The mindset I wish I had during my undergrad

I distinctly remember how guilty I felt on graduation day because I saw all of my math classes as just hoops to jump through. It felt like all I had done was memorize formulas, theorems, and definitions in each class for 4 years, and on graduation day, nothing really stuck. In this talk, I will share what I wish I could've told my undergrad self while we play with elementary math puzzles as inspiration.

An elementary problem equivalent to the Riemann hypothesis

In this talk, I will speak about my absolute favorite paper from the American Mathematical Monthly which is about an elementary problem equivalent to the infamous Riemann hypothesis which concerns the complex (nontrivial) zeros of the Riemann zeta function.

This elementary problem of Lagarias concerns the sum of divisors function and the harmonic number. If time allows, I will talk about Robin's inequality and superabundant numbers.

Big numbers matter too!

Consider the number 61,917,364,224. What's so special about it? Nothing really comes to mind. But this exact number was crucial towards a two-sentence published paper that gave a counterexample to one of Euler's famous conjectures that tried to generalize Fermat's Last Theorem. In this talk, I'll discuss why we can't just assume conjectures from famous people are "obviously'' true. This talk is a recap and continuation from last semester.

Max Engelstein - Winding for Wave Maps

Wave maps are harmonic maps from a Lorentzian domain to a Riemannian target. Like solutions to many energy critical PDE, wave maps can develop singularities where the energy concentrates on arbitrary small scales but the norm stays bounded. Zooming in on these singularities yields a harmonic map (called a soliton or bubble) in the weak limit. One fundamental question is whether this weak limit is unique, that is to say, whether different bubbles may appear as the limit of different sequences of rescalings.