Past Events

In this talk I will discuss distribution results for traces of Frobenius for various families of elliptic curves with respect to the Lang--Trotter conjecture and extremal primes. These are related to the work of Sha--Shparlinski on the average Lang-...

John Milnor's attempt at the higher algebraic K-groups of a field uses the field units as generators and the Steinberg relation as the only relation. The resulting Milnor K-groups map to the higher algebraic K-groups Daniel Quillen defined slightly...

Fairness in machine learning classification has been a topic of great interest given the increasing use of such classifiers in critical settings. There are many possible definitions of fairness and many potential sources of unfairness. Given this...

In this talk, we are interested in a general class of multiplicative functions. For a function that belongs to this class, we will relate its “short average” to its “long average”. More precisely, we will compute the variance of such a function over...

Supracellular actomyosin cables often drive morphogenesis in development. The origin of these cables is poorly understood. We show theoretically and computationally that under external loading, cell-cell junctions capable of mechanical feedback could...

The property |z||w| = |zw| of complex numbers leads naturally to the following question concerning sums of squares: in the polynomial ring R = Z[x_1,...,x_r, y_1,... y_s], what is the minimal n such that [(x_1)^2 + ... +(x_r)^2] [(y_1)^2 + ... +(y_s)...

Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-Kahler manifolds, and arise independently in mathematical physics. We reinterpret this condition in terms of...

In this talk we will give an exact characterization for the asymptotic distribution of quadratic forms in IID random variables with finite second moment, where the underlying matrix is the adjacency matrix of a graph. In particular we will show that...

Humans have been discussing the benefits and drawbacks of democratic vs. authoritarian governance for millennia, with perhaps the earliest and most famous discussion favoring enlightened authoritarian rule contained in Plato's 'Republic'. The...

In 1900, Hilbert posed the following problem: “Given a Diophantine equation with integer coefficients: to devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in (rational)...