#Simon Donaldson

[isomorphismes]

“the Yang-Mills equations are nonlinear, therefore there is little hope of finding a closed-form solution.” Such a statement seems plausible. Linear differential equations with constant coefficients are the only differential equations for which a general solution is given in closed form. As often occurs in life, however, the exceptions to the rule are sometimes more interesting than the rules themselves. Let us digress from quantum physics to the motion of water, where British shipbuilder John Scott Russell noticed a solitary wave in a canal in August 1834. Neither Airy nor Stokes accepted this observation, yet in 1895 Korteweg and de Vries found an equation for a wave travelling in shallow water in one direction: u̇ + 6•u•uₓ + uₓₓₓ = 0. The KdV equation is easily solved by restricting from two independent space-time dimensions (x,t) to a single dimension x−λt — a frame matching the speed λ of a travelling wave.

Mikhail Ilʹich Monastyrskiĭ, Riemann, Topology, and Physics

[purple-1995]

Imagine that boyfriend that is always the hornier one in the relationship.

Imagine him daily coming up to you with all kinds of ideas for your sex life. You will be minding your business and out of nowhere he will show you his phone with a random porn video. Would you like to try it, baby? 😏 Or he will show you a sex shop page with a toy you aren't even sure what it is supposed to do. But don't worry, he will explain it to you with heavy details 😋 He will even come up to you and tell you about this trick his best friend told him about, that he did on his girlfriend and she came so hard that she almost fainted! 🤯 Can he do it on you? 😍🙏🏻 If you are ok with his proposition, he will be SO excited! He will wait anxiously for the moment, like a child in front of the oven waiting for the cookies to be ready 🍪 If you are hesitant, he will turn on his puppy slutty face and try to change your mind, whining and moaning about how it will feel sooo good 🤤 All while touching you, kissing you and humping his hard on against your body 🥴 If you flat out refuse, he will pout but will understand 🥺 Will he ask you for a handjob as a consolation prize? Yes. After all, every relationship is made of compromises 😇

Horny!Boyfriend

[florabellalove]

LET ME SPEAK MY TRUTH 🦢🫶🏼

sometimes I just want to read a reverse comfort fic about some big burly character absolutely breaking down, call it a saviour kink or whatever but there seems to be an absence in this world

[m30wk1ttycat]

i need him, biblically.

[livefastdriveyoung]

A person can learn about a sport and come to like it through a WAG. Just saying. It's how I learned Football, because despite growing up in an American home, it wasn't until I realized that Gisele Bundchen was at that point married to one of them that I was like "huh, must be interesting."

If you've actively gotten into Football because of Taylor Swift, Hailee Steinfeld, or Olivia Culpo, or Simone Biles, or any other WAG, welcome. It's a really really complicated game of catch. Don't call it that to some people's faces, they will get very angry. You can cry when your team loses, you can cry when the other team has an underdog story. I cried like a baby over Brock Purdy. It's fun. Sports are fun.

If you got into F1 because of Nicole Scherzinger, first of all, hi, you're a real trooper. If you got into F1 because of Shakira, or Taylor, or Carmen or Alexandra, or Lily, or Charlotte, or Isa, or Rebecca, welcome. The sport is insanely toxic also. But like it's really fun to play "Are they gay or just European?" The cars are fast, they're insane, and they compete at a scale that is practically unheard of for a sport. They are the top 20. You can have a favorite driver and a different favorite team. You can have a favorite team principal. You can think a penalty is absolute trash, or that one was warranted. You can think some tracks are better than others. You can run the race on high speed if you watch it after the fact.

It's a valid way to join the sport. I promise.

Women bring women together in so many capacities. My friend got her first job because she went to a networking event for women in a field dominated by men. Why can't women bring women into sports?

[idciminlove]

Masterlists

Challengers Masterlist

COD Masterlist

Overwatch 2 Masterlist

[kath-reviews]

my beautiful blog

[deadqueerboys]

Y'all know what I'm talking about..

Tubs. Medium, fat.

Tom. Medium (almost big), not that fat or skinny.

Will. Big, skinny. We all know that.

Dreamie. It has to be fat and large or else i kms.

Sappy. Yk what they say about short boys.. medium almost big, fat.

Gogy. Medium, skinny. Fight me.

Karl. Bro has exactly 6.5 inches (16.7 cm), not fat tbh.

Jimmy. Big and fat. We all saw his Twitter and Instagram.

Nolan. Big, medium skinny.

Kris. Almost big, fat. My lady have a big cock, I wanna droll on it while calling her "mommy".

[transformers-mosaic]

Transformers: Mosaic #474 - "Darkest Spark"

Originally posted on April 12th, 2010

Story - Greg Donaldson Art - Lindsay Smith Letters - Franco Villa Thanks to - Simon Reeves

deviantART | Seibertron | TFW2005 | BotTalk

wada sez: So far as I can tell, this strip was adapted from a short story of Donaldson’s which I reckon preceded it? What the hell, I’ll archive the whole thing below. The year prior, Fun Publications had namedropped a Shattered Glass incarnation of Wheelie in Sky Lynx’s magazine profile; on deviantART, Donaldson said: “Simon and I bounced around the idea but it wasn't until afterwards that somewhat "offical" information came out regarding SG Wheelie and it matched the black and goldenrod coloring we had decided for him!” I have no idea what “official” information he’s referring to, so let me know if you have the source.

"Easy Decepticons. Hold your positions," Galvatron soothed over the communicator.

His laser rifle aimed into the darkness beyond the cargo bay entrance, Scourge had to fight the sensation that was causing his hands to tremble. He looked over at Cyclonus and quickly back, careful not to take his eyes off the blackness for more than an astrosecond. He squinted his optics to focus the available light and he thought he saw movement.

A scream in the distance.

Scourge tensed up immediately and tightened his finger on the trigger. “It’s him,” he whispered under his breath. From the area in front of him a glint of metal streaked toward him. Panicked, he fired his weapon erratically into the darkness. The black was intermittently lit by the muzzle flash and the flying metallic object bounced off his chest and fell to the ground in a wet thump. Liquid splattered on his body and on his chin. He looked down to see the object was square.

Scourge gasped as he realized it was Skywarp's severed head. A terrible death to be sure as his mouth was contorted in agony forever. Scourge fired into the still air, screaming.

Cyclonus followed suit as did Thrust and Dirge who were kneeling in front of them, arm cannons blasting into the distance.

Nothing. They ceased fire. Scanners on full spectrum.

Searchlights revealed 3 Sweeps bodies offlined. Then a vehicle emerged racing toward them. A silhouette as dark as deep space. They opened fire again but the sleek car easily evaded their laser fire and grenades. Missiles sailed past him. It transformed.

SLICE!

Thrust was offlined.

THUNK!

Dirge was down.

CRACK!

Cyclonus looked down to see an energon blade sticking out of his chest. His spark was pierced and he felt the life draining from him. He looked wearily over at Scourge who had slid to the floor leaving a trail of lubricant on the wall. His optics were black. Offlined.

Slowly Cyclonus turned his head and saw crimson optics glaring back at him. He felt chilled. A mech was clinging to his torso, holding on by Cyclonus' winged shoulders, legs around his waist. He was black with goldenrod accenting.

The dark mech looked into him and spoke quietly, "The optics are the window to the spark, Cyclonus. Watching you die this close is a bonus." He grabbed the energon blade and withdrew it from the Decepticon's chest. Thrusting it into the Con's optics, he pushed off the handle of the blade and jumped from the Decepticon while somersaulting in the air.

Cyclonus fell to the ground with a loud clang as the sinister mech landed on top of him.

"Decepticons die so easy, I think Prime sent me here to tease me.”

As he surveyed the carnage he had wrought, he pulled his weapon from the offlined Decepticon and wiped it clean of fluids. Slipping it into its sheath, his wrist communicator blipped. Annoyed at the disruption of the eerie silence he had proudly created, he didn't acknowledge the transmitter as it blared, "Wheelie, where are you?"

[cbjustmusic]

Nina Simone performing "Love Me Or Leave Me" on The Ed Sullivan Show in 1960. ________________________ Love Me Or Leave Me Music by Walter Donaldson; Lyrics by Gus Kahn

Love me or leave me and let me be lonely You won't believe me but I love you only I'd rather be lonely than happy with somebody else

You might find the night time the right time for kissing Night time is my time for just reminiscing Regretting instead of forgetting with somebody else

There'll be no one unless that someone is you I intended to be independently blue

I want your love, don't wanna borrow Have it today to give back tomorrow Your love is my love There's no love for nobody else

Say, love me or leave me and let me be lonely You won't believe me but I love you only I'd rather be lonely than happy with somebody else

You might find the night time the right time for kissing Night time is my time for just reminiscing Regretting instead of forgetting with somebody else

There'll be no one unless that someone is you I intended to be independently blue

Say I want your love, don't wanna borrow Have it today to give back tomorrow Your love is my love My love is your love There's no love for nobody else

[cryptfile]

ᝰ FANDOMS I’M CURRENTLY WRITTING FOR:

those marked in colored letters are the ones i’m currently simping on. Feel free to send promps, requests of characters or anything honestly. Always nice to recieve a message! / This list will be updated regularly so you guys can know what i’m into, also, if I forgot someone.

THE BOYS

Billy Butcher, Soldier Boy, Victoria Neuman, Starlight/Annie January, The Deep, A-Train, Frenchie, Sister Sage, Queen Maeve, Firecracker, Homelander, Hughie Campbell, Kimiko.

GEN V

Cate Dunlap, Jordan Li, Sam and Luke Riordan, Marie Moreau, Emma Myers.

HOUSE OF THE DRAGON

Rhaenyra Targaryen, Daemon Targaryen, Alicent Hightower, Jacaerys Velaryon, Aemond Targaryen, Aegon Targaryen, Harwin Strong, Criston Cole.

MARVEL

Loki Laufeyson, Sylvie Laufeydottir, Moonknight x3, Hawkeye/Comic!Clint Barton [recasted as Oliver Jackson-Cohen], Yelena Belova, Kate Bishop, Scarlet Witch/Wanda Maximoff, Pietro Maximoff, Steve Rogers, Matt Murdock/Daredevil, Deadpool, Peter Parker/Spider-Man’s in general, X-Men’s in general, Thor Odinson, Carol Danvers, Tony Stark, Doctor Strange, Bucky Barnes, Fantastic Four, Adam Warlock, Ant Man, Druig, Natasha Romanoff, and more since there are too many characters, feel free to ask!

HARRY POTTER

Remus Lupin [marauders era, post I war, nothing weird], Sirius and Regulus Black [marauders!era], James Potter [usually recasted as Dev Patel], Draco Malfoy, Theodore Nott.

BRIDGERTON

Eloise Bridgerton, Anthony Bridgerton, Benedict Bridgerton, Colin Bridgerton, Francesca Bridgerton, Daphne Bridgerton, Simon Basset, King George.

THE BEAR

Carmy Berzatto, Sydney Adamu, Richie Jerimovich, Luca.

TWILIGHT

Carlisle Cullen, Charlie Swan, Bella Swan, Edward Cullen, Alice Cullen, Rosalie Hale, Emmett Cullen, Jasper Hale, Leah Clearwater, Alec and Jane Vulturi, Benjamin.

YELLOWJACKETS

Natalie Scatorccio, Jackie Taylor, Shauna Sadecki, Van Palmer, Lottie Matthews, Taissa Turner, Misty Quigley.

GRISHAVERSE

Nikolai Lantsov, Kaz Brekker, Alina Starkov, Matthias Helvar, Aleksander Morozova / The Darkling, Nina Zenik, Inej Ghafa, Malyen Oretsev, Zoya Nazyalenski.

DAISY JONES AND THE SIX

Daisy Jones, Karen Sirko, Billy Dunne, Warren Rhodes, Eddie Roundtree.

THE HUNGER GAMES

Peeta Mellark, Finnick Odair, Young!Haymitch Abernathy, Katniss Everdeen, Johanna Mason.

STAR WARS

Anakin Skywalker, Qimir / The Stranger, Kylo Ren [yes, I have a type], Shin Hati, Han Solo.

MISC

Rafe Cameron [OBX], James Beaufort [Maxton Hall], Drew Starkey, Dean and Sam Winchester [Supernatural], Aaron Taylor Johnson in most of his roles aka Kick-Ass or Bullet Train, Robin Buckley [Stranger Things], Steve Harrington [Stranger Things], Rick Flag [DC], Harley Queen [DC], Battinson [DC], Art Donaldson, Mike Faist, Nicholas Chavez.

[blueopinions49]

Healthy/ Unhealthy Type 9

Healthy Social 9

Jean Grey 9w1 (so/sx)- In the pursuit of fairness and peace. Jeans looks to help others and create a more peaceful world.

Judy Hale 9w1 (so/sx)- Well meaning and all Judy tries her best to protect and take care of those around her. Even messing up from time to time.

Orel Puppington (9w1 so/sx)- Raised in a very toxic environment he looks to find a sense of peace and goodness in the world. Eventually growing up and becoming a great loving father.

Unhealthy Social 9

Cate Dunlap (9w1 so/sx)-I considered her to bean SX9 however her desire to be superior and her outgoing nature com through in the end when she has fully disintegrated towards her 6

Lottie Matthews (9w1 so/sp)- While stuck in the wilderness she seems to have lost her meds and eventually stops realizing the difference between reality and not.

Yoda (9w8 so/sp)- Took pore care of Anakin and when he lost the war he just retreated into exile. Until look came and even so he didn't do much.

Healthy Self Preservation 9

Carlos Oliveira (9w8 sp/so)- In the remake we a Carlos more focused on helping others and making sure everybody is okay while the end of raccoon city is happening.

Marceline (9w8 sp/sx)- She seems a bit detached in the beginning but as the show goes on we learn how much she craves connection and company.

Gregory Eddie (9w1 sp/so)- Struggling with his purpose on S1 we see him eventually deciding to stay in abbott and enjoying the company and people he meets.

Unhealthy Self Preservation 9

Queen Meave (9w8 sp/sx)- She becomes fully uninterested in the world and seems to have pretty nihilistic version of everyone. In the end she sacrifices herself for starlight and quotes being a hero.

Denji (9w8 sp/sx)- Due to his upbringing Denji seems only interested in the physical world and is constantly trying to settle for the small things in life.

Homer Simpson (9w8 sp/sx)- He has fully settled for the little things in life being neglectful and crude to his family.

Healthy Sexual 9

Bella Swan (9w8 sx/sp)- Unpopular opinion but other than new moon. Bella is quite healthy her only desire seems to be with Edward and finding love. Eventually rising to being a vampire.

Sophie Hatter (9w1 sx/so)- Her arc is all about that integration to 3 she becomes more assertive and starts to lover herself at her own age. Her confidence grows stronger as the movie goes on.

Betty Grof (9w1 sx/so)- While in AT I could see her as unhealthy I believe her saying goodbye to Simon and eventually being okay with being Golb is an example of her integration to 3.

Unhealthy Sexual 9

Adam (9w1 sx/sp)- his desire for connection and company drives him to complete isolation.

Art Donaldson (9w1 sx/so)- His desire to please Tashi makes him not have his own desire and his interest in tennis is only there for her.

Senua 9w8 (sx/sp) - Due to the treatment of his father she ends up isolating herself. She spends all of the first game trying to find her lover once again.

[mymanreedus]

My Ten, Norman Reedus, New York Times

1. 'Wild God by Nick Cave and the Bad Seeds

Nick Cave and Warren Ellis’s album “Carnage” was my go-to for the entire French filming portion of the first two seasons, and in Spain it’s this album. It just sings, full of life and stories and beautiful thundering bliss. I don’t know anyone that doesn’t love this band. Not one person.

2. ‘Nina Simone’s Gum’ by Warren Ellis

I met Warren in Paris and we immediately hit it off. When he told me of this book, I immediately got it. I find it interesting to learn of the things that inspire the people that inspire me. He had noticed Nina Simone take out her gum before a show and stick it under the piano. As soon as the show was over, he bolted toward the piano and ripped the gum out. He had a gold cast made of it. He was wearing it as a necklace.

3. Eggs Benedict at Coffee Parisien

My family and I are spending more time in Paris these days, and to have a good breakfast spot that serves up some taste of home is nice. And the staff are so cool. I think they know I stole a coffee cup, and they kind of looked the other way.

4. Julia Donaldson’s ‘Gruffalo’ Books

This has become the nightly story-time reading for me and my beautiful daughter, Nova. The whole series is great and it allows me to put on my Gruffalo voice, which I’m guessing is what he sounds like. I told her that I mentioned this book, and she asked why I didn’t mention “Creepy Crayon!,” which is another book that we love.

5. Yohji Yamamoto Pants

I walked in his Paris show and luckily didn’t fall. He walked up to me, put his hands in my hair, made it super messy and went, “You’re so sexy.” Then he pushed me out into the runway. I was terrified. I kind of got introduced to his pants at the show and I was like, “These are the most comfortable, flowy pants ever.” My suitcase has two types of pants: his and Dickies.

6. Prado Museum

I’m an executive producer on the show, so I have to do things with casting and locations and script revisions. My friend Ian Astbury, who sings in the Cult, was like, “Just stop working today and go to the Prado.” I put on my headphones and walked around in a glorious daze staring at the Goyas and my all-time favorite, Hieronymus Bosch. Just magic.

7. Cafe Gitane

It’s a spot I go to a lot. Luc Lévy, who owns the place, is a good friend and maybe the coolest person in New York. There’s all this history on that street. I’d ride my BMX bike through SoHo, back in the day, and I’d run over there and see people just sitting out front and catch up.

8. Erik Foss

Erik and I go way back and I have a lot of his art. I’ve seen it get better and better and cooler and cooler. It has this childlike quality but is also specific and so thought-out. I stare at what I have on the walls, and it puts me in the best mood.

9. Chateau Marmont

I used to live in L.A. when I was in my 20s, so I have a group of artist friends that live there, and I only see them at the Chateau Marmont. It always feels like home even if some rager is going on next door.

10. Hammam

I like to just sit in there for as long as I can take it. It’s like riding a motorcycle and putting on your helmet: You just kind of disappear. I like that.

Norman Reedus, The New York Times

[frank-olivier]

From Knots to Quantum: A Cultural and Mathematical Transformation

Shiing-Shen Chern was born in Jiaxing, China, in 1911, during a time of great change and upheaval in his homeland. From an early age, he displayed a remarkable aptitude for mathematics, and his journey in the world of differential geometry began at Nankai University and Tsinghua University, where he laid the foundation for his future academic endeavors. Chern's education took him to Germany, where he pursued his graduate studies at the University of Hamburg under the mentorship of Wilhelm Blaschke. It was here that Chern's passion for geometry flourished, and his doctoral research on the theory of webs marked the beginning of a brilliant career in mathematics.

Chern's contributions to differential geometry are vast and profound. He made significant advancements in the calculus of variations, the theory of differential forms, and the study of characteristic classes. His most celebrated achievement, the Chern-Weil theory, provides a powerful framework for constructing and understanding characteristic classes, which are essential tools in algebraic topology and differential geometry. The introduction of Chern classes revolutionized the study of complex manifolds and algebraic varieties. These classes capture the topological and geometric intricacies of these spaces and have become indispensable in various branches of mathematics. Chern's proof of the generalized Gauss-Bonnet theorem further solidified his place among the greatest geometers.

Beyond his mathematical prowess, Shiing-Shen Chern played a pivotal role in fostering mathematical exchange and collaboration between China and the Western world. In the mid-20th century, as China emerged from a period of isolation, Chern became a key figure in re-establishing mathematical connections with the international community. Upon his return to China in the 1980s, he took on the task of revitalizing mathematical research and education. Chern founded the Mathematical Research Institute of the Chinese Academy of Sciences, which became a hub for mathematical excellence and international collaboration. His vision and leadership attracted mathematicians from around the world, fostering a vibrant and diverse intellectual environment.

Chern's dedication to nurturing the next generation of mathematicians is evident in his establishment of the Nankai Institute of Mathematics at Nankai University and his later contributions to Zhejiang University. Through these institutions, he inspired and mentored countless students, many of whom became leading mathematicians.

Shiing-Shen Chern's influence extends far beyond pure mathematics, significantly impacting the field of Topological Quantum Theory (TQFT). TQFT is a fascinating area of mathematical physics that explores the connections between topology, geometry, and quantum mechanics, and Chern's contributions have been instrumental in its development.

Chern-Simons theory stands as a testament to the deep interplay between geometry and quantum theory. Named after Shiing-Shen Chern, Simon Donaldson, and James Simons, this topological quantum field theory is a masterpiece in mathematical physics. Chern-Simons theory assigns complex amplitudes to manifolds and knots, relying on the Chern-Simons form, a differential form derived from the curvature of connections on principal bundles. The Chern-Simons action functional, a central object in the theory, captures the geometric and topological aspects of manifolds, providing a powerful tool for understanding quantum systems. This theory finds applications in various areas of physics, including knot theory, quantum gravity, and condensed matter physics, offering insights into topological phases of matter.

Chern's work on characteristic classes, particularly the Chern classes, has been instrumental in the study of topological invariants, which are crucial in TQFT. These invariants remain unchanged under continuous deformations of manifolds and play a vital role in classifying topological phases. Chern classes, along with other characteristic classes, provide a rich toolkit for constructing and analyzing these topological invariants. The Chern-Simons invariant, derived from Chern-Simons theory, is a prime example with far-reaching implications. It distinguishes different 3-manifolds and connects to knot invariants like the Jones polynomial, which are of great interest in TQFT.

Chern's contributions to differential geometry have also influenced the study of quantum states and their geometric properties. The geometry of the space of quantum states, known as the projective Hilbert space, has become an important research area in mathematical physics. Chern's work on complex geometry and Kähler manifolds provides valuable insights into the structure of these spaces and their associated geometric invariants. Additionally, the concept of Berry phases in quantum mechanics, arising from the geometric properties of quantum state spaces, is connected to Chern's work on connections and curvature. These geometric phases find applications in quantum computing and quantum information theory.

The interplay of mathematics, history, and cultural exchange is captured in the documentary "Taking the Long View" by George Paul Csicsery. The film portrays Chern's life, his enduring legacy, and the tapestry of his contributions to mathematics and the cultural exchange between East and West.

Taking the Long View - The Life of Shiing-shen Chern (George Paul Csicsery, 2000)

Knots have been an integral part of human civilization for thousands of years, dating back to ancient times when they were used for practical purposes such as sailing, fishing, and weaving. However, the systematic study of knots as a mathematical discipline is a relatively modern development that has evolved over the centuries, intertwining with various scientific and intellectual pursuits.

In ancient civilizations like Egypt, Greece, and China, knots were used for practical purposes, such as securing objects, creating fishing nets, and recording information. The ancient Inca civilization in South America even developed a sophisticated system of recording information called "quipu," which used knotted strings to encode numerical data and possibly even more complex information.

During the Renaissance, knots continued to play a role in various crafts and trades, but the mathematical study of knots as a distinct field was not yet established..

The 19th century saw significant advancements in mathematics and physics, and it was during this time that knot theory began to take shape as a mathematical discipline. One of the pioneering figures in this field was the Scottish physicist and mathematician Peter Guthrie Tait. In the 1870s, Tait and his colleagues, including Thomas Kirkman and C.N. Little, embarked on a project to classify all possible knots with a given number of crossings. This effort, known as the "Tait Conjecture," aimed to create a table of knots and links, which would serve as a foundation for understanding their properties.

Tait's work laid the groundwork for the systematic study of knots, and he is often considered one of the founders of knot theory. He introduced the concept of "alternating knots" and developed techniques for distinguishing and classifying knots based on their diagrams.

In the early 20th century, mathematicians continued to build upon Tait's work and made significant contributions to knot theory. James Waddell Alexander II, a prominent American mathematician, introduced the concept of "knot invariants," which are mathematical quantities that remain unchanged under various deformations of a knot. These invariants provided a powerful tool for distinguishing and classifying knots.

Another influential figure during this period was Max Dehn, a German mathematician who made important contributions to the study of three-dimensional manifolds and knot theory. Dehn introduced the concept of "Dehn surgery," a technique for modifying three-dimensional spaces by cutting out and gluing back solid tori, which has deep connections with knot complements and the topology of three-dimensional spaces.

The mid-20th century witnessed a revolution in physics with the development of quantum mechanics. Surprisingly, this new branch of physics would have profound implications for knot theory. In the 1980s, the discovery of the Jones polynomial by Vaughan Jones, a mathematician working in the field of operator algebras, marked a significant turning point.

The Jones polynomial is a knot invariant that assigns a Laurent polynomial to each knot or link. It was initially discovered in the context of von Neumann algebras and subfactors in quantum physics, but its significance for knot theory was quickly recognized. The Jones polynomial provided a powerful tool for distinguishing knots and led to the development of other knot polynomials, such as the HOMFLYPT polynomial, which further enriched the theory.

The connection between knot theory and quantum physics deepened with the emergence of topological quantum field theories, mathematical models that describe the behavior of quantum systems in terms of topological and geometric properties. Edward Witten played a pivotal role in this development.

Edward Witten's foray into knot theory began in the late 1980s, a period marked by significant advancements in mathematical physics. Witten, already renowned for his contributions to string theory and quantum field theory, turned his attention to the intricate world of knots and links, seeking to understand their topological and geometric properties. Witten's interest in knot theory was not merely academic; he sought to uncover the deep connections between knot theory and quantum physics.

Shiing-Shen Chern's work in differential geometry and topology provided a crucial foundation for Witten's exploration of knot theory. Witten's groundbreaking insight was to relate Chern-Simons theory to knot invariants, such as the Jones polynomial. He showed that the Jones polynomial could be obtained from Chern-Simons theory, providing a physical interpretation for this important mathematical object.

Witten's exploration of knot theory has led to a deeper understanding of the role of knots and links in quantum field theory. He has studied the behavior of quantum fields in the presence of knotted configurations, revealing the intricate interplay between topology and quantum phenomena. This research has opened up new avenues for understanding the mathematical structure of quantum field theories and their connection to knot invariants.

Witten's research has explored the geometry of quantum state spaces, known as projective Hilbert spaces. He has used geometric and topological concepts, such as Kähler manifolds and Berry phases, to understand the structure and behavior of quantum systems in these spaces. This work builds upon Chern's contributions to differential geometry and topology, particularly in the study of complex manifolds and their geometric properties.

By building upon Chern's mathematical foundations, Witten has revealed the deep connections between geometry, topology, and quantum phenomena, opening up new avenues for research and a deeper understanding of the mathematical structure of the physical world.

Prof. Edward Witten: Knots and Quantum Theory (Institute for Advanced Study, April 2012)

Wednesday, October 9, 2024

[microwaveable-squish-cheese13]

✧.. information !!

ੈ♡˳ : hello!! my name is eden and this is my blog! i'm a july leo annnndd my favorite color is red, my favorite animal would be deer or like cats or something idk

ੈ♡˳ : my interests currently are outer banks, call of duty mw2, avatar (big blue people, not the last airbender), stranger things, hazbin hotel/helluva boss, jujitsu kaisen, marvel, challengers, sleep token, good girls, dune, harry potter, arcane, across/into the spiderverse, moon knight, the umbrella academy, annndd young sheldon !!!

ੈ♡˳ : i write for ... simon "ghost" riley, könig, art donaldson, steve harrington, viktor, literally any of the jjk men, miguel o'hara, loki laufeyson, bucky barnes, five hargreeves, paul atreides, marc spector, steven grant, vessel, ii, iii, iv, jj maybank, jake sully, or neteyam :)

ੈ♡˳ : i write angst, fluff, and whatever else besides smut bc idk how to write that .. 😻

ੈ♡˳ : aaannnnddd requests are open!!

.. and that's it !! goodbye for now, lovelies !!! ..

[ervotica]

𝐜𝐡𝐚𝐫𝐚𝐜𝐭𝐞𝐫 𝐥𝐢𝐬𝐭

crossed out = not currently writing, bold = favs

mcu; loki laufeyson, bucky barnes, steve rogers, miguel o’hara, wanda maximoff, pietro maximoff, kate bishop, natasha romanoff

the last of us; joel miller

challengers; art donaldson, patrick zweig, tashi duncan

jujutsu kaisen; nanami kento, satoru gojo

the marauders; regulus black, barty crouch jr, evan rosier, james potter, remus lupin, sirius black, marlene mckinnon, lily evans (poly combinations always preferred; wolfstar x reader, jegulus x reader, moonwater x reader, rosekiller x reader, poly!marauders, poly!slytherins)

fourth wing; xaden riorson, liam mairi, bodhi durran, garrick tavis, brennan sorrengail, aaric (cam) greycastle, ridoc gamlyn

greys anatomy; mark sloan, alex karev

criminal minds; aaron hotchner, derek morgan, spencer reid

acotar; azriel, rhysand, cassian, eris vanserra, nesta archeron, elain archeron, lucien vanserra, tamlin (+ my special polycule; elucien x tamlin x reader)

call of duty; simon “ghost” riley, könig, johnny “soap” mactavish, captain john price

house of the dragon; daemon targaryen, aegon ii targaryen, ser harwin strong

outer banks; rafe cameron, jj maybank, john b routledge, pope heyward

the maze runner; gally, thomas, minho

twilight; jasper hale, edward cullen, rosalie hale, emmett cullen, paul lahote, sam uley, seth clearwater (plus poly combinations)

the hunger games; finnick odair, peeta mellark, cato hadley, young coriolanus snow, sejanus plinth

stranger things; eddie munson, steve harrington, jim hopper

harry potter; fred weasley, mattheo riddle, theo nott, lorenzo berkshire, draco malfoy

chris evans/seb stan and co; lloyd hansen, andy barber, jake jensen, ransom drysdale, ari levinson, lee bodecker, charles blackwood, nick fowler, carter baizen

writing flings; felix catton, oliver quick