If $n$ is congruent to 0 or 4 modulo 6, there are infinitely many primes of the form $x^2 + ny^2$ with both $x$ and $y$ prime. (Joint work with Mehtaab Sawhney, Columbia)
Consider definable sets over the family of finite fields $\mathbb{F}_q$. Ax proved a quantifier-elimination result for this theory, in a reasonable geometric language. Chatzidakis, Van den Dries and Macintyre showed that to a first-order approximation, the cardinality of a definable set $X$ is definable in a very mild expansion of Ax's theory. Can such a statement be true of the next higher order approximation, i.e. can we write $|X(\mathbb{F}_q)| = aq^{d} + bq^{d-1/2} + o(q^{d-1/2})$, with $d,a,b$ varying definably with $X$ in a tame theory? Here $b$ must be viewed as real-valued so continuous logic is needed. I will report on joint work in progress with Will Johnson.
Join us on Monday 13th May at 6:30 in L2 to celebrate International Women in Maths Day. Traditionally celebrated on May 12th, Mirzakhani's birthday, this is an occasion to celebrate all the wonderful women and non-binary people that make up our mathematical community. This event will be open to all, regardless of gender identity.
I will exposit some recent joint work with Paul Larson and Grigor Sargsyan that uses higher models of the Axiom of Determinacy---models with nontrivial structure above $\Theta$, the least ordinal which is not the surjective image of the reals---to show that instances of the fundamental problem of inner model theory, the iterability conjecture, consistently fail.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.