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@sc_griffith It's so tiny I love this bunny so much

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@sc_griffith It's so tiny I love this bunny so much

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The universe is expanding. This means at one point in time it was the size of a rabbit

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The universe is expanding. This means at one point in time it was the size of a rabbit

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At 41 years old, Cuban Greco-Roman wrestler Mijaín López has just won his 5th gold medal in his 5th Olympic games (2008, 2012, 2016, 2020, and 2024), something no Olympic athlete has ever done before.

Anyway here is a screenshot of him saying something relatable

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At 41 years old, Cuban Greco-Roman wrestler Mijaín López has just won his 5th gold medal in his 5th Olympic games (2008, 2012, 2016, 2020, and 2024), something no Olympic athlete has ever done before.

Anyway here is a screenshot of him saying something relatable

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Screenshot of an interview with Mijaín López, he is saying "the pains in the body are there"

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Teddy Riner, already the most decorated judo practitioner of all time, just got his *fourth* Olympic gold medal. Here he is hitting a judo throw (seems to be a Harai Goshi) on a Teddy Bear:

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Teddy Riner, already the most decorated judo practitioner of all time, just got his *fourth* Olympic gold medal. Here he is hitting a judo throw (seems to be a Harai Goshi) on a Teddy Bear:

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Teddy Riner hitting a judo throw on a Teddy Bear

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New preprint (with coauthors Taylor Dupuy, Colin Ingalls, and Adam Logan) is now out!

Maybe you've heard about the hyperbolic plane - a very weird example of non-Euclidean geometry where parallel lines diverge away from each other and where the sum of the angles of a triangle are less than 180 degrees. The attached picture is M.C. Escher's "Circle Limit III" depicting the hyperbolic plane.

The hyperbolic plane (in the form of the upper half-plane) is also home to important objects in number theory such as modular forms.

Now there are also higher-dimensional hyperbolic spaces - for instance if you consider space and time as one entity (Minkowski spacetime) it is a 4D hyperbolic space.

Can we also have a theory of modular forms in such higher-dimensional hyperbolic spaces? The answer is yes. In 3D hyperbolic space for instance we have "Bianchi modular forms", very notable for not being directly accessible by algebraic geometry! These were studied by mathematicians such as John Cremona and many others.

In our work we go even higher and lay down foundations for studying certain (I would say number-theoretic) aspects of higher-dimensional hyperbolic spaces such as modular forms, using the theory of Clifford algebras and spin. Please check it out if you are interested!

https://arxiv.org/abs/2407.19122

#Math #Mathematics #NumberTheory #Geometry

# orderedItems[].object.contentMap.en
New preprint (with coauthors Taylor Dupuy, Colin Ingalls, and Adam Logan) is now out!

Maybe you've heard about the hyperbolic plane - a very weird example of non-Euclidean geometry where parallel lines diverge away from each other and where the sum of the angles of a triangle are less than 180 degrees. The attached picture is M.C. Escher's "Circle Limit III" depicting the hyperbolic plane.

The hyperbolic plane (in the form of the upper half-plane) is also home to important objects in number theory such as modular forms.

Now there are also higher-dimensional hyperbolic spaces - for instance if you consider space and time as one entity (Minkowski spacetime) it is a 4D hyperbolic space.

Can we also have a theory of modular forms in such higher-dimensional hyperbolic spaces? The answer is yes. In 3D hyperbolic space for instance we have "Bianchi modular forms", very notable for not being directly accessible by algebraic geometry! These were studied by mathematicians such as John Cremona and many others.

In our work we go even higher and lay down foundations for studying certain (I would say number-theoretic) aspects of higher-dimensional hyperbolic spaces such as modular forms, using the theory of Clifford algebras and spin. Please check it out if you are interested!

https://arxiv.org/abs/2407.19122

#Math #Mathematics #NumberTheory #Geometry

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Once upon a time there were equal amounts of matter and antimatter in the universe. Then rabbits chewed the antimatter

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Once upon a time there were equal amounts of matter and antimatter in the universe. Then rabbits chewed the antimatter

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@DensityPoint Congratulations!

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@DensityPoint Congratulations!

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@sc_griffith Hope you're doing okay, "skull fractures" sound super scary to me

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@sc_griffith Hope you're doing okay, "skull fractures" sound super scary to me

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People say you should find a job doing something you love but honestly there is really no such thing. Once you start doing something for a living it is no longer that same thing you used to do out of love

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People say you should find a job doing something you love but honestly there is really no such thing. Once you start doing something for a living it is no longer that same thing you used to do out of love

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The choice of hard shell vs soft shell taco depends on whether you want to prioritize armor or mobility

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The choice of hard shell vs soft shell taco depends on whether you want to prioritize armor or mobility

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Just trained at El Niño Training Center at South San Francisco, which is headed by former UFC title contender Gilbert Melendez

I couldn't make their MMA class so I settled for their Muay Thai sparring class followed by their jujitsu class (and I only had one hour of sleep last night!)

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Just trained at El Niño Training Center at South San Francisco, which is headed by former UFC title contender Gilbert Melendez

I couldn't make their MMA class so I settled for their Muay Thai sparring class followed by their jujitsu class (and I only had one hour of sleep last night!)

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While any part of my body remains in contact with the ground I will never be defeated. This is because there are bunnies under the ground

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While any part of my body remains in contact with the ground I will never be defeated. This is because there are bunnies under the ground

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@ach I guess so I've never used much of anything else

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@ach I guess so I've never used much of anything else

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I hate computers

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I hate computers

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Windows decided to update in the middle of a zoom meeting computers are amazing

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Windows decided to update in the middle of a zoom meeting computers are amazing

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I'm at a conference again (or rather a workshop, on Koszul duality in the local Langlands program in Moraga, CA) so you know what that means - pictures of ducks

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I'm at a conference again (or rather a workshop, on Koszul duality in the local Langlands program in Moraga, CA) so you know what that means - pictures of ducks

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Turtles

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Turtles

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Famous Bridge

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Famous Bridge

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Picture of the Golden Gate Bridge surrounded by fog