*In Progress*

**Irrational Exuberance: Correcting Bias in Probability Estimates**

*In Progress*

**Imperfect Supervision under the Neyman-Pearson Paradigm**

*Feburary, 2017*

**Introduction to R - LSE Talk / Workshop**

On February 20th, 2017 I held a 2 hour introduction to R workshop at the London School of Economics for the LSESU Applicable Mathematics Society.

*November, 2016*

**Horse Racing Bias**

In the Fall 2016 semester I completed a report analyzing different stall biases in horse racing. Specifically I looked at 4 U.K. racing courses in order to see if there was a difference in probability of winning any given race due to a horses starting position. This report can be viewed at the link below.
This work was primairly conducted and compiled into PDF format using the R language.

Report

*December 2015 - Present*

**Probability of Certain Rare Events**

I am currently helping a third party create probability models to predict certain random events. The results of which are being submitted for publication (confidential until published).

*January 2014 - September 2014*

**P-Colorability by paris as a Knot Invariant**

3-colorability is a well-known knot invariant that is very easy to construct while also being very limited in its use. In particular, it does not distinguish a knot from its mirror image. Recall that a knot diagram is tri-colorable if you can color all of its strands using at least 2 or at most 3 colors such that at each crossing, either the 3 different colors come together or the crossing only has 1 color. In 2011, Roger Fenn defined the 3-colorability by pairs as a knot invariant that allowed him to show that the right trefoil is different from the left trefoil.
In this research project, we first used 3-colorability by pairs to show that the 6-1, 7-7, and 8-5 knots are chiral (namely different from their mirror image). We then studied the behavior of this invariant with respect to the composition of knots. This invariant’s use is limited to knots that are 3-colorable in the classic meaning. We therefore proceeded to define p-colorability by pairs (for p is any prime number) and proved that it is a knot invariant (namely that it is unchanged by all 3 Reidemeister moves).
The invariant for p-colorability by pairs (as for 3-colorabilty defined by Fenn) is not just the coloring. The useful invariant is the list of crossings that appear in the knot diagram. The list of all possible crossings through the p-coloring gives us the structure of an abelian group, which allows us to show that it is a knot invariant. As an example, we computed the crossing lists of the 5-1 and 7-4 knots (both of which are 5-colorable) along with their mirror images.
Note that all of the knots mentioned above were already known to be chiral but it required much more involved topological tools such as the Jones Polynomial among others.

Abstract -
Write Up -
Presentation

*August 2015*

**Introduction to Topological Data Analysis**

In the Summer of 2015 I was an intern at Summit Consulting and while I was there I took it upon myself to research a new area of data analysis called Topological Data Analysis (TDA). One of my goals with this research was to see if it was possible for a consulting company like Summit to apply this technique to their future work and to assist their clients.

Blog Post

*2014 - 2015*

**LSESU Applicable Maths Society Java Series**

In the 2014-2015 academic year I attended the London School of Economics and Political Science. While I was there I realized that since the LSE was a strictly social science only university, there were no outlets for the undergraduates to learn mathematics (without an economics application) and computer science. In fact, there was no math society at the LSE at all. That is why I took it upon myself to found the LSE Applicable Mathematics Society so I could introduce students to topics in mathematics and computer science that were not traditionally taught at the LSE.

First term I gave miscellaneous lectures in Topology, Geometry, and Algebra and second term I started a lecture series in Java Programming since I realized that there was a growing interest to learn programming but no formal way the students could be taught. There lectures were hugely successful and our member base grew to over 100 students in the first semester. Example lectures are listed on the societies website below.

Currently, the Applicable Mathematics Society has become the first society to be supported by the LSE Mathematics Department and is currently continuing on exploring topics not formally addressed at the LSE through Python Programming, Algorithmic Trading, and Pure Mathematics. It currently is the biggest math society at the London School of Economics, serving over 200 members.

*May 2014*

**UCLA Data Fest**

In the Summer of 2014 I competed in a regional DataFest competition (a statistics like hackathon) with the goal of extracting the most useful information we could from a dataset in 2 and a half days. Our data originated from a company called Gridpoint where they monitor energy usage of different companies in order to evaluate ways they can cut down on their energy expenditure. Our recommendation involved examining companies located in Texas and monitoring their electricity usage at night during the summer. Through this we were able to identify a way to save that company 16% on their electricity bill alone.
My teams presentation won the Best Insight into the Data award out of over 140 participants. The slide deck is posted below.

Presentation