Colloquia & Seminars

Title: Moduli of subcanonical points

Algebra Seminar Speaker: Dawei Chen, Boston College Title: Moduli of subcanonical points Abstract: Subcanonical points are special Weierstrass points on smooth algebraic curves whose semigroups are symmetric. In this talk, I will explain the rich geometry of the moduli space of subcanonical points, with a focus on its connected components, birational geometry, topology, and the deformation theory of related monomial singularities.

Title: Member Seminar

Member Seminar Speaker: tba

Title: The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields

Algebra Seminar Speaker: Matt Broe, Boston University Title: The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields Abstract: The Beilinson-Bloch conjecture is a generalization of the Birch and Swinnerton-Dyer conjecture, which relates the ranks of Chow groups of smooth projective varieties over global fields to the order of vanishing of L-functions. We prove the conjecture for certain classes of non-isotrivial varieties over Fq(t), including some cubic threefolds and fivefolds. We deduce the Birch and Swinnerton-Dyer conjecture for their intermediate Jacobians, and use it to establish new cases of the Tate conjecture over finite fields.  

Title: Member Seminar

Member Seminar Speaker: tba

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar Speaker: Tianqin Zhu, Columbia University

Title: Member Seminar

Member Seminar Speaker: tba

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar Speaker: Seraphim Jarov (Perimeter Institute)

Title: Facets of link homology

Colloquium Speaker: Mikhail Khovanov, Johns Hopkins University Title: Facets of link homology Abstract: We will review some link homology theories of algebraic origin and their connections to representation theory and geometry.

Title: Multiplicities of graded families of ideals on Noetherian local rings

Algebra Seminar Speaker: Dale Cutkosky, University of Missouri Title: Multiplicities of graded families of ideals on Noetherian local rings Abstract: Let $R$ be an arbitrary $d$-dimensional Noetherian local ring with maximal ideal $m_R$. In this talk, we give a generalization of the multiplicity $e(I)$ of an $m_R$-primary ideal $I$ of $R$ to a multiplicity $e(\mathcal I)$ of a graded family of $m_R$-primary ideals $\mathcal I$ in $R$. This multiplicity gives the classical multiplicity $e(I)$ if $\mathcal I=\{I^n\}$ is the $I$-adic filtration, and agrees with the volume, $\lim_{n\rightarrow \infty}d!\frac{\ell(R/I_n) }{n^d}$ for $R$ such that $\dim N(\hat R)>d$, the required condition for the volume of graded families of $m_R$-primary ideals to exist as a limit. We will show that many...

Title: Member Seminar

Member Seminar Speaker: tba

Title: Interpolation for points in $\mathbb{P}^N, N\geq 2$

Algebra Seminar Speaker: Dipendranath Mahato, Tulane University Title: Interpolation for points in $\mathbb{P}^N, N\geq 2$ Abstract: Interpolation problems study hypersurfaces in projective space passing through prescribed sets of points. Classically, one asks how many independent conditions a collection of points imposes on hypersurfaces of a fixed degree, a question that can be studied algebraically via homogeneous ideals and their Hilbert functions. In this talk, I will begin with the classical interpolation problem for reduced points and introduce the algebraic framework used to study it. I will then move to fat point schemes, where points are assigned multiplicities and hypersurfaces are required to vanish to higher order. In this setting, interpolation problems naturally lead to symbolic powers of ideals...

Title: Member Seminar

Member Seminar Speaker: tba

Title: Colloquium

Colloquium Speaker: Anuj Srivastavam Johns Hopkins University  

Title: Differential Geometry and Physics Seminar

Differential Geometry and Physics Seminar Speaker: François Greer, MSU

Title: Member Seminar

Member Seminar Speaker: tba