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| Creator | Title | Description | Subject | Date | ||
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Sullivan, Steven M. | A trace formula for G2 | An n-dimensional matrix representation of a group G on a vector space V is a homomorphism from G to GL(V). For our purposes, we consider an irreducible representation to be a representation which cannot be decomposed into the direct sum of smaller-dimensional representations. Let H be a subgroup of ... | Trace formulas | 2013-05 |
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Bowen, Brady | Fractal geometry of melt ponds: Modeling the fractal geometry of arctic melt ponds using the level sets of random surfaces | During the late spring, most of the Arctic Ocean is covered by sea ice with a layer of snow on top. As the snow and sea ice begin to melt, water collects on the surface to form melt ponds. As melting progresses, sparse, disconnected ponds coalesce to form complex, self-similar structures which are c... | Melt pond geometry | 2016-04 |
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Wang, Wenyi | Imaging in a homogeneous aluminum plate by using ultrasonic waves | This project is about detecting and imaging damage (such as cracks) in a plate by using ultrasonic waves. The waves are generated by a source (an ultrasonic transducer) that is part of a robot that can move on the plate. The waves traveling in the plate are recorded at a receiver (another ultrasonic... | Ultrasonic transducer - Mathematics; Kirchoff migration - Research | 2014-12 |
| 4 |
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Zhao, Michael | Binary Hermitian Forms and Optimal Embeddings | Let L=K be a quadratic extension of global fields, and OL the ring of integers of L. We prove two correspondences between (i) binary L-hermitian forms which represent 1 and optimal embeddings of L into a quaternion algebra, (ii) integral binary OL-hermitian forms which represent 1 and embeddings of ... | 2017 | |
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Bull, August John | Studying Galois Representations Using Elliptic Curves | Diophantine equations and their solution sets are prominent subjects of study in number theory. These equations are often studied modulo prime numbers or prime ideals in field extensions. Galois Theory is well-suited to study field extensions, but Galois groups are often mysterious. To remedy this, ... | 2020 | |
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Johnson, Dylan | Modular forms, Elliptic Curves, and Their Connection to Fermat's Last Theorem | Fermat's Last Theorem (FLT) states that if n is an integer greater than three, the equation xn + yn = zn has no integer solutions with xyz 6= 0. This incredible statement eluded proof for over three-hundred years: in that time, mathematicians developed numerous tools which finally proved FLT in 1995... | 2020 |
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