Student evaluations of teaching (SET) are widely used in academic personnel decisions as a measure of teaching effectiveness. The way SET are used is statistically unsound--but worse, SET are biased and unreliable. Observational evidence shows that student ratings vary with instructor gender, ethnicity, and attractiveness; with course rigor, mathematical content, and format; and with students' grade expectations. Experiments show that the majority of student responses to some objective questions can be demonstrably false. A recent randomized experiment shows that giving students cookies increases SET scores. Randomized experiments show that SET are negatively associated with objective measures of teaching effectiveness and biased against female instructors by an amount that can cause more effective female instructors to get lower SET than less effective male instructors. Gender bias also affects how students rate objective aspects of teaching. It is not possible to adjust for the bias, because it depends on many factors, including course topic and student gender. Students are uniquely situated to observe some aspects of teaching and students' opinions matter. But for the purposes of evaluating and improving teaching quality, SET are biased, unreliable, and subject to strategic manipulation. Reliance on SET for employment decisions disadvantages protected groups and may violate federal law. For some administrators, risk mitigation might be a more persuasive argument than equity for ending the use of SET in employment decisions: union arbitration and civil litigation over institutional reliance on SET are on the rise. Several major universities in the U.S. and Canada have already de-emphasized, substantially re-worked, or abandoned SET for personnel decisions.

I will consider random matrices in the general linear group GL(N;C) distributed according to a heat kernel measure.
This may also be described as the distribution of Brownian motion in GL(N;C) starting at the identity. Numerically,
the eigenvalues appear to cluster into a certain domain $\Sigma_t$ as $N$ tends to infinity. A natural candidate for
the limiting eigenvalue distribution is the “Brown measure” of the limiting object, which is Biane’s ``free multiplicative Brownian motion.'' I will describe recent work with Driver and Kemp in which we compute this Brown measure. The talk will be self contained and will have lots of pictures.

The coordinate ring $S = \mathbb{C}[x_{i,j}]$ of the space of $m \times n$ matrices carries an action of the group $GL_m \times GL_n$ via row and column operations on the matrix entries. If we consider any $GL_m \times GL_n$-invariant ideal $I$ in $S$, the syzygy modules $\mathrm{Tor}_i(I,\mathbb{C})$ will carry a natural action of $GL_m \times GL_n$. By the BGG correspondence, they also carry an action of $\bigwedge^{\bullet}(\mathbb{C}^m \otimes \mathbb{C}^n)$. It turns out that we can combine these actions together and make them modules over the general linear Lie superalgebra $\mathfrak{gl}(m \mid n)$. We will explain how this works and how it enables us to commute all Betti number of any $GL_m \times GL_n$-invariant ideal $I$. This latter part will involve combinatorics of Dyck paths.

It is well-known that the Ricci flow will generally develop singularities if one flows an arbitrary initial metric. Ancient solutions arise as limits of suitable blow-ups as the time approaches the singular time and thus play a central role in understanding the formation of singularities. By the work of Hamilton, Perelman, Brendle, and many others, ancient solutions are now well-understood in two and three dimensions. In higher dimensions, only a few classification results were obtained and many examples were constructed. In this talk, we show that for any dimension $n \geq 4$, every noncompact rotationally symmetric ancient $kappa$-solution to the Ricci flow with bounded positive curvature operator must be the Bryant soliton, extending a recent result of Brendle to higher dimensions. This is joint work with Yongjia Zhang.

The starting point for this talk comes from population genetics: how should we estimate evolutionarily relevant parameters from DNA sequence data taken from samples of individuals? I will give a brief overview of what we learned, starting from the Ewens Sampling Formula and touching on Approximate Bayesian Computation as an inference method when likelihoods are intractable. To illustrate ABC, I will give an example concerning inference of the number of distinct DNA sequences in a sample, given only information about the frequency of point mutations in the samples. This example provides an introduction to inference from typical cancer sequencing data, in which individuals are replaced by cells and in which typically we do not know which mutations occur in which cells. I will give a brief overview of what cancer evolution is about, the sort of statistical and computational problems it poses, and where we are in addressing some of them. Time permitting, I will describe some novel experimental methods we are developing to understand the 3D structure of tumors, paving the way for some challenging inferential problems that will require engagement from data scientists and others.

The classical Tannaka reconstruction theorem allows one to recover a compact group $G$ (up to isomorphism) from the monoidal category of finite dimensional representations of $G$ over $\mathbb{C}$, $\text{Rep}_{\mathbb{C}}(G)$, as the tensor preserving automorphisms of the forgetful functor $\text{Rep}_{\mathbb{C}}(G) \longrightarrow \text{Vec}_{\mathbb{C}}$.

Now let $G$ be a profinite group, $K$ a finite extension of $\mathbb{Q}_p$ and $\text{Ban}_G(K)$ the category of $K$-Banach space representations (of $G$). $\text{Ban}_G(K)$ can be equipped with a (completed) tensor product $(-)\hat\otimes_K(-)$ and has a forgetful functor $\omega : \text{Ban}_G(K) \longrightarrow \text{Ban}(K)$.

Using an anti-equivalence of categories between $\text{Ban}_G(K)$ and the category of Iwasawa $G$-modules due to Schneider and Teitelbaum, we prove that a profinite group $G$ can be recovered from $\text{Ban}_G(K)$, in particular $G \cong \text{Aut}^\otimes(\omega)$.

Mathematics can help Art Historians and Art Conservators in studying and understanding art works, their manufacture process and their state of conservation. The presentation will review several instances of such collaborations in the last decade or so. Some of them led (and are still leading) to interesting new challenges in signal and image analysis. In other applications we can virtually rejuvenate art works, bringing a different understanding and experience of the art to museum visitors as well as to experts.

Let G be a countable, discrete, group and f an element of the integral group ring over G. It is well known how to associate to f an action of G on a compact, metrizable, abelian group. It turns out to be particularly interested to consider those f with an $\ell^{2}$-inveres: i.e. a vector $\xi\in \ell^{2}(G)$ so that $f*\xi=\delta_{1}$. Many nice ergodic theoretic properties of the corresponding action have been established in this context. I will give certain examples of f,G for which we can say that this action is a quotient of a Bernoulli shift. When G is amenable, this implies that it *is* a Bernoulli shift.