Slides from recent talks that I have given for a variety of different audiences:

Research Talks

**Salem numbers and short geodesics****Sumar mu(n): un algoritmo elemental más rápido**(transparencias en Castellano/slides in Spanish)**Summing mu(n): an even faster elementary algorithm****Sumas de divisores**(transparencias en Castellano/slides in Spanish)**Counting and effective rigidity in algebra and geometry****Counting quaternion algebras****Espacios entre primos**(transparencias en Castellano/slides in Spanish)**Bounded gaps between primes and the length spectra of arithmetic hyperbolic 3-orbifolds****Divisor-sum fibers****Bounded gaps between primes****Abelian surfaces over finite fields with prescribed groups****The sign changes of Fourier coefficients of Eisenstein series****How often is #E(F_p) squarefree?****On the degrees of divisors of x^n-1**

Undergraduate Talks

**Twin primes and their kin****Curious patterns in the divisors of x^n-1****Number Theory and Security in the Digital Age****Bertrand's Postulate**

Pedagogy Talks

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