The University of Connecticut’s summer program brings together a small group of undergraduates to explore what it is like to do research in pure and applied mathematics. Over the course of 10-weeks, we follow research projects from beginning to end — starting with reading about the project, writing proofs/programs, performing calculations, and ending with writing up results. In the past many of our projects have culminated in published articles and conference talks.

As part of the Nation Science Foundation’s Research Experience for Undergraduates initiative, our focus is to show students who may be interested in math and science what it is like to pursue a career in scientific research. We try to maintain a high ratio of mentors to students — about 1 to 2. Our mentors, consisting of faculty and PhD candidates, are here not only to guide students through research, but also to give a peek into what life is like in graduate school and beyond. This happens through a high amount of individual attention, and through group meetings and discussions, where we share ideas and experiences.

### Contact

**MathPrograms.org** application

**MathPrograms.org**

Department of Mathematics

University of Connecticut

Henry R. Monteith Building

341 Mansfield Road U1009

Storrs, Connecticut 06269-1009

**Math REU coordinator: **Luke Rogers

**Fractals: **Luke Rogers, Sasha Teplyaev, Patricia Alonso-Ruiz, Gamal Mograby

**Math Ed: **Fabiana Cardetti

**Stochastics: **Masha Gordina, Phanuel Mariano, Fabrice Baudoin, Sasha Teplyaev, Patricia Alonso-Ruiz

### Announcements

# 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

# 2017 MathPrograms.org application open

**please submit your application** online at MathPrograms.org

**please submit your application**online at MathPrograms.org

# Archived 2015 Announcements

## Alexander Teplyaev – The Spectral Dimension of the Universe

May 29, 2015

Professor Alexander Teplyaev will explain some ideas behind the notion of spectral dimension and how they are related to research being done in our department.

## Masha Gordina – Random thoughts on Brownian motion

June 5, 2015

Professor Masha Gordina will talk about the fascinating history of the Brownian motion and its applications in the real world.

## Keith Conrad – Continued Fractions

June 12, 2015

Professor Keith Conrad will talk about continued fractions, how to compute them, some of their properties, and how to answer seemingly unanswerable questions like this: if an unknown fraction is roughly 2.32558, what is it? (The answer is *not* 232558/100000.)

## Thomas Laetsch – From Brownian motion cometh

June 19, 2015

Following Dr. Gordina’s talk developing Brownian motion, Thomas Laetsch will take us on a short drunkard’s walk through several theories stemming from or related to Brownian motion. R(E)U ready?

## Joe Chen – Drunkard, Octopus, and Electrical Networks

June 26, 2015

Joe Chen will summarize the main ideas behind electrical networks and describe two unexpected applications to probability.

# Archived 2013 Announcements

## Brian Hartmann

July 25, 2013

Professor Brian Hartmann of the University of Connecticut will speak.

## Graduate School Panel

July 19, 2013

There will be a panel discussion on the process of applying to grad school, life as a graduate student and beyond.

## Johanna Franklin

July 12, 2013

Professor Johanna Franklin of the University of Connecticut will speak.

## Aaron Bailey – π, e and Other Irrational Numbers

July 9, 2013

Professor Aaron Bailey will give a talk based on the epinonimous 1986 paper of Alan Parks.

## Chen-Yun Lin – Calculus of Variations

June 27 & 28, 2013

Professor Chen-Yun Lin will give a two part discussion of variational methods in optimization problems.

## Daniel Kelleher – Infinite Dimensional Linear Algebra

June 21 & 25, 2013

Daniel Kelleher of the University of Connecticut will give a two part discussion of the complications that arise in concepts of linear algebra in infinite dimensional vector spaces.

## Reed Solomon – The Continuum Hypothesis

June 18, 2013

Professor Reed Solomon of the University of Connecticut will give a talk.

## Rebecca Tramel – Projective Space and Bezout’s Theorem

June 14, 2013

Rebecca Tramel of the University of Edinburgh will give a presentation about curves in the projective plane, and Bezout’s theorem concerning their intersection.

## Keith Conrad – The ABC Conjecture

June 11, 2013

Professor Keith Conrad of the University of Connecticut will give a presentation on the current state of the ABC conjecture.

## Introduction to Mathematica

June 7, 2013

Alex Baldenko will be conducting an introduction to the computer algebra system Mathematica.

## Introduction to Latex

June 5, 2013

Gabe Feinberg will be conducting an introduction to the typesetting program LaTeX