Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over the same ring. We compute the asymptotic distribution of the cokernel of P(X(n)) as n goes to infinity. When P(t) is square-free modulo p, this […]
Title: Reading Topology from Open Books Speaker: Bahar Acu, Department of Mathematics, Pitzer College Abstract: How can we study topological shapes that are outside the realm of our imagination? In this talk, we will explore potential answers to that question by diving deep into dimensionality and topology via open books. Topology is the study of properties of shapes that […]
Title: A common pathway to cancer: oncogenic mutations abolish p53 oscillations. Abstract: The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to […]
Given votes for candidates, what is the best way to determine the winner of the election, if some of the votes have been corrupted or miscounted? As we saw in Florida in 2000, where a difference of 537 votes determined the president of the United States, the electoral college system does not seem to be […]
Title: Wallis and Landen: A Tale of two integrals Speaker: Victor Moll, Department of Mathematics, Tulane University Abstract: Victor Moll Abstract I was born in Santiago, Chile during the […]
Using elementary methods from differential equations and analysis we will consider the existence and multiplicity of solutions to semilinear partial differential equations with boundary conditions.
Title: PLSS: A Projected Linear Systems Solver (joint work with Michael Saunders) Abstract: Iteratively solving linear systems has proven to be useful for many large applications. Projection methods use sketching […]
Discrete Calculus studies discrete structures, such as sequences and graphs, using techniques similar to those used in Calculus for continuous functions. The basic idea of generating functions is to associate […]
Title: Sequential: A Meditation on Recurrence Speaker: Ghassan Sarkis, Department of Mathematics, Pomona College Abstract: Though I will share some adventures in sequence-generating neural networks just for fun, the majority […]
Title: Modeling size distributions and collisions in cloud microphysics Abstract: Feedbacks between a warming atmosphere, emission of aerosols, and clouds and precipitation are one of the most difficult aspects for […]
It is elementary and well known that a nonzero polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. It […]
