Spring 2026
Spring 2026
Embedded Files
2/4/26 -- Alex Ballow -- (Notes)
Abstract: Systems of particles in Newtonian mechanics; conservative forces, total momentum and center of mass of a system, angular momentum.
2/11/26 -- Eric Metzger -- (Notes)
Abstract: Introducing Hamiltonian mechanics, Hamilton's equations; definition of Poisson bracket of functions; examples of solutions to Hamilton's equations, preserved quantities.
2/18/26 -- Jenna Stitt -- (Notes)
Abstract: Kepler's laws of planetary motion; the Laplace-Runge-Lenz vector and other conserved quantities; solutions to planetary motion with positive, zero, or negative energies.
3/4/26 -- Matthew Helmer -- (Notes)
Abstract: Introduction to special relativity; Maxwell's equations and the constant speed of light; the Lorentz group and Lorentz transformations; some consequences
3/11/26 -- Thomas Carlson -- (Notes)
Abstract: Symplectic vector spaces; bases and symplectic maps; symplectic, isotropic, coisotropic, and Lagrangian subspaces; the symplectic group.
3/25/26 -- Jonathan Pal -- (Notes)
Abstract: Defining symplectic forms and manifolds, examples and non-examples; volume forms and orientability of symplectic manifolds; Darboux' theorem; Hamiltonian vector fields.
4/1/26 -- Eric Metzger -- (Notes)
Abstract: Symplectic structures on cotangent bundles, defining the Poisson bracket of smooth functions on a symplectic manifold; (locally) Hamiltonian flows and symplectic vector fields, examples; Hamiltonian systems and conserved quantities.
4/8/26 -- Ryan Grady -- (Notes)
Abstract: What is a quantum system (modeled by)? Hilbert space model of states and observables; the Born rule, non-commuting of observations, examples, the Stern-Gerlach experiments (spin-1/2); free particle in one dimension, rigged Hilbert spaces.
4/15/26 -- Chris Boehlert -- (Notes)
Abstract:
4/29/26 -- Lucus Brady -- (Notes)
Abstract:
Fall 2025
Fall 2025
8/27/25 -- Ahsan Ali -- (Notes)
Abstract: An introduction to smooth manifolds and cobordism. Examples of smooth manifolds (with boundary), (null-)cobordisms, cardinality of the set of closed n-dimensional smooth manifolds modulo cobordism. Smooth maps of manifolds, the regular value theorem, and examples.
9/3/25 -- Chris Boehlert -- (Notes)
Abstract: The tangent space at a point in a manifold. Introduction to bundles (vector, tangent, normal), with examples. The differential of a smooth map of manifolds. The tubular neighborhood theorem.
9/10/25 -- Jenna Stitt -- (Notes)
Abstract: Submersions of manifolds and the local submersion theorem. Regular values of smooth maps, and the regular value theorem, examples. Critical values, Sard's theorem, transversality, examples, and ideas about genericity.
9/17/25 -- Luke Tinel -- (Notes)
Abstract: Applications and examples of regular value theorem, tubular neighborhood theorem. Maps between the set of smooth maps of spheres transverse to zero and the set of closed manifolds with trivial normal bundles, Thom collapse map, statement of equivalence of the above sets modulo homotopy and cobordism, respectively.
10/1/25 -- Hadley Wells -- (Notes)
10/8/25 -- Judah Towery -- (Notes)
10/15/25 -- Grace Stroh -- (Notes)
10/29/25 -- Alex Ballow -- (Notes)
11/5/25 -- Ziyal Jandrasi -- (Notes)
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