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Kiran Kedlaya, UCSD/IAS
We classify all possible configurations of vectors in three-dimensional space with the property that any two of the vectors form an angle whose measure is a rational multiple of pi. As a corollary, we find all tetrahedra whose six dihedral angles are all rational multiples of pi. While these questions (and their answers) are of an elementary nature, their resolution will take us on a tour through cyclotomic number fields, computational algebraic geometry, and an amazing fact about the geometry of tetrahedra discovered by two physicists in the 1960s. Joint work with Sasha Kolpakov, Bjorn Poonen, and Michael Rubinstein.
Rob Oakley, Temple University
Abstract: Let $M$ be a closed, connected, oriented, 3-manifold. Alexander proved that every such $M$ contains a fibered link. In this talk I will describe work that uses this idea to show that for hyperbolic fibered knots in $M$, the volume and genus are unrelated. I will also discuss a connection to a question of Hirose, Kalfagianni, and Kin about volumes of hyperbolic fibered 3-manifolds that are double branched covers.
Sean Howe, University of Utah
tba
Malena Espanol, Arizona State University
Discrete linear and nonlinear inverse problems arise from many different imaging systems, exhibiting inherent ill-posedness wherein solution sensitivity to data perturbations prevails. This sensitivity is exacerbated by errors arising from imaging system components (e.g., cameras, sensors, etc.), necessitating the development of robust regularization methods to attain meaningful solutions. Our presentation commences with the exposition of distinct imaging systems, and their mathematical formalism, and subsequently introduces regularization techniques tailored for linear inverse problems. Then, we delve into the variable projection method, a powerful tool to address separable nonlinear least squares problems.
There are no conferences next week.