Academics

Algebraic Geometry Seminar | Contact loci of arcs

Time:Friday, 15:30-16:30 May 31, 2024

Venue:C548, Shuangqing;Zoom Meeting ID: 262 865 5007 Passcode: YMSC

Organizer:Caucher Birkar, 曲三太,陈炳仪

Speaker:Nero Budur (KU Leuven)

Abstract:

Contact loci are sets of arcs on a variety with prescribed contact order along a fixed subvariety. They appear in motivic integration, where motivic zeta functions are generating series for classes of contact loci in appropriate Grothendieck groups. We give an overview of recent results relating the basic topology of contact loci of hypersurfaces with a Floer theory and with log minimal models.

DATEMay 30, 2024
SHARE
Related News
    • 0

      Contact 3-manifolds and contact surgery

      AbstractContact structures on 3-manifolds are given by a hyperplane distribution in the tangent bundle satisfying a condition called "complete non-integrability". Contact structures fall into one of two classes: tight or overtwisted. Ozsvath and Szabo introduced invariants of contact structures using Heegaard Floer homology. In this talk, I will survey some recent results about the tightness an...

    • 1

      Differential Geometry Seminar | Recovering contact forms from boundary data

      Abstract:Let $X$ be a compact connected smooth manifold with boundary. The paper deals with contact $1$-forms $\beta$ on $X$, whose Reeb vector fields $v_\b$ admit Lyapunov functions $f$. We prove that any odd-dimensional $X$ admits such a contact form.We tackle the question: how to recover $X$ and $\beta$ from the appropriate data along the boundary $\partial X$? We describe such boundary dat...