Podcasts about Group theory

Richard Borcherds is a mathematician and professor at University of California Berkeley known for his work on lattices, group theory, and infinite-dimensional algebras. His numerous accolades include being awarded the Fields Medal in 1998 and being elected a fellow of the American Mathematical Society and the National Academy of Sciences. Patreon (bonus materials + video chat): https://www.patreon.com/timothynguyen In this episode, Richard and I give an overview of Richard's most famous result: his proof of the Monstrous Moonshine conjecture relating the monster group on the one hand and modular forms on the other. A remarkable feature of the proof is that it involves vertex algebras inspired from elements of string theory. Some familiarity with group theory and representation theory are assumed in our discussion. I. Introduction 00:25: Biography 02:51 : Success in mathematics 04:04 : Monstrous Moonshine overview and John Conway 09:44 : Technical overview II. Group Theory 11:31 : Classification of finite-simple groups + history of the monster group 18:03 : Conway groups + Leech lattice 22:13 : Why was the monster conjectured to exist + more history 28:43 : Centralizers and involutions 32:37: Griess algebra III. Modular Forms 36:42 : Definitions 40:06 : The elliptic modular function 48:58 : Subgroups of SL_2(Z) IV. Monstrous Moonshine Conjecture Statement 57:17: Representations of the monster 59:22 : Hauptmoduls 1:03:50 : Statement of the conjecture 1:07:06 : Atkin-Fong-Smith's first proof 1:09:34 : Frenkel-Lepowski-Meurman's work + significance of Borcherd's proof V. Sketch of Proof 1:14:47: Vertex algebra and monster Lie algebra 1:21:02 : No ghost theorem from string theory 1:25:24 : What's special about dimension 26? 1:28:33 : Monster Lie algebra details 1:32:30 : Dynkin diagrams and Kac-Moody algebras 1:43:21 : Simple roots and an obscure identity 1:45:13: Weyl denominator formula, Vandermonde identity 1:52:14 : Chasing down where modular forms got smuggled in 1:55:03 : Final calculations VI. Epilogue 1:57:53 : Your most proud result? 2:00:47 : Monstrous moonshine for other sporadic groups? 2:02:28 : Connections to other fields. Witten and black holes and mock modular forms.   Further reading: V Tatitschef. A short introduction to Monstrous Moonshine. https://arxiv.org/pdf/1902.03118.pdf Twitter: @iamtimnguyen Webpage: http://www.timothynguyen.org

Antoine GeorgesPhysique de la matière condenséeAnnée 2022-2023Réseaux de neurones, apprentissage et physique quantiqueSéminaire : Giulio Biroli - Renormalization Group Theory and Machine LearningIntervenant(s) :Giulio Biroli, ENS, Paris

In this episode of The Thinking Voice Podcast, hosts Robert Sussuma, Stephen King, and Dr. Jenevora Williams dive into the world of voice pedagogy and explore the concept of running courses in groups. The trio starts by discussing Berne's Group Theory, which is a theoretical framework for understanding human relationships and communication patterns in groups. They delve into the benefits of group learning, including the creation of a supportive community and the opportunity to learn from others.Robert, Stephen, and Jenevora also discuss the unique challenges of teaching voice in a group setting, including the need to tailor the course to the diverse needs and abilities of each student. They also touch on the importance of creating a safe and inclusive learning environment, where students feel comfortable sharing their thoughts and ideas.Throughout the episode, the trio shares their experiences and insights into the world of voice pedagogy, offering practical tips and advice for anyone considering running a voice course in a group setting. Whether you're a seasoned voice teacher or just starting out, this episode of The Thinking Voice Podcast is sure to provide valuable insights and inspiration.

Joining me us the Deep End today is Minn Kim. Minn spent a few years as an investor at Ridge, Bloomberg Beta and On Deck, backing founders as early as possible and is now building Plymouth to help extraordinary talent immigrate to the US. In this conversation we go deep into Minn's core belief – that technology enables step changes in human agency. We discuss navigating the idea maze, picking who to start a company with, why immigration is key to innovation and so much more.

Alex Kontorovich is a Professor of Mathematics at Rutgers University and served as the Distinguished Professor for the Public Dissemination of Mathematics at the National Museum of Mathematics in 2020–2021. Alex has received numerous awards for his illustrious mathematical career, including the Levi L. Conant Prize in 2013 for mathematical exposition, a Simons Foundation Fellowship, an NSF career award, and being elected Fellow of the American Mathematical Society in 2017. He currently serves on the Scientific Advisory Board of Quanta Magazine and as Editor-in-Chief of the Journal of Experimental Mathematics. In this episode, Alex takes us from the ancient beginnings to the present day on the subject of circle packings. We start with the Problem of Apollonius on finding tangent circles using straight-edge and compass and continue forward in basic Euclidean geometry up until the time of Leibniz whereupon we encounter the first complete notion of a circle packing. From here, the plot thickens with observations on surprising number theoretic coincidences, which only received full appreciation through the craftsmanship of chemistry Nobel laureate Frederick Soddy. We continue on with more advanced mathematics arising from the confluence of geometry, group theory, and number theory, including fractals and their dimension, hyperbolic dynamics, Coxeter groups, and the local to global principle of advanced number theory. We conclude with a brief discussion on extensions to sphere packings. Patreon: http://www.patreon.com/timothynguyen I. Introduction 00:00: Biography 11:08: Lean and Formal Theorem Proving 13:05: Competitiveness and academia 15:02: Erdos and The Book 19:36: I am richer than Elon Musk 21:43: Overview II. Setup 24:23: Triangles and tangent circles 27:10: The Problem of Apollonius 28:27: Circle inversion (Viette's solution) 36:06: Hartshorne's Euclidean geometry book: Minimal straight-edge & compass constructions III. Circle Packings 41:49: Iterating tangent circles: Apollonian circle packing 43:22: History: Notebooks of Leibniz 45:05: Orientations (inside and outside of packing) 45:47: Asymptotics of circle packings 48:50: Fractals 50:54: Metacomment: Mathematical intuition 51:42: Naive dimension (of Cantor set and Sierpinski Triangle) 1:00:59: Rigorous definition of Hausdorff measure & dimension IV. Simple Geometry and Number Theory 1:04:51: Descartes's Theorem 1:05:58: Definition: bend = 1/radius 1:11:31: Computing the two bends in the Apollonian problem 1:15:00: Why integral bends? 1:15:40: Frederick Soddy: Nobel laureate in chemistry 1:17:12: Soddy's observation: integral packings V. Group Theory, Hyperbolic Dynamics, and Advanced Number Theory 1:22:02: Generating circle packings through repeated inversions (through dual circles) 1:29:09: Coxeter groups: Example 1:30:45: Coxeter groups: Definition 1:37:20: Poincare: Dynamics on hyperbolic space 1:39:18: Video demo: flows in hyperbolic space and circle packings 1:42:30: Integral representation of the Coxeter group 1:46:22: Indefinite quadratic forms and integer points of orthogonal groups 1:50:55: Admissible residue classes of bends 1:56:11: Why these residues? Answer: Strong approximation + Hasse principle 2:04:02: Major conjecture 2:06:02: The conjecture restores the "Local to Global" principle (for thin groups instead of orthogonal groups) 2:09:19: Confession: What a rich subject 2:10:00: Conjecture is asymptotically true 2:12:02: M. C. Escher VI. Dimension Three: Sphere Packings 2:13:03: Setup + what Soddy built 2:15:57: Local to Global theorem holds VII. Conclusion 2:18:20: Wrap up 2:19:02: Russian school vs Bourbaki Image Credits: http://timothynguyen.org/image-credits/

Today we talk again with Dr Zack Wolske about the amazingly abstract topic of Group Theory. Come along for the ride. To all our listeners out there, we are so happy to say that you can head over to https://brilliant.org/mpp , and the first 200 of you to sign up will get 20% off your premium membership.   Discord: https://discord.gg/M6TMgFA4xb Instagram: @math.physics.podcast Email: math.physics.podcast@gmail.com Twitter: @MathPhysPod  

In this episode Cody Roux teaches some interesting concepts that people care about in Mathematics and Logic as a way to try to understand what is going on in the universe around us! In particular we will try to explain concepts such as Impredicativity, Excluded Middle, Group Theory, Model Theory, Kripke Models, Realizability, The Markov Principle, Cut Elimination, and other stuff! Links Cody's website Cody's dblp

In this episode Cody Roux teaches some interesting concepts that people care about in Mathematics and Logic as a way to try to understand what is going on in the universe around us! In particular we will try to explain concepts such as Impredicativity, Excluded Middle, Group Theory, Model Theory, Kripke Models, Realizability, The Markov Principle, Cut Elimination, and other stuff! Links Cody's website Cody's dblp

In this episode Cody Roux teaches some interesting concepts that people care about in Mathematics and Logic as a way to try to understand what is going on in the universe around us! In particular we will try to explain concepts such as Impredicativity, Excluded Middle, Group Theory, Model Theory, Kripke Models, Realizability, The Markov Principle, Cut Elimination, and other stuff! Links Cody's website Cody's dblp

Buckle your seatbelt for another math-heavy episode.  Today we are joined by Dr. Paul "Connor" Whitaker, who dives into his research into group theory and its application to atomic physics.  

Today we talk with Jon from the YouTube channel Epic Math Time. Enjoy this great discussion as we get somewhat of an introduction to the amazing world of Group Theory. Epic Math Time: https://www.youtube.com/channel/UCisjF-Un7hf9lsMhoStF3OQ Power Log Video: https://www.youtube.com/watch?v=ofy2Kw2sIZg   To all our listeners out there, we are so happy to say that you can head over to brilliant.org/mpp, and the first 200 of you to sign up will get 20% off your premium membership.   Instagram: @math.physics.podcast Tiktok: @math.physics.podcast Email: math.physics.podcast@gmail.com Twitter: @MathPhysPod

References: Abstract Algebra - Wikipedia https://en.wikipedia.org/wiki/Abstract_algebra “Group theory, abstraction, and the 196,883-dimensional monster” - 3Blue1Brown https://www.youtube.com/watch?v=mH0oCDa74tE Axiomatic System - Wikipedia https://en.wikipedia.org/wiki/Axiomatic_system Axiom - Wikipedia https://en.wikipedia.org/wiki/Axiom Pure Mathematics - Wikipedia https://en.wikipedia.org/wiki/Pure_mathematics Group Theory - Wikipedia https://en.wikipedia.org/wiki/Group_theory Group (Algebra) - Wikipedia https://en.wikipedia.org/wiki/Group_(mathematics) Main Classes of Groups in Group Theory - Wikipedia https://en.wikipedia.org/wiki/Group_theory#Main_classes_of_groups Classification of Finite Simple Groups - Wikipedia https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups Finite Group - Wikipedia https://en.wikipedia.org/wiki/Finite_group Lie-Type Group - Wolfram Mathworld https://mathworld.wolfram.com/Lie-TypeGroup.html Monster Group - Wikipedia https://en.wikipedia.org/wiki/Monster_group Monstrous Moonshine - Wikipedia https://en.wikipedia.org/wiki/Monstrous_moonshine J-invariant and Q-expansion - Wikipedia https://en.wikipedia.org/wiki/J-invariant#The_q-expansion_and_moonshine Continuous Symmetry - Wikipedia https://en.wikipedia.org/wiki/Continuous_symmetry Geometric Group Theory - Wikipedia https://en.wikipedia.org/wiki/Geometric_group_theory

Our guest this week, Sam Fisher, just completed his Master's in Mathematics at McGill University and is now embarking on a transatlantic PhD in Mathematics at the University of Oxford. He treats us to a journey through the conceptual underpinnings of his research in the field of Geometric Group Theory. Whether you're a math enthusiast, or just a curious mind, you'll find this episode to be refreshing reminder of the beauty and elegance of mathematics. Enjoy! Tune in for Answers to Questions Like What is Geometry, and what kinds of geometric spaces can we imagine? What would giant triangles look like on the surface of the earth? Why are some mathematicians incapable of differentiating between mugs and donuts? How do you create mathematically complex transformations every time you tie your shoelaces? Where do symmetries crop up in the mathematical and real world? and many, many, many more! Topics & Concepts Mathematical Insights Mathematical Physics Geometry Euclidean & Non-Euclidean Spaces Curvature ft. Totally Trippy Triangles Topology Rubber-Sheet Geometry Mugs & Donuts Knot Theory Group Theory Geometric Group Theory Betti Numbers Sam's "Aggressive Saddles" The Secret Life of Words Audio Course (Coupon Code) Using 'TEACHER60' or this link (https://listenable.io/web/plans/?coupon=TEACHER60) you can get 60% off your first year of Listenable (it's only $24, or $2/mo)! It expires by May, 10th. Btw, it's the biggest discount Listenable has ever offered. Exciting, right? Keep that wallet thick and expand your brain volume at the same time! My New Audio Course on Listenable: The Secret Life of Words https://listenable.io/web/courses/402/the-secret-life-of-words/ Does free will exist? Maybe. Regardless, please share your cherished feedback with me at abstractcast@gmail.com! Liking the show? Drop us a juicy 5-star rating or a written review on Apple Podcasts! Support the show by Following & Subscribing on: Spotify, Facebook, Instagram & Twitter --- Send in a voice message: https://anchor.fm/abstractcast/message

Nadir Jeevanjee is one of those rare people who have both depth and breadth in their skills. He is probably the only person who ever wrote a textbook about tensors and group theory while taking a few years off from grad school to tour with a rock band, and that fact alone should make you want to listen to this interview. Nadir was born and raised in Los Angeles, and when he was 12 or 13, he got obsessed with music, especially with drumming. Towards the end of high school, he joined The Calling, a rock band that had a huge hit on the radio in the early 2000s. He went to college with the goal of becoming a professional musician, but found himself enjoying physics classes more than music theory, so much so that he embarked on a PhD in physics at UC Berkeley. About three years into it and struggling with a bit of a "mid-PhD crisis", Nadir left academia for what turned out to be four years, to tour the country with another band — that's when he wrote that textbook about tensors. Eventually, though, he finished his PhD and moved into atmospheric science. He is now a Research Physical Scientist at NOAA's Geophysical Fluid Dynamics Laboratory in Princeton, where he studies the physics of clouds, radiation, and climate, using a hierarchy of approaches ranging from pencil-and-paper theory to comprehensive computer simulations. His specialty is to condense the complexity of the atmosphere into simple, elegant frameworks that are tractable for human brains. Nadir is also deeply engaged in the communication of climate science to the wider world and confounded a group called Climate Up Close, which tries to make the essentials of climate science accessible to a broad audience and give people the opportunity to talk directly with climate scientists. "So I started to give public talks called "Climate Science: How Do We Know What We Know?", trying to focus on evidence and trying to de-emphasize the consensus on climate change. It's a very useful fact for people who don't know it, but for people who do know there's a consensus but aren't convinced by that, I think that beating them over the head with it if they've already heard it, I think can backfire. And so I wanted to try an approach where I just focused on the evidence. [...] And not only try to share a little bit of what we know about climate science, but also get face time." The interview with Nadir Jeevanjee was recorded in November 2020.  Nadir's website  His book, An Introduction to Tensors and Group Theory for Physicists Climate Up Close Three blackboard lectures on simple models in climate science, which Nadir gave in February 2018 in Princeton

Juan & Terence attempt to tackle the monster topic of Yang-Mills theory. Gauge Theory, topology, quantum field theory, differential geometry, group theory, and more all have a relationship with Yang-Mills theory.

You can understand why one need to learn group theory in their topic abstract algebra is explained here in Simplified manner. --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app

How group theory begun . . .

The bloody weather again. Gunnar cooks professionally as meat engine with guanciale.  Tyler gets ignored.  Chefs are sleezy used car salesmen who add value to meats by cutting them to pieces like the property brothers on love it or list it.  MAGNITUDINALLY BETTER cooking tips with Gunnar who HATES tomatoes. The GOD frequency and PURE music.  Gunnar teaches us about Buddhist and christian music traditions.  Healing crystal music and religious discrimination.  Tyler still gets ignored, and 6 dimensional music. Exciting technical difficulty that made it into the final cut where Tao artfully, clearly, and concisely expounds SECRET music EXPERT insights. Tyler stops being ignored and becomes a BAKER to avoid declaring bankruptcy.  Sourdough bread should KILL US ALL. Tao hates nice things and is an unknowing car bigot. Scientist chef, Gunnar Leitner, suggests eating moldy bread, and instructs the monkeys on the health benefits of botulism. Fromage connoisseur tip EXPLAINED: Slaughtering baby goats is a reliable means to finding quality cheeses. Rotten cabbage evolutionary innovations > economically viable electric cars and controlled fusion. Gunnar's SCIENTIFIC dog cereal with 20% rotten science milk TM.  Buy his upcoming SCIENTIFIC cookbook to learn more. Ducks die from bread, but Tyler won't go bankrupt because ducks don't BUY bread, human's do, but humans put the bread in the milk to get it soggy for 3 hours - PARISIAN dog le chien oui/non bibliothèque bonjour. AKA Feeding your dogs EXPLAINED: put a smile on your dog's face, feed it science milk bread in cereal. GODS HAVE NO EMOTION, but Gunnar's dog is a genuinely happy boy. Pet food conspiracies:  Pigeons and old people have a deep connection (unity through opposites Heraclitus style) through bread. Komodo dragons are DEATH. Simple microtone sampler by Michael Dean (Just Intonation vst): https://biptunia.com/?p=3990 Planets piano video: https://youtu.be/zvG4fXo-UK0 Infinite Monkeys FASHION (we all SUPPORT this (not sponsored, we just love the products)): https://goop.com/ Heraclitus (ignore the relativist and flux interpretations of his work - they're bullshit): https://en.m.wikipedia.org/wiki/Heraclitus Heraclitus basically anticipated Group Theory 2300 years before it emerged in 1800s: https://en.m.wikipedia.org/wiki/Group_theory www.tylerjwenzel.com www.gunnarleitner.com www.taogaede.com

Children who are being taught mathematics often balk at the idea of negative numbers, thinking them to be fictional entities, and often only learn later that they are useful for expressing opposite extremes of things, such as considering a debt an amount of money with a negative sum. Similarly, students of mathematics often are puzzled by the idea of complex numbers, saying that it makes no sense to be able to take the square root of something negative, and only realizing later that these can have the meaning of two-dimensional direction and magnitude, or that they are essential to our modern understanding of electrical engineering. Our discussion today will be much more abstract than that. Much like in our discussion in episode five, "Language of the Universe", we will be discussing how math and physics draw inspiration from one another; we're going to talk about what different fields (such as the real, complex, and quaternion fields) seem to predict about our universe. So how are real numbers related to classical mechanics? What does this mean complex numbers and quaternions are related to? And what possible physicses exist? License is Creative Commons Attribution-ShareAlike 4.0 (See https://creativecommons.org/licenses/by-sa/4.0/) --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

Nick chats with Elise and Mandi, about some Sake concepts. From deductive wine tasting to advanced cocktail techniques, Medium Plus is all about elevating the taste and skills associated with enjoying these fine beverages.

Adam Hansen is the VP of Innovation at Ideas to Go and co-author of the book, "Outsmart Your Instincts: How the Behavioral Innovation™ Approach Drives Your Company Forward." How does someone who challenges assumptions for a living view his own faith? And when a marriage and family was then built on the shared belief system, what is the role of communication, religious pluralism, and grace in the process? It's a fascinating conversation to be had. (Especially if you like to geek out on Human Behavior and things like Group Theory like us....) ;) And if you haven't taken part in our completely anonymous (unless you don't want it to be!) 3 minute survey yet, we'd love to have you join us!

References: Prasanna Venkatesh on LinkedIn What is a Group? Youtube What is Group theory? Wikipedia Rubik’s Cube group Wikipedia Notes for a 2-week course on Rubik’s Cube and Group Theory taught by Janet Chen – a senior preceptor at Harvard University A course on Modern Algebra Intro and Outro music by Lee Rosevere ‘Here’s the thing‘ from Music for Podcasts 3 Corrigendum: A 180 degree rotation for a rectangle is also a symmetry. A zero degree rotation is the identity element for the rectangle symmetry group.

Remarks by Fr. Thomas Hosinski, CSC, UP Emeritus Professor of Theology, as we celebrate the launch of his new book, The Image of the Unseen God: Catholicity, Science & Our Evolving Understanding of God, 11/1/17. Hosted by the Garaventa Center.

Associative array mathematics. Relevant operations on an associative array. Semirings and matrices. See MIT Press book "Mathematics of Big Data."

The understanding of the possible geometries in dimension 3 is one of the triumphs of 20th century mathematics. In this talk Martin Bridson explains why such an understanding is impossible in higher dimensions. When one wants to describe the symmetries of any object or system, in mathematics or everyday life, the right language to use is group theory. How might one go about understanding the universe of all groups and what kinds of novel geometry might emerge as we explore this universe? Martin Bridson became Head of the Mathematical Institute on 01 October 2015. To mark the occasion he gave this Inaugural Chairman's Public Lecture.

The understanding of the possible geometries in dimension 3 is one of the triumphs of 20th century mathematics. In this talk Martin Bridson explains why such an understanding is impossible in higher dimensions. When one wants to describe the symmetries of any object or system, in mathematics or everyday life, the right language to use is group theory. How might one go about understanding the universe of all groups and what kinds of novel geometry might emerge as we explore this universe? Martin Bridson became Head of the Mathematical Institute on 01 October 2015. To mark the occasion he gave this Inaugural Chairman's Public Lecture.

Introducing reducible representations: what happens if we apply two symmetry operations to a molecule in sequence?

Assigning an irreducible representation to molecular vibration

If you experience any technical difficulties with this video or would like to make an accessibility-related request, please send a message to digicomm@uchicago.edu. Partha Niyogi Memorial Conference: "The Computational Magic of the Ventral Stream: From Visual Development to Group Theory, Hebbian Learning, and Wavelets". This conference is in honor of Partha Niyogi, the Louis Block Professor in Computer Science and Statistics at the University of Chicago. Partha lost his battle with cancer in October of 2010, at the age of 43. Partha made fundamental contributions to a variety of fields including language evolution, statistical inference, and speech recognition. The underlying themes of learning from observations and a rigorous basis for algorithms and models permeated his work.

If you experience any technical difficulties with this video or would like to make an accessibility-related request, please send a message to digicomm@uchicago.edu. Partha Niyogi Memorial Conference: "The Computational Magic of the Ventral Stream: From Visual Development to Group Theory, Hebbian Learning, and Wavelets". This conference is in honor of Partha Niyogi, the Louis Block Professor in Computer Science and Statistics at the University of Chicago. Partha lost his battle with cancer in October of 2010, at the age of 43. Partha made fundamental contributions to a variety of fields including language evolution, statistical inference, and speech recognition. The underlying themes of learning from observations and a rigorous basis for algorithms and models permeated his work.

Core Group Theory discussion with bestselling author Art Kleiner. Kleiner reveals that every organization is driven by a desire to satisfy a Core Group of influential individuals and explains why understanding this group’s expectations is the key to success.

A conversation about econophysics, generating genuine randomness and the rise of blogs with mathematical journalist and blogger Brian Hayes, author of Group Theory in the Bedroom. [download show] [MOI home] [MOI archive]

Gary Stix discusses his July Scientific American cover article on DNA evidence for the history of human migration. And editor in chief, John Rennie, talks about the neuroscience of dance, the quantum cosmos and Rubik's Cubes. Plus, we'll test your knowledge of some recent science in the news. Web sites mentioned on this episode include www.sciam.com/sciammag

Professor Ian Stewart talks about the life of Evariste Galois – the failed revolutionary who developed Group Theory and changed the way we think about mathematics, physics and the world around us.