# TBA

## Speaker:

## Institution:

## Time:

## Host:

## Location:

# Selected applications of Dynamical Systems to Probability, Spectral Theory, and Logic

## Speaker:

## Speaker Link:

## Institution:

## Time:

## Host:

## Location:

# TBA

## Speaker:

## Institution:

## Time:

## Host:

## Location:

# The almost-sure theories of finite graphs and finite metric spaces

## Speaker:

## Institution:

## Time:

## Host:

## Location:

Given a property P of graphs, it is natural to wonder how likely a given finite graph satisfies property P, that is, given some fixed natural number n, what proportion of the n vertex graphs satisfies property P. If P is a "first-order" property, then there is a 0-1 law that says the proportion of graphs of size n that satisfy P approaches either 0 or 1 as n tends to infinity. A simple proof of this fact uses the model theory of the so-called random (or Rado) graph. We will present the proof of this result and then discuss recent work, joint with Bradd Hart and Alex Kruckman, which show these ideas can be used to prove an approximate 0-1 law for finite metric spaces. The metric space version of the random graph that is relevant turns out to be somewhat surprising!

# TBA

## Institution:

## Time:

## Host:

## Location:

# Graduate Seminar

## Speaker:

## Institution:

## Time:

## Host:

## Location:

TBA

# A sketch of the neoclassical electromagnetic theory

## Speaker:

## Speaker Link:

## Institution:

## Time:

## Host:

## Location:

**Abstract**

This presentation is about our recently developed neoclassical theory of electromagnetic interactions. We demonstrate that the classical EM theory can be extended down to atomic scales so that many phenomena at atomic scales, usually explained in the quantum-mechanical framework, can be explained in our neoclassical framework. The proposed extension bridges the classical and quantum-mechanical approaches, so they are not separated by a gap but rather overlap in a large common domain. Our theory, though similar to QM in some respects, is markedly different from it. In particular: (i) there is no need in our theory for the correspondence principle and consequent quantization procedure to obtain the wave equation; (ii) the Heisenberg uncertainty principle, though quite often applicable, is not a universal principle; (iii) there is no configuration space; (iv) there is no probabilistic interpretation of the wave function.

Our theory features a new spatial scale - the size a_{\mathrm{e}} of a free electron. This scale is special to our theory and does not appear in either classical EM theory nor in the quantum mechanics where electron is always a point-like object. Our current assessed value for this scale is a_{\mathrm{e}}\approx100a_{\mathrm{B}} where a_{\mathrm{B}} is the Bohr radius, and consequently a_{\mathrm{e}}\approx5 nm. In our theory any elementary charge is a distributed in space quantity. Its size is understood as the localization radius which can vary depending on the situation. For instance, if an electron is bound to a proton in the Hydrogen atom then its the size of is approximately 1 Bohr radius, that is a_{\mathrm{B}}\approx0.05 nm, and when the electron is free its size is a_{\mathrm{e}}\approx100a_{\mathrm{B}}\approx5 nm.

Interestingly, the upper bound 25 nm is the skin depth and that implies that a nanosystem of size smaller than 25 nm is transparent to the external field. The same transparency should hold for a nanostructured surface indicating such a surface is better for nearly ideal field electron emission. There is an experimental evidence showing that the highest current densities were obtained for nanotips with sizes about 1nm yet another important fact supporting a possibility of a fundamental nanoscale.

# Codes from Polynomials over Finite Fields

## Speaker:

## Speaker Link:

## Institution:

## Time:

## Host:

## Location:

Suppose we are trying to communicate over a 'noisy channel'. I want to send you a single bit, a 1 or a 0, but there is some probability that the bit I send is not the bit you receive. We could communicate more reliably by agreeing to repeat the intended message, for example, instead of sending '0’ or '1’, I would send '000’ or '111’. But, there is a cost to this repetition. A major goal in the theory of error-correcting codes is to understand how to efficiently build redundancy into messages so that we can identify and correct errors. In this talk we will focus on error-correcting codes that come from families of polynomials over finite fields, starting from the classical example of Reed-Solomon codes. We will emphasize connections between coding theory, algebraic geometry, and number theory. This talk will assume no previous familiarity with coding theory or algebraic geometry. We will start with the basics and emphasize concrete examples.