Author: pam07016

2017 Announcements

Phanuel Mariano – The volume of the unit ball in n dimensions

July 28, 2017

Phanuel Mariano from the University of Connecticut will be giving a talk computing the volume of the unit ball in arbitrary dimension.

Michelle Rabideau – Continued Fractions and the Fibonacci Sequence

July 21, 2017

Michelle Rabideau from the University of Connecticut will be giving a talk related to Continued Fractions.

Hugo Panzo – Laplace’s method and applications to probability

July 14, 2017

Hugo Panzo from the University of Connecticut will be giving a talk related to Laplace’s method.

Patricia Alonso Ruiz – Resistance metric – an electric interpretation of measuring distances

July 7, 2017

Any weighted graph can be seen as an electric linear network where the current flows between nodes (vertices) connected by resistors (weighted edges). This electric interpretation provides a special way to measure distances in a graph via the so-called effective resistance metric. What does this metric actually do, how it is related to energy minimizers and why it is so helpful when graphs become infinite are some of the questions we will address in this talk.

Keith Conrad – An algebraic characterization of differentiation

July 30, 2017

The derivative is defined using limits while the basic rules of differentiation (sum rule, product rule, chain rule) have an algebraic flavor. We will see how differentiation, and more generally differential operators, can be characterized purely algebraically by putting all the analytic conditions into the functions that we want to differentiate.

Ambar Sengupta – Random Matrices: Pictures From Traces and Products

July 23, 2017

Professor Ambar Sengupta will give a talk based on Random Matrices.

Zihui Zhao – Harmonic Measure

June 16, 2017

Zihui Zhao form the University of Washington will be an introductory talk in harmonic measure.

Luke Rogers – Length and volume

June 9, 2017

I will talk a little about Euclidean length and volume, the lengths of curves, Peano curves, the positive area curves of Osgood, and a delightful theorem of Hajlasz and Strzelecki that shows one can measure volume with a string.

Daniel Kelleher – The metric space of metric spaces

June 2, 2017

Metric spaces are sets which have a notion of distance. We will compare two different metric spaces, and see that this comparison makes the set of metric spaces into a metric space (Don’t worry, after that it’s turtles the rest of the way down). The focus will be put on length spaces — metric spaces where distance is given as the length of the shortest curve connecting two points. For these spaces we discover a sense of curvature

Multiplicative LLN and CLT and their Applications

Group Members

Lowen PengAnthony SistiRajeshwari Majumdar

Supervisors

Phanuel Mariano, Masha Gordina, Sasha Teplyaev, Ambar Sengupta, Hugo Panzo

Overview

We study the Law of Large Numbers (LLN) and and Central Limit Theorems (CLT) for products of random matrices. The limit of the multiplicative LLN is called the Lyapunov exponent. We perturb the random matrices with a parameter and we look to find the dependence of the the Lyapunov exponent on this parameter. We also study the variance related to the multiplicative CLT. We prove and conjecture asymptotics of various parameter dependent plots.

Publication

TBA

Presentation