Upcoming Events

Multisite studies are increasingly used to study human health across different populations and countries. However, a common challenge in using data from multiple studies is the presence of systematically missing values – when some studies have not recorded information on certain variables. Although it is possible to use data from sites with recorded observations to impute the missing values, this process becomes challenging when data pooling is not feasible because of logistic or legal constraints. In this talk, I am going to introduce a framework for multiple imputation in distributed data networks allowing for the imputation of missing values across study sites without the need of sharing individual data. Some motivating examples alongside further steps and developments will be discussed.

We will pick up where we left off in the fall and go over Chapter 5.1-5.2 of Gompf-Stipsicz.

Abstract: Given a spin structure s on a closed oriented surface S, the spin mapping class group Mod(S,s) is the subgroup of Mod(S) stabilizing s. These groups are intimately related to the spin geometry of 3- and 4-manifolds. In this talk, we will discuss our results on generating Mod(S,s) with minimal number of generators, including some generalisations to r-spin groups.

 The hyperbolic vanishing mean curvature (HVMC) equation in Minkowski space is a quasilinear wave equation that serves as the hyperbolic counterpart ofthe minimal surface equation in Euclidean space. This talk will concern the modulated nonlinear asymptotic stability of the $1+4$ dimensional hyperbolic catenoid, viewed as a stationary solution to the HVMC equation. This stability result is under a ``codimension-one'' assumption on initial perturbation, modulo suitable translation and boost (i.e. modulation), without any symmetry assumptions. In comparison to the $n \geq 5$ case addressed by Lührmann-Oh-Shahshahani, proving catenoid stability in $n = 4$ dimensions shares additional difficulties with its $3$ dimensional analog, namely the slower spatial decay of the catenoid and slower temporal decay of waves. To overcome these difficulties for the $n = 3$ case, the strong Huygens principle, as well as a miracle cancellation in the source term, plays an important role in the work of Oh-Shahshahani to obtain strong late time tails. Without these special structural advantages in $n = 4$ dimensions, our novelty is to introduce an appropriate commutator vector field to derive a new hierarchy with higher $r^p$-weights so that an improved pointwise decay can be established. 

In this talk, I will first give an outline of the proof and then focus on a model case to illustrate our approach to achieving an improved decay in $4$ dimensions. 

Our lab is focused on developing tumor forecasting methods by integrating advanced imaging technologies with mathematical models to predict tumor growth and treatment response.  In this presentation, we will focus on how quantitative magnetic resonance imaging (MRI) data can be employed to calibrate mathematical models built on first-order effects related to well-established “hallmarks” of cancer including proliferation, migration/invasion, vascular status, and drug-related tumor growth inhibition and cell death.  In particular, we will present some of our recent results on using these models to build personalized digital twins that provide a rigorous, but practical, methodology for optimizing therapeutic interventions on a patient-specific basis.

Singularities of Schubert subvarieties of a flag variety are well known to play a major role in the representation theory of the corresponding complex reductive group.  Similarly, singularities of symmetric subvarieties of a flag variety have many connections with the representation theory of the corresponding real form of the group.  The first kind of singularities have been characterized via the classical combinatorial notion of pattern avoidance.  I will indicate how this plays out in the symmetric variety setting for real classical groups.

TBD

Homepage: https://leihuan-mp.github.io/

This talk is based on joint work with Carlsson. We give a geometric construction of a monomial space of the space of double coinvariants DH_n. The space is the quotient of the ring C[x₁,..,x_n,y₁,..y_n] by the ideal generated by the S_n-symmetric polynomials without a constant term. Our basis gives an elementary proof of the shuffle conjecture. The key idea is to study a flag version of the compactified Jacobian for xⁿ=yⁿ⁺¹, also known as ASF. We show that this ASF is a bouquet of Hessenberg varieties.