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Guest lectures and seminars

Upcoming

Time and place: , NHA B1120

Donaldson-Thomas and Pandharipande-Thomas theory are two approaches to counting curves on projective threefolds in terms of their moduli spaces of sheaves. An important special case in understanding the DT/PT correspondence the equivariant geometry of affine three-space with the natural coordinate action of the rank 3 torus. I will show how one can use new wall-crossing techniques to prove the equivariant K-theoretic DT/PT correspondence in this situation, which was previously known only in the Calabi-Yau limit.

This is part of an ongoing project with Felix Thimm and Henry Liu in which we aim to prove wall-crossing for virtual enumerative invariants associated to equivariant CY3 geometries by extending a vertex algebra formalism for wall-crossing developed by Joyce.

Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

his talk discusses a nonparametric inference framework for occupation time curves derived from wearable device data. Such curves provide the total time a subject maintains activity above a given level as a function of that level. Taking advantage of the monotonicity and smoothness properties of these curves, we develop a likelihood ratio approach to construct confidence bands for mean occupation time curves.  An extension to fitting concurrent functional regression models is also developed. Application to wearable device data from an ongoing study of an experimental gene therapy for mitochondrial DNA depletion syndrome will be discussed. Based on joint work with Hsin-Wen Chang (Academia Sinica).

 

Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

Structural equation models are simultaneous equation regression models, whose variables are latent, and measured via a confirmatory factor model (that is, with measurement error and repeated measurements). When the functional form of the simultaneous equation system is unknown, it has previously been observed in simulations that factor scores inputted into non-parametric regression methods approximate the true functional form. Factor scores estimate the latent variables (per person), and several types exist. We provide a theoretical (though population-based) analysis of this procedure, and provide assumptions under which it is theoretically justified in using Bartlett factor scores, which are simple linear transformations of the data. In simulations, we compare this suggestion to an already available though understudied non-linear and computationally heavy procedure, and observe that the simple Bartlett approach appears to work better.

Time and place: , NHA B1120


Abstract: Tropical curves are piecewise linear objects arising as degenerations of algebraic curves. The close connection between algebraic curves and their tropical limits persists when considering moduli. This exhibits certain spaces of tropical curves as the tropicalizations of the moduli spaces of stable curves. It is, however, still unclear which properties of the algebraic moduli spaces of curves are reflected in their tropical counterparts.

In work with Renzo Cavalieri and Hannah Markwig we defined, in a purely tropical way, tropical psi classes in arbitrary genus. They are operational cocycles on a stack of tropical curves, which enjoy several properties that we know from their algebraic ancestors. We also computed two examples in genus one and gave a tropical explanation for the psi class on the moduli space of 1-marked stable genus-1 curves to be 1/24 times a point.

In my talk, I will report on joint work in progress with Renzo Cavalieri, where we explore the missing piece in the story: the link to algebraic geometry. I will explain how to obtain, if we are lucky, a family of tropical curves from a family of algebraic curves. Naturally, there also is a correspondence-type theorem that equates algebraic and tropical intersection products with psi classes, thus showing that the tropical computations done with Cavalieri and Markwig faithfully reflect the algebraic world.

Time:

C*-algebra seminar by Eduard Vilalta (Chalmers University of Technology / University of Gothenburg)