TENTATIVE SCHEDULE (all times in Mountain time)

For questions and comments, please email  padi.fuster@colorado.edu

Land Acknowledgement

CU Boulder, founded the same year Colorado became a state in 1876, recognizes that it sits on the traditional territories and ancestral homelands of the Arapaho, Cheyenne, Ute and many other Native American nations. Recognizing the history of the state, the university and the campus’s origin story, however difficult, and the histories and experiences of the Indigenous peoples who have lived in these territories for millennia aligns with the campus’s academic and research missions as Colorado’s flagship public research university.

You can learn more about indigenous mathematicians here: https://indigenousmathematicians.org/

This conference is partially funded by NSF and the Department of Mathematics at the University of Colorado Boulder.

Abstracts

(In alphabetical order)

Speaker: Andrew Campbell (University of Colorado Boulder)

Title: Polynomial roots under repeated differentiation: perspectives from the worlds of PDEs, Probability, and Operator Algebras

Abstract: A series of, initially unrelated, recent papers revealed a surprising connection between derivatives of real rooted polynomials and Hermitian random matrices/free probability. Roughly, this connection asserts that, up to a rescaling, the roots of the $(tn)$-th derivative of a degree n real rooted polynomial have the same behavior as the eigenvalues of the $(1-t)n\times(1-t)n$ principal submatrix of an $n\times n$ Hermitian matrix. Both of which can be related to the sum of free elements of a von Neumann. We will briefly discuss the partial differential equations which first suggested this connection, before considering the challenges of exploring this connection in the complex root setting. This talk will be based on joint work with Sean O'Rourke and David Renfrew. 

Speaker: Evan Camrud  (Colorado State University)

Title: What does your morning coffee have to do with machine learning? – Convergence of Langevin dynamics

Abstract: Langevin dynamics describes the motion of “heavy” particles suspended in a “lighter” medium, just as stray coffee grounds may jitter about in your morning coffee. Meanwhile, Markov chain Monte Carlo (MCMC) methods provide us with a useful tool for computing statistical samples from high-dimensional, high-complexity probability distributions, which are enormously useful in sampling large data sets for machine learning and molecular dynamics calculations. An incredibly common MCMC method is that of Hamiltonian Monte Carlo, which approximates a Hamiltonian dynamics with first a leap-frog (Verlet) algorithm, and second a Metropolis-Hastings accept/reject step. A modification of this method is to replace the Metropolis-Hastings step with an autoregressive Gaussian damping step, in which case the algorithm converges to the Langevin dynamics as the step-size approaches zero. We may therefore gain approximate convergence rates of these MCMC algorithms by means of proving explicit convergence rates of Langevin dynamics to its invariant measure. In this talk, we will describe the motivation for using Langevin dynamics as the “idealized” MCMC method, as well as our recent results on explicit convergence rates for a particular class of probability distributions.

Speaker: Serena DiLeonardo

Title: 

Decline of Downslope Windstorms in the Front Range: A 21-Year Climatological Analysis

Abstract: 

Downslope windstorms occur regularly on the Eastern slope of the Rocky Mountains, and are known to exacerbate wildfires and cause structural damage. The 2021 Marshall Fire in Colorado serves as a prominent example, which rapidly became the most destructive in state history by destroying 1091 buildings and burning about 6,200 acres. To better understand these windstorms and their recent trends, this paper outlines a methodology for their classification based on wind speed, wind direction, and windstorm duration criteria. This climatology of downslope windstorms in Boulder, Colorado is derived from 10-meter wind data measured by a meteorological tower at the National Renewable Energy Laboratory's Flatirons Campus (formerly the National Wind Technology Center). After removing seasonal trends, a statistically significant negative trend emerges in yearly windstorm frequency between 2002 and 2022. Negative trends have also been observed in both the intensity and duration of downslope windstorms during this period. Overall, strong westerly winds have decreased by approximately 14 hours annually, accompanied by significant decreases in the 90th, 95th, and 99th percentile wind speeds. This study provides critical insights into the recent changes in extreme wind events occurring in the Front Range of the Rocky Mountains.

Speaker. Manuel Lladser. University of Colorado Boulder

Title. Exact and Approximate Spectra of Ultrametric Matrices

Abstract. Ultrametric matrices have a rich structure that is not apparent from their definition. Nevertheless, they arise in various fields, mainly as so-called phylogenetic covariance matrices. In this talk, we use discrete wavelets of a Haar-type to change basis and sparsify them---exploiting a representation of ultrametric matrices as phylogenetic trees. We characterize the matrices completely diagonalized by the wavelets and show that large but random ultrametric matrices are asymptotically diagonalized with high probability. This work has been partially funded by the NSF BIGDATA grant 1836914.

Speaker: Vlad Margarint (CU Boulder)

Title: Planar Statistical Physics and Complex Analysis: How one can study scaling limits of interfaces of Planar Statistical Physics models?

Abstract:  Schramm-Loewner Evolution (SLE) was introduced in 2000 by Oded Schramm in order to give meaning to scaling limits of interfaces of some models of Planar Statistical Physics. In the last years, there were many models that were proven to have their interfaces in the scaling limit described by SLE. The SLE curves are studied through the Loewner Differential Equation with a Brownian motion driver. I will describe the model and present my results on the continuity of this model in a natural parameter. I will also present some recent work on extensions of this model to multiple SLE curves. The latter model has many connections with other major fields of research: Conformal Field Theory and Random Matrices.

Speaker: Ian Miller (CU Boulder)

Title: Dichotomy Questions for the Electromagnetic Nonlinear Schrodinger Equation

Abstract: The nonlinear Schrodinger equation (NLS) is a well studied PDE. For an important subset of initial data, NLS enjoys results classifying solutions which exist globally in time and those which blow up in finite time. The electromagnetic nonlinear Schrodinger equation (emNLS) is a variant of NLS which has attracted the attention of many researchers in recent years. In this talk we will discuss recent work extending the classification results from NLS to emNLS. This is joint work with Magdalena Czubak and Svetlana Roudenko.

Speaker. Kirsten Morris (University of Nebraska-Lincoln)

Title:  Absorbing Set Analysis of Quantum LDPC Codes

Abstract:  Key to understanding the performance of quantum low density parity check codes (QLDPC) is to understand their decoding failures. Using the Tanner Graph representation of QLDPC codes we study the subsets of variable nodes that, when in error, cause a decoding failure under the Gallager B syndrome-based iterative decoder. In this talk we analyze a specific class of variable nodes, known as absorbing sets, to understand their impact in decoding failures. This is joint work with Christine Kelley and Tefjol Pllaha.

Speaker: Sam Zhang (CU Boulder)

Title: Labor advantages drive the greater productivity of faculty at elite universities

Abstract: Faculty at prestigious institutions dominate scientific discourse, producing a disproportionate share of all research publications. Environmental prestige can drive such epistemic disparity, but the mechanisms by which it causes increased faculty productivity remain unknown. Here, we combine employment, publication, and federal survey data for 78,802 tenure-track faculty at 262 PhD-granting institutions in the American university system to show through multiple lines of evidence that the greater availability of funded graduate and postdoctoral labor at more prestigious institutions drives the environmental effect of prestige on productivity. In particular, greater environmental prestige leads to larger faculty-led research groups, which drive higher faculty productivity, primarily in disciplines with group collaboration norms. In contrast, productivity does not increase substantially with prestige for faculty publications without group members or for group

members themselves. The disproportionate scientific productivity of elite researchers can be largely explained by their substantial labor

advantage rather than inherent differences in talent.