In this late-breaking use of an empty seminar slot :), we will watch some subset of Castryck & Decru's YouTube talks on the subject of their break of SIDH. We'll pause and discuss as needed to sort out the details together. These attacks use genus two isogenies to completely break the SIDH variant of supersingular isogeny based cryptography.
I will discuss some properties of varieties which are not Maltsev-definable relative to the class of all varieties, but which are Maltsev-definable relative to the class of varieties having a Taylor term.
Relative Maltsev definability
Sep. 27, 2022 2:30pm (MATH 3…
Lie Theory
Jay Taylor (University of Manchester)
X
Complex irreducible characters of finite groups have two main invariants that are used to measure their rationality: their character field, and their Schur indices. In this talk we’ll survey what is known about these invariants and the many questions that remain open.
Rationality Questions for Finite Reductive Groups Sponsored by the Meyer Fund
Sep. 27, 2022 3:30pm (MATH 3…
Topology
Howy Jordan (CU Boulder)
X
Fragments of logic can be internalized in appropriately structured categories, and topoi have enough structure to interpret full higher order theories. There are two caveats. First, the internal logic is constructive in general. Second, there are two natural notions of morphisms between topoi and the more common of these, geometric morphisms which act like continuous maps between spaces, only preserve a certain (quite large) fragment of logic.
We'll consider in particular how this affects the real numbers. The classical constructions of the naturals, integers, and rationals go through as expected. The reals, however, split into multiple notions. Classically equivalent ways to construct the reals become distinct objects, and these correspond to interesting topologies on the real line. We consider the corresponding objects in a few categories and discuss the relevance on theories of normed algebras in topoi.