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**

**Math REU coordinator: **Luke Rogers

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

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

Department of Mathematics

University of Connecticut

Henry R. Monteith Building

341 Mansfield Road U1009

Storrs, Connecticut 06269-1009

### Northeast Mathematics Undergraduate Research Mini-Symposia

# 5th Northeast Mathematics Undergraduate Research Mini-Symposium

### University of Connecticut, August 3rd*, 2017*

#### Organizers: Luke Rogers, Phanuel Mariano, and Gamal Mograby

#### Participating Schools: Amherst, Smith, UConn and UMass

**5th Mini-Symposium full program (2017)**

# 3rd Northeast Mathematics Undergraduate Research Mini-Symposium

**Organizers**

#### Participating Schools: Amherst, Colgate, Smith, UConn, UMass, Williams

#### 3rd Mini-Symposium full program (2015)

(photo courtesy Megan Brunner)

### Announcements

# Math UConn REU at JMM 2018

Two of our REU (2017 Stochastics) participants, Raji Majumdar and Anthony Sisti, will be presenting posters Applications of Multiplicative LLN and CLT for Random Matrices and Black Scholes using the Central Limit Theorem on Friday, January 12 at the MAA Student Poster Session, and both of them will be giving talks on Saturday, January 13 at the AMS Contributed Paper Session on Research in Applied Mathematics by Undergraduate and Post-Baccalaureate Students.

Their travel to the 2018 JMM has been made possible with the support of the MAA and UConn’s OUR travel grants.

# 5th Northeast Mathematics Undergraduate Research Mini-Symposium

### University of Connecticut, August 3rd*, 2017*

#### Organizers: Luke Rogers, Phanuel Mariano, and Gamal Mograby

#### Participating Schools: Amherst, Smith, UConn and UMass

# 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