Methane is a powerful greenhouse gas and a precursor for tropospheric ozone, as well as an important near-term energy source. It is a priority for climate mitigation efforts by many countries and an increasing number of subnational governments and private companies. However, the causes for observed changes in the atmospheric growth rate of methane remain poorly understood and there is compelling evidence of higher than predicted fugitive methane emissions across many economic sectors including energy, waste management, and agriculture. Multiple studies have exposed a long-tail distribution of methane emissions associated with a relatively small fraction of sources that dominate the emissions of key sectors and regions, suggesting potential low-hanging fruit for climate action. These “super-emitters” are often stochastic, highly intermittent and distributed over large areas – complicating efforts to detect and mitigate them.  Recent advances in atmospheric measurements using a variety of techniques and vantage points together with data science offer the potential to dramatically advance methane mitigation. In this talk I will summarize findings from the first systematic surveys of methane super-emitters using remote sensing technology and provide some perspectives on future research and policy directions. I will also present case studies where collaborative efforts with facility operators and local agencies in California directly resulted in measurable mitigation. Finally, I will describe efforts to launch a constellation of climate satellites, a new airborne science program, and potential transdisciplinary carbon center at UA.

Next Monday 2/24, the undergraduate math club, MathCats will be hosting a fundraiser at Chipotle from 4-8pm. MathCats provides students of all majors with opportunities to learn about mathematical research and careers, work on challenging problems, and give back to the community through outreach. Your support allows us to continue to improve our outreach activities and give undergraduates around campus opportunities to grow outside their major coursework.

Random Matrix Theory arose as an attempt to understand, in a qualitative way, the behavior of large quantum mechanical systems in the setting of randomness and symmetry. Subsequent developments brought into play remarkably effective methods from quantum field theory to analyze the asymptotic behavior of these mechanical systems that in turn led to surprising connections with classical dynamical problems. This talk will present an elementary survey of some of these classical connections in the context of Laplace growth models for simplified interface evolution such as Darcy's law.

We prove a systematic construction of all 70 strongly rational,
holomorphic VOAs $V$ of central charge 24 with non-zero weight-one space
$V_1$ as cyclic orbifold constructions associated with the 24 Niemeier
lattice VOAs $V_N$ and certain 230 "good" automorphisms of small order
in $\Aut(V_N)$.

We show that up to algebraic conjugacy these automorphisms are exactly
the generalised deep holes, as introduced in [Möller-Scheithauer-2019],
of the Niemeier lattice VOAs with the additional property that their
orders are equal to those of the corresponding outer automorphisms.

Together with the constructions in [Höhn-2017] and
[Möller-Scheithauer-2019] this gives three different *uniform*
constructions of these VOAs, which are however related through 11
algebraic conjugacy classes in $\Co_0$.

Finally, by considering the inverse orbifold constructions associated
with the 230 "good" automorphisms, we give the first *uniform* proof of
the fact that each strongly rational, holomorphic VOA $V$ of central
charge 24 with non-zero weight-one space $V_1$ is uniquely determined by
the Lie algebra structure of $V_1$.

This is joint work with Gerald Höhn.

Short-term evolution is determined by the G matrix, whose covariance terms represent a combination of pleiotropy and linkage disequilibrium, shaped by the population's history. Observed genetic covariance is most often interpreted in pleiotropic terms. In particular, functional constraints restricting which phenotypes are physically possible can lead to a stable G matrix with high genetic variance in fitness-associated traits and high pleiotropic negative covariance along the phenotypic curve of constraint. We describe the evolution of G when pleiotropy is excluded by design, such that all covariance comes from linkage disequilibrium, which reaches high levels in rapidly adapting microbial populations. To do this, we extended the influential one-dimensional travelling wave model of rapid adaptation of an asexual population into two dimensions, representing two distinct fitness-associated traits in an asexual population. We find that the associated G-matrix maintains a stable orientation, but is far less stable in magnitude than predicted by previous models. Different mechanisms drive the instabilities along different principal components of G. Their origin is not drift, but rather small amounts of linkage disequilibria generated by mutations on the fittest backgrounds, which are subsequently amplified during competing selective sweeps. By competing one trait with a higher beneficial mutation rate with another with larger mutational effect sizes, we illustrate the range of parameters for which mutation-driven adaptation is possible.

Exponential random graphs are powerful in the study of modern networks. By representing a complex global configuration through a set of tractable local features, these models seek to capture a wide variety of common network tendencies. This talk will look into the asymptotic structure of weighted exponential random graphs and formulate a quantitative theory of phase transitions. The main techniques that we use are variants of statistical physics. Based on joint work with multiple collaborators.

We investigate the inverse source problem for the wave equation arising in photoacoustic and thermoacoustic tomography.  If one assumes that the speed of sound is a known constant, then there are many previously developed inversion formulas for the solution of this problem.  These formulas require that the data is measured on a closed surface completely surrounding the object or on certain unbounded surfaces. However, in many practical applications, data can only be measured on a finite open surface. In this talk, we will present a non-iterative approach to this problem that yields an approximate solution under certain geometric restrictions on finite open surfaces. This solution coincides with the true solution microlocally--that is, the error is a smooth function. In practical applications, such reconstructions result in qualitatively correct images. For the case of a circular acquisition surface, our method can be implemented with explicit, asymptotically fast methods.  We demonstrate the work of these algorithms in a series of numerical simulations.

The current penalized regression methods for selecting predictor variables and estimating the associated regression coefficients in the Cox model are mainly based on partial likelihood. In this paper, an empirical likelihood method is proposed for the Cox model in conjunction with appropriate penalty functions when the dimensionality of data is high. Theoretical properties of the resulting estimator for the large sample are proved. Simulation studies suggest that empirical likelihood works better than partial likelihood in terms of selecting correct predictors without introducing more model errors. The well-known primary biliary cirrhosis data set is used to illustrate the proposed empirical likelihood method.  

This is joint work with Dongliang Wang and Tong Tong Wu.

Elevation of neuronal activity in the brain is rapidly accompanied by an increase in local cerebral blood flow (CBF) to allow adequate supply of oxygen and nutrients to active neurons. This process, known as neurovascular coupling (NVC) or functional hyperemia, is essential for normal functioning of the brain and is disrupted in a wide range of neurological disorders. Despite the utmost importance of this process, its underlying mechanisms are not fully understood. In this research, we utilize a multiscale mathematical modeling approach to identify the key determinants of this process in health and their disruption in pathological conditions, in particular during small vessel disease and cortical spreading depression, in realistic microvascular networks.

Love it or hate it, many people believe that mathematics gives humans access to a kind of truth that is more absolute and universal than other disciplines. If this claim is true, we must ask: what makes the origins and processes of mathematics special and how can our messy, biological brains connect to the absolute? If the claim is false, then what becomes of truth in mathematics? In this public session, we will discuss beliefs about truth and how they play out in the mathematics classroom, trying to understand a little about identity, authority, and the Liberal Arts.

We consider the problem of imaging sparse scenes from a few noisy data using an l1-minimization approach. This problem can be cast as a linear system of the form Ax=b. The dimension of the unknown sparse vector x is much larger than the dimension of the data vector b. The l1-minimization alone, however, is not robust for imaging with noisy data. To improve its performance we propose to solve instead the augmented linear system [A|C]x=b, where the matrix C is a noise collector. It is constructed so as its column vectors provide a frame on which the noise of the data can be well approximated with high probability. This approach  gives rise to a new parameter-free imaging method that has a zero false discovery rate for any level of noise. We also obtain exact support recovery if the noise is not too large.