Undergraduate research in mathematics and related areas

Undergraduate research in mathematics never stops at the University of Rochester. In addition to summer programs described on this website, research group are working year-around on topics they are interesting in. When the Fall semester begins, we are going to decide on a meeting time. If you are interested in joining one of the research groups or starting another one, please come to my office next Friday. If you have any questions beforehand, please feel free to email me at iosevich@gmail.com.

Several of my colleagues, both from Rochester and beyond, played a crucial role in the success of this program over the years. Charlotte Aten, Steven Kleene, Azita Mayeli, Sevak Mkrtchyan, Jonathan Pakianathan and several others made this program possible and continue to make it possible to this day.

The topics we will be research during the Fall 2024 semester are yet to be determined, but with very high probability we are going to run a research group on signal recovery. The basic idea is the following. Suppose that $f: \left\{\mathbb Z\right\}_N^d \to \left\{\mathbb C\right\}$ and we wish to transmit it via its Fourier transform $f\left(x\right)=\sum_\left\{m \in \left\{\mathbb Z\right\}_N^d\right\} \chi\left(x \cdot m\right) \widehat\left\{f\right\}\left(m\right).$However, if some of the frequencies are missing, for example if $\left\{\\left\{\widehat\left\{f\right\}\left(m\right)\\right\}\right\}_\left\{m \in S\right\}$ are unobserved for some $The question we ask is, under$what reasonable assumptions can we still recover the function (or the signal, as electrical engineers tend to call it) exactly? We are also going to explore some applications of signal recovery to data science. This project will be running during the StemForAll2024 workshop this summer.

Another project that is likely to run during the Fall semester is the investigation of the Erdos distance problem on Riemannian manifolds. I will add a description shortly.

Python/Pandas/Tensorflow Learning Materials:

A full course on python YouTube course:

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