Talk

In this talk, we first review some classical results in the theory of the Mahler measure. Using classical results and assuming Lehmer’s conjecture, we then provide a proof of a conjecture due to P. Moree and A. Herrera-Poyatos.

We conclude by presenting some open questions concerning potential connections between Lehmer’s problem and the Mahler measure of polynomials arising from numerical semigroups.



 

I’ll discuss and motivate a theory of synthetic equivariant spectra in which equivariant stable homotopy types are suitably resolved by  even-dimensional cells. This recovers the Adams—Novikov spectral sequence based on equivariant complex bordism and additionally admits an interpretation in terms of motivic homotopy theory over the complex numbers.

The Hankel determinants built on moment sequences and their connection with transfinite diameter show their usefulness in proving irrationality of meaningful mathematical constants (think of the values of logarithm and $\pi$). They can be also viewed as particular generalisations of the celebrated Selberg integral, a closed-form period evaluation possessing a symmetry of root system. In my talk I will take a detour and discuss a general case of such Selberg-type integrals which a priory has nothing to do with irrationality. What are those creatures?!