seminar

• Geometry & Analysis Student Seminar
• Morse index of the $\xi_{g,1}$ Lawson surfaces in the 3-sphere (in further detail) and Hsiang's embedded $O(2) \times O(2)$ minimal hypersurfaces in the 4-sphere
• By David Wiygul (University of Trento)
• Abstract: I will fill in more details of the computation with Kapouleas of the index of $\xi_{g,1}$ Lawson surfaces. Afterward I will describe recent joint work with Alessandro Carlotto and Mario Schulz which apply some similar ideas---drawing again from the work of Montiel and Ros---toward estimating the index of Hsiang's rotationally invariant embedded minimal hypersurfaces in the 4-sphere.

• Geometry & Analysis Student Seminar
• Morse index of the $\xi_{g,1}$ Lawson surfaces in the 3-sphere (an overview of the computation)
• By David Wiygul
• Abstract: I will present another project (Camb. J. 2020) with Kapouleas: the calculation of the Morse index and nullity of an infinite subfamily of Lawson's embedded minimal surfaces, including surfaces of every genus. In this talk I will explain the strategy---motivated in part by work of Montiel and Ros regarding the index of complete minimal surfaces of finite total curvature in Euclidean space---and some details of the computation.

• Geometry & Analysis Student Seminar
• Title: Characterization of Lawson's embedded minimal surfaces in the 3-sphere by their symmetries and genus
• By David Wiygul
• Abstract: I will focus on joint work (Crelle 2022) with Nicos Kapouleas in which we showed that each of Lawson's embedded minimal surfaces is uniquely determined (up to congruence) by its symmetry group and genus. I will additionally explain some more recent work (also joint with Kapouleas) in pursuit of uniqueness results of a similar nature for other minimal surfaces in the 3-sphere (specifically a family constructed by Choe and Soret (Math. Ann. 2016) and other desingularizations of Clifford tori).

• Estimation of finite population proportions for small areas -- a statistical data integration approach
• By: Partha Lahiri, University of Maryland College Park
• Abstract: Empirical best prediction (EBP) is a well-known method for producing reliable proportion estimates when the primary data source provides only small or no sample from finite populations. There are potential challenges in implementing existing EBP methodology such as limited auxiliary variables in the frame (not adequate for building a reasonable working predictive model) or unable to accurately link the sample to the finite population frame due to absence of identifiers. In this paper, we propose a new data linkage approach where the finite population frame is replaced by a big probability sample, having a large set of auxiliary variables but not the outcome binary variable of interest. We fit an assumed model on the small probability sample and then impute the outcome variable for all units of the big sample to obtain standard weighted proportions. We develop a new adjusted maximum likelihood (ML) method so that the estimate of model variance doesn't fall on the boundary, which is otherwise encountered in commonly used ML method.  We also propose an estimator of the mean squared prediction error using a parametric bootstrap method and address computational issues by developing an efficient Expectation Maximization algorithm. The proposed methodology is illustrated in the context of election projection for small areas.My talk will be based on my collaborative research with Ms. Aditi Sen.

Seminario de Ecuaciones diferenciales by Elena Salguero (Max Planck Institute for Mathematics in the Sciences, Leipzig)

Abstract:  The Stokes-transport system describes the evolution of a density scalar advected by a velocity field that satisfies the Stokes equation with gravitational forcing. This system of PDEs belongs to the class of active scalar equations and models the dynamics of highly viscous fluids with heterogeneous density. In this talk, we will combine a Lagrangian approach with harmonic analysis techniques to find global solutions for this system in 2D, with a focus on the case where the density takes two distinct constant values. This leads to a two-phase problem that models the evolution of two different immiscible fluids in a 2D domain.

Seminario de jóvenes investigadores. "Is the sum of optimal transports again optimal?" by Ruben Medina Sabino.

Abstract: We are going to talk about the connections between the transportation cost space (also known as Lipschitz free space) and the canonical Banach space $\ell_1$. We will give a partial answer to a problem posed by Dilworth, Kutzarova and Ostrovskii in 2020 and that has
been around since these spaces were defined. Namely, to find a metric characterization of the Banach-Mazur distance between the Lipschitz free space and $\ell_1$

La ponencia también podrá seguirse a través del enlace
https://meet.google.com/uoh-dyyr-jss

Datos: Seminario de Ecuaciones Diferenciales.

Conferenciante: Sergio Cruz Blázquez (Universidad de Granada)

Título: Conformal metrics on the four-dimensional upper hemisphere with symmetric Q and T curvatures

Seminario 2 IMAG, 15/10/2024, 12:00

We address the problem of prescribing non-constant $Q$ and boundary $T$ curvature on the upper hemisphere $\mathbb{S}^4_+\subset \mathbb{R}^5$, via a conformal change of the background metric. This is equivalent to solve a fourth-order non-linear elliptic boundary value problem with a third-order non-linear equation and homogeneous Neumann conditions at the boundary. The problem admits a Mean-field type variational formulation, similar to the one obtained by Cruz-Blázquez and Ruiz in \cite{cruzruiz2018}, with the associated energy functional being bounded from below but, in general, not coercive. By imposing symmetry conditions, we are able to prove the existence of minimizers, especially when $Q,T\geq 0$.

Talk 1: 12 horas día 4 de octubre

Conferenciante: Edoardo Saccenti, Associate Professor. Laboratory of
Systems and Synthetic Biology, Wageningen University & Research, the
Netherlands

Título: Multivariate experimental errors in Principal Component
Analysis: from correlations to loadings

Abstract:

Multivariate measurement errors are ubiquitous in all experimental
sciences. Depending on the experimental platform used to acquire data,
diverse types of errors are introduced, amounting to an admixture of
additive and multiplicative error components that can be uncorrelated or
correlated. In this talk I will review how experimental error affect
correlations, the building blocks of multivariate statistical methods,
and how this connect to the recovery of the subspace with Principal
Component Analysis (PCA) as obtained by using numerical simulations. I
will how show different error characteristics (variance, correlation,
correlation structure), loading structures and data distributions
influence the accuracy to estimate an error-free (true) subspace from
sampled data with PCA.

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Talk 2: 12:45 horas día 4 de octubre

Conferenciante: Age K. Smilde. Emeritus-Professor of Biosystem Data
Analysis, Swammerdam Institute for Life Sciences, University of
Amsterdam and professor of Computational Systems Biology at the
Department of Plant and Environmental Sciences at the University of
Copenhagen.

Título: Multidimensional Latent Path Models

Abstract:

In many cases in the life sciences we are confronted with measurements
performed on a biological system that can be arranged in multiple data
sets pertaining to different entities being measured, such as
metabolites, proteins, gene-expressions, microbiome compositions.
Traditionally such multiset data has been analyzed by multiblock or
multiset methods from chemometrics and psychometrics. Such an analysis
can be supervised, _e.g_., for predicting an outcome, or unsupervised,
_e.g._, exploratory analysis. Both types of analyses ignore the topology
of the individual data blocks, _i.e._, the way in which these individual
data blocks can be or must be arranged. In the social sciences methods
have emerged combining factor analysis with structural equation models
resulting in so-called latent path models, such as PLS-Path Modeling,
that deal with such topology. These latent path models usually assume
one latent variable per data block which is not sufficient for
high-dimensional life science data. In this talk, I will discuss how
this can be generalized to more than one latent variable per block. This
is not trivial and I will discuss methods, algorithms and interpretation
of such models. I will touch upon the topic of causality and will give
an example from the field of plant sciences.

Rigidity for Serrin's problem in Riemannian manifolds

By Allan Freitas Universidade Federal da Paraíba (UFPB)

Abstract: In this lecture, we address Serrin-type problems in Riemannian manifolds. We begin by establishing a Heintze-Karcher inequality and proving a Soap Bubble theorem, with its corresponding rigidity, in the context of ambient spaces with a Ricci tensor bounded from below. We then focus on Serrin’s problem within bounded domains of manifolds endowed with a conformal vector field. A key tool in this analysis is a new Pohozaev identity that incorporates the scalar curvature of the manifold. Applications involve Einstein and constant scalar curvature spaces. This lecture is based on joint works with A. Roncoroni (Politecnico di Milano, Italy), M. Santos (UFPB, Brazil), M. Andrade (UFS, Brazil), and Diego Marín (Universidad de Granada, Spain)