Rajan Mehta

Math, physics, hot sauce enthusiast, assistant LEGO builder

[Rajan Mehta @RealRajanMehta]

New preprint with H. Bursztyn, A. Cattaneo, and M. Zambon. This project started in the year of our lord 2006 so it has been a long time coming. https://t.co/7Y5gv8hDzE

Here’s a thread explaining what it’s about, starting with some preliminaries:
1/14

[Rajan Mehta @RealRajanMehta]

A little-known fact about Lindsay Graham is that he had a Ph.D. in Math. Wrote his thesis about the binomial theorem. Not the best thesis ever but he gets points for effort.

[arXiv math.AT Algebraic Topology @mathATb]

Marx, Mehta: Coherent span-valued 2D TQFTs https://t.co/BzEM4yxUgf https://t.co/w9zjUEO0Zc https://t.co/Gf3kxH36Ua

[Rajan Mehta @RealRajanMehta]

Teaching my students that (2,2) + (2,2) = (5,5)

(in the elliptic curve y^2 = x^3 + 5x^2 - x over F_11)

don’t know if western civilization can recover from this

[Rajan Mehta @RealRajanMehta]

Met a guy with a physics background who said he thinks photons have mass. What’s the story here, is this a real theory people are working on?

[Rajan Mehta @RealRajanMehta]

Ideally it would be something where you apply stokes and it helps to elucidate the geometric meaning in terms of surface areas on the sphere

[Rajan Mehta @RealRajanMehta]

(xdy^dz + ydz^dx + zdx^dy)/r^3 is the standard example of a 2-form that is closed but not exact on R^3-{0}. But of course it is exact on, say, the region where z>0. Is there a “nice” formula for a primitive there?

[Rajan Mehta @RealRajanMehta]

@adittyachaudhu1 Congratulations!

[Rajan Mehta @RealRajanMehta]

Since we’re scrutinizing dissertations, I can think of a certain thesis about the binomial theorem that deserves to be put under the microscope

[Rajan Mehta @RealRajanMehta]

@PatNicodemus Thanks, in retrospect this seems obvious! Any references you can point me to where this comes up?

[Rajan Mehta @RealRajanMehta]

If X is a monoid object in a monoidal category C then the slice category C/X is monoidal, and we can talk about monoid objects there. What does all this look like in terms of data on C? Is there a good reference where these things are worked out?

[Rajan Mehta @RealRajanMehta]

@LEMpropaganda Cool! A simple example of this is {0,1,2,3,many} which, if we believe the child psychologists, is the number system we’re born with!

[Rajan Mehta @RealRajanMehta]

What are some good examples of commutative monoids that don’t satisfy cancellation, i.e. there exist x,y,z such that x+y = x+z but y doesn’t equal z

[Rajan Mehta @RealRajanMehta]

@ptwiddle @mdelhoyo18 Very cool, I hadn’t thought of this!

[Rajan Mehta @RealRajanMehta]

@VigeVigoleis Nice!

[Rajan Mehta @RealRajanMehta]

@mdelhoyo18 Yes, these are good! I think we shouldn’t forgive the K-theorists for turning a perfectly good monoid into a group

[Rajan Mehta @RealRajanMehta]

I have had it with twinkle twinkle little star. Like it’s 2023, we know exactly what they are

[Rajan Mehta @RealRajanMehta]

In other words, the Law of Conservation of Energy is a property that is *built into the structure of symplectic geometry*

Noether’s Theorem (correspondence between symmetries and conserved quantities) also holds similarly

This and other cool stuff some other time 7/7

[Rajan Mehta @RealRajanMehta]

A couple of months ago there was a symplectic geometry lovefest going on, but I didn’t have time to chime in. So here goes. I’ll try to explain WHY symplectic geometry is the thing for Hamiltonian mechanics 1/

[Rajan Mehta @RealRajanMehta]

This is why symplectic geometry works for mechanics. If you take the function that describes the energy in a system, its Hamiltonian vector field describes how the system changes over time.

It *automatically* points in a direction where the energy stays constant. 6/