the universe, from tiny subatomic particles to immense clusters of galaxies. In the decades since, generations of researchers have continued wor
From playlist Explore the World Science Festival
How can we test a Theory of Everything?
Today I explain what physicists mean by a Theory of Everything, what is the difference between a Grand Unified Theory, Quantum Gravity and a Theory of Everything, and how we can experimentally test a Theory of Everything. I tell you about some of the candidates for such a Theory of Everyth
From playlist Physics
After Dinner Speeches: Tamiaki Yoneya and John H. Schwarz
https://strings2015.icts.res.in/schedule.php
From playlist Strings 2015 conference
The Search for a Theory of Everything – with Yang-Hui He
The search for a theory of everything spans centuries, from Kepler, Galileo and Newton, to Faraday and Maxwell, to Einstein, Bohr, Dirac, and C.N.Yang, to recent advances in superstring theory. Watch the Q&A: https://youtu.be/FB7aeEevo3g This event is in collaboration with the London Inst
From playlist Ri Talks
Philosophy of Math: What math would aliens know? (Clement Hongler) | Ep. 12
Clement Hongler is a professor of mathematics at EPFL in Lausanne, Switzerland. We discuss some issues in the philosophy of mathematics, namely the relationship of mathematics to the real world, how math can be "natural" or historically contingent, the prospects of fundamental or unified t
From playlist Daniel Rubin Show, Full episodes
Brian Greene and Alan Alda Discuss Why Einstein Hated Quantum Mechanics
Albert Einstein was not a fan of quantum mechanics. He was annoyed by the uncertain, random nature of the universe it implied (hence the famous quote "God does not play dice with the universe"). So, Einstein tried to develop a unified theory that would circumvent what he saw as quantum mec
From playlist The Best of Brian Greene
Category theory for JavaScript programmers #24: monoidal functors
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers