NTS ABSTRACT

Return to NTS Spring 2016

Sep 8

Arunabha Biswas

Limiting values of higher Mahler Measure and cyclotomic polynomials.

We consider the k-higher Mahler measure m_k(P) of a Laurent polynomial P as the integral of log^k |P| over the complex unit circle. In number theory, Lehmer's conjecture and the appearance of higher Mahler measures in L-functions are the main sources of motivation for studying various properties of m_k(P). Beyond number theory, Mahler measure has connections with topological entropies of dynamical systems and polynomial knot invariants. In this talk I shall present (1) an explicit formula for the value of |m_k(P)|/k! as k approaches infinity, (2) some asymptotic results regarding m_k(P) and (3) a scheme to approximate special values of a class of L-functions.

Sep 22

Alex Smith

title coming soon

abstract coming soon

Sep 29

Steve Lester

title coming soon

abstract coming soon

Oct 6

Nicole Looper

Arboreal Galois representations of higher degree polynomials and Odoni's Conjecture

Since the mid-1980s, when the study of arboreal Galois representations first began, most results have concerned the representations induced by quadratic rational maps. In the higher degree case, by contrast, very little has been known. I will discuss some recent results pertaining to higher degree polynomials over number fields. This will include a partial solution to a conjecture made by R.W.K. Odoni in 1985.

Oct 13

Ling Long

title coming soon

abstract coming soon

Oct 20

Jack Klys

title coming soon

abstract coming soon

Oct 27

William Duke

Dec 15

Efrat Bank

Primes in short intervals on curves over finite fields

abstract coming soon