Research Areas

Take a finite set of points and a finite set of lines. How many incidences can there be between them? In the reals, this is the Szemeredi-Trotter theorem, but what about over arbitrary fields?

https://arxiv.org/pdf/1609.06284.pdf

Given a finite set of numbers, how much arithmetic structure can it have? Can it have both additive and multiplicative structure?

https://arxiv.org/abs/2005.11145 [sum product]

https://arxiv.org/pdf/1607.05053.pdf [energy variant]

I give you n points in the plane. Between every pair of points you measure a distance and write it down in a notebook. What's the fewest different numbers you could have written?

https://arxiv.org/pdf/2003.00510.pdf