Mathematics
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1
Article
- Author(s):
- Greyson C. Wesley
- Abstract:
We investigate lifting projective representations in matrix Lie groups to unitary representations. After establishing preliminary notions, we discuss finite- and infinite-dimensional representations of matrix Lie groups, emphasizing the relationship between SU(2) and SO(3) and thus providing applications in quantum physics. The application of cohomological methods in studying the lifting of projective representations is then highlighted, along with the concept of one-dimensional central exten…
- Date Created:
- 2023-04-15
- Record Visibility:
- Public
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2
Manuscript
- Author(s):
- Edward John Roe
- Abstract:
It is sometimes stated that there are only two exactly solvable problems in classical mechanics–the simple harmonic oscillator and the two-body central force problem. This is not strictly true (we shall consider systems other than these which admit exact solutions), but what is true is that the conditions under which one can find exact solutions to a system of differential equations describing a physical system are rarely satisfied. The point of this thesis is to describe what is necessary i…
- Date Created:
- 2023-05-08
- Record Visibility:
- Public
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- Author(s):
- Xiaotong Yang
- Abstract:
The standard random walk is easy to describe. Flip a fair coin with faces labelled ±1. If the face 1 shows up take a step of size 1 in the positive direction (along the x-axis) while if the face −1 shows up take a step of size 1 in the negative direction. We denote by Sn your location after n steps. The random walk is formally the sequence of random variables S0, S1, S2, … Throughout we assume that the walk starts at the origin of the x-axis, i.e. S0 = 0. If we think that we flip the coin…
- Date Created:
- 2023-05-03
- Record Visibility:
- Public
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4
Document
- Author(s):
- Ethan Kirsch
- Abstract:
Minimal surfaces are an object within differential geometry. Differential geometry is a field of mathematics which studies geometric objects that can be described by smooth, i.e. infinitely differentiable maps. These geometric objects are called manifolds. Within this context, minimal surfaces are manifolds which minimize area among all surfaces with the same boundary. This leads to minimal surfaces playing a role in the study of partial differential equations, as this minimal area correspond…
- Date Created:
- 2023-04-29
- Record Visibility:
- Public
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- Author(s):
- Patrick Conway
- Abstract:
Einstein’s theory of general relativity is, fundamentally, a theory about the geometry of the universe. The mathematical framework for the theory is found in the study of pseudo-Riemannian geometry, a generalization of, the much more commonly studied, Riemannian geometry. The first half of this thesis is devoted to the study of pseudo-Riemannian geometry, and in the remaining half we study general relativity itself as well as a few classical applications of the theory.
- Date Created:
- 2023-04-28
- Record Visibility:
- Public
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6
Doctoral Dissertation
- Author:
- Richard A. P. Birkett
- Advisory Committee:
- Jeffrey A. Diller
- Degree Area:
- Mathematics
- Degree:
- Doctor of Philosophy
- Defense Date:
- 2023-03-30
- Record Visibility:
- Public
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7
Doctoral Dissertation
- Author:
- Eric Jovinelly
- Advisory Committee:
- Eric B. Riedl
- Degree Area:
- Mathematics
- Degree:
- Doctor of Philosophy
- Record Visibility:
- Public
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8
Doctoral Dissertation
- Author:
- Daniel Soskin
- Advisory Committee:
- Michael Gekhtman
- Degree Area:
- Mathematics
- Degree:
- Doctor of Philosophy
- Defense Date:
- 2023-04-04
- Record Visibility:
- Public
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9
Doctoral Dissertation
- Author:
- Wern Yeen Yeong
- Advisory Committee:
- Eric B. Riedl
- Degree Area:
- Mathematics
- Degree:
- Doctor of Philosophy
- Defense Date:
- 2023-04-04
- Record Visibility:
- Public
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10
Doctoral Dissertation
- Author:
- Luan Doan
- Advisory Committee:
- Brian C. Hall, Michael Gekhtman, Liviu Nicolaescu, Pavel Mnev
- Degree Area:
- Mathematics
- Degree:
- Doctor of Philosophy
- Defense Date:
- 2022-03-25
- Record Visibility:
- Public
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11
Doctoral Dissertation
- Author:
- Nikolai Konovalov
- Advisory Committee:
- Mark J. Behrens
- Degree Area:
- Mathematics
- Degree:
- Doctor of Philosophy
- Defense Date:
- 2023-03-31
- Record Visibility:
- Public
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12
Doctoral Dissertation
- Author:
- Zhao Gao
- Advisory Committee:
- Claudiu Raicu
- Degree Area:
- Mathematics
- Degree:
- Doctor of Philosophy
- Defense Date:
- 2022-03-30
- Record Visibility:
- Public