Let $X=\mathrm{SL}_3(\mathbb{R})/\mathrm{SL}_3(\mathbb{Z})$ and $a(t)=\mathrm{diag}(t^2,t^{-1},t^{-1})$. The expanding horospherical group $U^+$ is isomorphic to $\mathbb{R}^2$. A result of Shah tells us that the $a(t)$-translates of a non-degenerate real-analytic curve in a $(U^+)$-orbit get equidistributed in $X$. It remains to study degenerate curves, i.e. planar lines $y=ax+b$. In this talk, we give a Diophantine condition on the parameter $(a,b)$ which serves as a necessary and sufficient condition for equidistribution.
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Joint work with Kleinbock, Saxcé and Shah. If time permits, I will also talk about generalisations to $\mathrm{SL}_n(\mathbb{R})/\mathrm{SL}_n(\mathbb{Z})$. Joint work with Shah.

Given a nontrivial band sum of two knots, we may add full twists to the band to obtain a family of knots indexed by the integers. In this talk, I'll show that the knots in this family have the same knot Floer homology, the same instanton homology, but distinct Khovanov homology, generalizing a result of M. Hedden and L. Watson. A key component of the argument is a proof that each of the three knot homologies detects the trivial band. The main application is a verification of the generalized cosmetic crossing conjecture for split links.

A quiver is defined as a directed graph with an attitude towards representation theory. In this talk, I will introduce quiver representations and discuss a fundamental classification result due to Gabriel. If time permits, I will also discuss one possible answer to the question, ``Why are quivers?'' There are no prerequisites, and there will be many examples.

Prognostic models in survival analysis are aimed at understanding the relationship between patients' covariates and the distribution of survival time. Traditionally, semi-parametric models, such as the Cox model and the Additive Hazards model, have been assumed. In this talk I will derive a measure of explained variation under the Additive Hazards model showing its properties. Moreover I will describe the development of a new flexible method for survival prediction: DeepHazard, a neural network for time-varying risks. I will show its performance on popular real datasets.

I will discuss the problem of understanding the collapsing behavior of Ricci-flat Kahler metrics on a Calabi-Yau manifold that admits a holomorphic fibration structure, when the Kahler class degenerates to the pullback of a Kahler class from the base. I will present new work with Hans-Joachim Hein where we obtain a priori estimates of all orders for the Ricci-flat metrics away from the singular fibers, as a corollary of a complete asymptotic expansion.

The University of Minnesota Talented Youth Mathematics Program
(UMTYMP) is a selective, five-year accelerated mathematics program for
students in grades 6-12. During the course of the program, students take
advanced mathematics courses on University of Minnesota campuses,
starting with algebra and continuing through logic and proofs, linear
algebra, and multivariable calculus. The majority of UMTYMP students come
from one of three demographic groups: White/Caucasian, East Asian/East
Asian American, and South Asian/South Asian American. We use the term Asian/Asian American to describe students in the latter two demographic groups.
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The model minority stereotype (MMS) is the classification of Asian/Asian
American students as gifted, ``academic whizzes'' who outperform their
peers (Choi \& Lahey, 2006). In 2020, we initiated an IRB-approved study
to understand the impact of MMS on Asian/Asian American students who are
labelled as ``gifted" and/or ``talented." In this talk, I will
discuss the process and results of the study, propose best practices for
instructors who interact with students navigating MMS, and suggest ideas
for follow-up studies on this topic.

We consider the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (2018).
We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph
which makes the PABM an attractive choice for modeling networks that appear in biological sciences.
We expand the theory of PABM to the case of an arbitrary number of communities which possibly
grows with a number of nodes in the network and is not assumed to be known. We produce estimators
of the probability matrix and the community structure and provide non-asymptotic upper bounds for the
estimation and the clustering errors. We use the Sparse Subspace Clustering (SSC) approach for
partitioning the network into communities, the approach that, to the best of our knowledge, has not been
used for clustering network data. The theory is supplemented by a simulation study. In addition, we
show advantages of the PABM for modeling a butterfly similarity network and a human brain functional
network.

We explain how Hodge theory unifies three a priori very different
types of deformations of K3 surfaces: twistor spaces, Brauer (or Tate-Shafarevich)
families and Dwork families. All three share the property of transporting
complex multiplication from one fibre in the Noether-Lefschetz locus to
any other. This phenomenon is at the moment observed in all three cases but
geometrically only explained for Brauer families. The motivation comes
from the Hodge conjecture for squares of K3 surfaces which is still open.