Given a space X, one may want to know if it can be embedded into a vector space in a controlled way. Interestingly, this question is of interest in both abstract mathematics (for example, it has implications for the Novikov Conjecture) and in data science, where such embeddings are a necessary preprocessing step to traditional…
The sum of Fibonacci numbers, i.e. the sequence 2, 4, 7, 12, 20, 33, 54, 88, ... has many combinatorial interpretations. For instance, the n-th term in this sequence is the number of length-n binary strings that avoid 001. In this talk, I will describe a related (but to my knowledge, new) interpretation: given a length-3 binary…
During each 50-minute First Year Research Seminar, two faculty give our new graduate students a short (~20-25 minute), accessible talk about their research or research area. First Year Research Seminar link
We consider a nonlocal reaction-diffusion equation that physically arises from the classical Peierls–Nabarro model for dislocations in crystalline structures. Our initial configuration corresponds to multiple slip loop dislocations in $\mathbb R^n$, $n\geq 2$. After suitably rescaling the equation with a small phase parameter $\epsilon>0$, the rescaled solution solves a fractional Allen–Cahn equation. We show that,…
Students often perceive Multivariable Calculus as a collection of disconnected ideas and approach problem solving in the course formulaically. Students need help from instructors in developing spatial reasoning and making connections between symbolic computations and graphical representations. In this talk I will share how I integrated results of research on students’ learning of differential calculus…
Neural operators such as Deep Operator Networks (DeepONet) and Convolutional Neural Operators (CNO) have been shown to be fairly useful in approximating an operator between two function spaces. In this talk, we will briefly review two inverse problems that arise in Medical Imaging, namely EIT and QPAT. We will also describe the relevant operator learning architectures.…
The past decade has witnessed a remarkable surge in breakthroughs in artificial intelligence (AI), with the potential to profoundly impact various aspects of our lives. However, the fundamental mathematical principles underlying the success of deep learning, the core technology behind these breakthroughs, is still far from well-understood. In this presentation, I will share some interesting…
Speaker's website: https://sites.google.com/view/ferroniluis
Speaker's Website: https://math.sciences.ncsu.edu/people/ejhanso3/
Speaker's website: https://home.olemiss.edu/~leth/
Speaker's website: https://jack-jeffries.github.io/
Speaker's website: https://pi.math.cornell.edu/~karola/