|
11:00am to 12:30pm - 440R - Logic Set Theory Michael Hehman - (UC Irvine) Algorithmic Randomness NOTE: Tuesday meeting This is the last lecture in an introductory survey of the theory of algorithmic randomness. The primary question we wish to answer is: what does it mean for a set of natural numbers, or equivalently an infinite binary sequence, to be random? We will focus on three intuitive paradigms of randomness: (i) a random sequence should be hard to describe, (ii) a random sequence should have no rare properties, and (iii) a random sequence should be unpredictable, in the sense that we should not be able to make large amounts of money by betting on the next bit of the sequence. Using ideas from computability theory, we will make each of these three intuitive notions of randomness precise and show that the three define the same class of sets. |
|
2:00pm - 510R Rowland Hall - Combinatorics and Probability Michael Cranston - (UCI) Erdos-Kac Central Limit Theorem The Erdos-Kac Central Limit Theorem says that if one selects an integer at random from 1 to N, then the number of distinct prime divisors of this number satisfies a Central Limit Theorem. We (the speaker in joint work with Tom Mountford) give new proof of this result using the Riemann zeta distribution and a Tauberian Theorem. The proof generalizes easily to other situations such as polynomials over a finite field or ideals in a number field. |
|
9:00am to 9:50am - Zoom - Inverse Problems Elisa Francini - (Università di Firenze) On the determination of polyhedral interfaces from boundary measurements |
|
1:00pm - RH 510R - Algebra Jonathan Beardsley - (University of Nevada, Reno) An Embedding of Matroids into Connes-Consani F₁-modules I will briefly review Connes and Consani's approach to algebra over F₁ via Segal Γ-sets. Then I will describe joint work with Nakamura which, building on work of Nakamura and Reyes, gives a faithful embedding of simple pointed matroids, and a fully faithful embedding of projective geometries, into this model. If there is time, I will suggest some consequences of Connes and Consani's which naturally suggest a homotopical approach to F₁. |
|
3:00pm - RH 306 - Number Theory Andrea Pulita - (Institut Fourier (IF), Universite Grenoble Alpes) De Rham cohomology on Berkovich curves The talk is an invitation to the theory of p-adic differential equations and their de Rham cohomology. I will give an overview of the existing results, with an emphasis on de rham cohomology. |
|
1:00pm - DBH 1200 - Graduate Seminar Nathan Kaplan - (UC Irvine) Counting sublattices and subrings of Z^n |