R. A. Fisher, the father of modern statistics, proposed the idea of fiducial inference during the first half of the 20th century. While his proposal led to interesting methods for quantifying uncertainty, other prominent statisticians of the time did not accept Fisher's approach as it became apparent that some of Fisher's bold claims about the properties of fiducial distribution did not hold up for multi-parameter problems. Beginning around the year 2000, the speaker and collaborators started to re-investigate the idea of fiducial inference. They discovered that Fisher's approach, when suitably generalized, would open doors to solve many important and challenging inference problems. They termed their generalization of Fisher's idea as generalized fiducial inference (GFI).

After more than a decade of investigations, the speaker and collaborators have developed a unifying theory for GFI and provided GFI solutions to many challenging practical problems in different fields of science and industry. Overall, they have demonstrated that GFI is a valid, useful, and promising approach for conducting statistical inference.

This talk will provide a brief introduction to GFI and report the speaker's ongoing work on applying GFI to some statistical and machine learning problems, including high-dimensional additive models, random forest prediction, matrix completion, and network data analysis.

It is joint work with Wei Du, Qi Gao, Jan Hannig, Hari Iyer, Randy Lai, Yi Su, Suofei Wu, and Chunzhe Zhang.

Attendees will participate in an interactive demonstration of several of Liljedahl’s 14 recommended teaching practices.We will briefly consider the theoretical and methodological bases for his book Building Thinking Classrooms in Mathematics (2021), Peter Liljedahl.

Abstract: TBA

Zoom: https://arizona.zoom.us/j/81150211038

Password: “arizona” (all lower case) 

Kudla-Rapoport conjecture predicts that there is an identity between the intersection number of special cycles on unitary Rapoport-Zink space and the derivative of local density of certain Hermitian form. However, the original conjecture was only formulated for RZ space with hyperspecial level structure over unramified primes . In this talk, I will motivate the original conjecture and discuss how to modify it at a ramified prime. Finally, I will sketch how to verify the modified conjecture for n=3. This is a joint work with Qiao He and Tonghai Yang.

Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are devastating conditions with poorly understood mechanisms and no known cure. Yet a striking feature of these conditions is the characteristic pattern of invasion throughout the brain, leading to well-codified disease stages visible to neuropathology and associated with various cognitive deficits. In this talk, I will show how we can use mathematical modelling to gain insight into this process and, doing so, gain some understanding on how the brain works. In particular, by looking at protein dynamics on the neuronal network, we can unravel some of the universal features associated with dementia that are driven by both the network topology and protein kinetics. If time permits, I will show that by further coupling this approach with functional models of the brain, we can explain important aspects of function loss during disease development.

Hybrid: Math Building, Room 402 & Zoom:  https://arizona.zoom.us/j/89712326534  Passcode: math (all lower case)

Abstract: TBA

Zoom https://arizona.zoom.us/j/85014462076 

Password:  “arizona” (all lower case)

The resolution of Serre's conjecture for modular forms by Khare-Wintenberger in the mid-2000s was a major achievement in the field of number theory. In this talk, I will begin by describing Serre's conjecture and its origins in the theory of congruences between modular forms.   I will then describe how the conjecture is connected to representation theory in finite characteristic.   This will naturally lead to higher dimensional analogues of the conjecture.  Finally, I will report on recent progress on these higher dimensional conjectures joint with Daniel Le, Bao V. Le Hung and Stefano Morra. 

Cylindrical targets are used to study instability growth in regimes relevant to inertial confinement fusion implosions, as they retain the effects of convergence while allowing for direct diagnostic access. Design parameters for experiments on the National Ignition Facility are informed by one-dimensional (1D) and two-dimensional (2D) radiation-hydrodynamics simulations, and these cylindrical implosions are most sensitive to parameters such as target radius, fill composition, and laser pulse shape. Even in 1D, the parameter space responsible for dictating the behavior of various implosion performance metrics is vast, and it can be difficult to ascertain which model parameters, or combinations thereof, have the most influence on these metrics. Additionally, uncertainty introduced via the addition of ad hoc parameters which are used as a proxy for complex underlying physics can result in mismatches between model results and experimental data. This talk applies model calibration techniques based on fidelity mapping to 1D simulations in order to examine the sensitivity of our model to such parameters, as well as identify regions of space where the error between model predictions and experimental results is relatively low.  William Gammel, Joshua P Sauppe, Samy Missoum, Bharath Pidaparthi

Place: Zoom:   https://arizona.zoom.us/j/82075792519 
Password:  150721

Thermodynamics provides a robust conceptual framework and set of laws that govern the exchange of energy and matter. Although these laws were originally articulated for macroscopic objects, nanoscale systems also exhibit “thermodynamic¬-like” behavior – for instance, biomolecular motors convert chemical fuel into mechanical work, and single molecules exhibit hysteresis when manipulated using optical tweezers. To what extent can the laws of thermodynamics be scaled down to apply to individual microscopic systems, and what new features emerge at the nanoscale? I will describe some of the challenges and recent progress – both theoretical and experimental – associated with addressing these questions.  Along the way, my talk will touch on non-equilibrium fluctuations, “violations” of the second law, the thermodynamic arrow of time, nanoscale feedback control, strong system-environment coupling, and quantum thermodynamics.

Title Tensor modeling in categorical data analysis and conditional association studies

Abstract In this talk, we offer new tensor perspectives for two classical multivariate analysis problems. First, we consider the regression of multiple categorical response variables on a high-dimensional predictor. A $M$-th order probability tensor can efficiently represent the joint probability mass function of the $M$ categorical responses. We propose a new latent variable model based on the connection between the conditional independence of the responses and the rank of their conditional probability tensor. We develop a regularized expectation-maximization algorithm to fit this model and apply our method to modeling the functional classes of genes. Second, we consider the three-way associations of how two sets of variables associate and interact, given another set of variables. We establish a population dimension reduction model, transform the problem to sparse Tucker tensor decomposition, and develop a higher-order singular value decomposition estimation algorithm. We demonstrate the efficacy of the method through a multimodal neuroimaging application for Alzheimer's disease research.

Each speaker will give a 30 minute talk with 5 minutes for questions at the end.  Full title and abstracts are to be announced.

Hybrid: Math, 501 and Zoom https://arizona.zoom.us/j/86997964863     Password:   Locute

I will report a joint work with Tong, concerning the structure of a certain submodule inside prismatic cohomology of a smooth proper scheme over a p-adic ring of integers. I will explain how this part of prismatic cohomology causes various pathologies, then say a few corresponding consequences of our structural result. If time permits, I shall also mention an interesting example.

A classic technique in PDE theory is that of multiplying by a carefully-chosen test function and integrating by parts. This method was famously used to prove bounds on the Helmholtz equation in the 1960s and 1970s by Cathleen Morawetz. Much-more sophisticated methods now exist for proving bounds on the Helmholtz equation, but (perhaps surprisingly) the multiplier method can still be used to prove new results. In this talk I will review the classic multiplier method, and then discuss a recent application of it to Helmholtz problems in the paper "Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization" https://arxiv.org/abs/2109.11267 , co-authored with Th\'eophile Chaumont-Frelet (INRIA, Nice).

Place: Hybrid, Math, 402 and
Zoom: https://arizona.zoom.us/j/81150211038 
Password: “arizona” (all lower case)

For details, see https://science.arizona.edu/academics/graduation-commencement 

Doors open at 1pm. COVID-19 protocols will be in place.