Itay Rosenbaum, 2018-2020
Thesis: The Alternative Clifford Algebra of Four Dimensional Quadratic Forms
Description in layman's terms: There is the classical theory of Clifford algebras of quadratic forms. They are defined to be associative. But what happens if they are only defined to be alternative? This question was raised by Stacy Musgrave in her PhD thesis (and subsequent paper). Uzi and I described the structure of these algebras when the dimension of the quadratic form is three, and Itay tackled the dimension 4 case.
Ilan Levin, 2022-2024 (summa cum laude)
Proposed thesis: Invariant for systems of Pfister forms
Description in layman's terms: Sivatski defined an invariant for quaternionic subgroups of the 2-torsion of the Brauer group of a field in characteristic not 2. A more nuanced invariant was defined in greater generality by Uzi Vishne, Shira Gilat and myself. This invariant in particular assigns a symbol in H^{n+k-1}(F,\mu_2) to sets of k quadratic n-fold Pfister forms that share a common (n-1)-fold factor. Ilan strives to extend this invariant to sets of Pfister forms with a common factor without restricting the dimensions of either the forms or the common denominator.