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Department of Mathematics

Upcoming Seminars

Memorial Union on sunny day

Join us for an upcoming seminar featuring mathematics faculty and invited speakers on one of our seven research topics. You may also see upcoming seminars by topic:

Rankin-Cohen Type Differential Operators on Automorphic Forms

STAG 263
Algebra and Number Theory Seminar

Speaker: Francis Dunn

In the classical setting, the derivative of a holomorphic modular form of integral weight on the complex upper half-plane is not in general a modular form since the derivative fails to satisfy the correct transformation properties. However, R. A. Rankin and H. Cohen were able to construct particular bilinear differential operators sending modular forms to modular forms. These Rankin—Cohen operators have several interesting properties and have been studied by D. Zagier, Y. Choie, T. Ibukiyama, and others.In this talk I will discuss the classical Rankin—Cohen operators, and some of their generalizations to automorphic forms in higher dimension, including ​​constructing Rankin—Cohen​ type differential operators on Hermitian modular forms of signature (n,n). Read more.

Improving the representation of snowpack processes and distribution with model-data fusion

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Mark Raleigh

ABSTRACT:Seasonal snowpack is the largest areal component of the global cryosphere and is a major source of summer water supply in regions such as western North America and High Mountain Asia. The amount of water stored in winter snowpack (snow water equivalent, SWE) can vary significantly in space and time due to heterogeneous climate and landscape processes that influence snow accumulation and melt processes. This critical water resource is under monitored due to sparse ground-based observational networks, and a lack of satellite remote sensing system that can measure SWE across all global snow types and conditions. However, emerging remote sensing techniques and new capabilities with model-data fusion offer the potential to improve our understanding and prediction of snow water resources. In this seminar, I will highlight how we can improve representation of SWE and related snowpack processes through the integration of numerical snowpack models and observations using data… Read more.

Digital Twins for Time Dependent Problems

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Juan Restrepo

ABSTRACT: A digital twin is a set of algorithms that connect the virtual world to the physical worl in a fully bi-directional way: for example, a predictive digital twin will use physics models, machine learned models, constraints as well as observations to make forecasts. A digital twin used as a controller would yield a virtual prescription, taking into account observations, that prescribes changes in the real world aimed at obtaining a certain desired real world outcome. I will describe ongoing work on developing a digital twin that will become central to an artificial intelligence framework for large scale electric grid resilience via adaptation. BIO: Juan M. Restrepo is a Distinguished Member of the R&D staff and the section head of the mathematics in computation section at Oak Ridge National Laboratory. His research concerns foundational aspects of machine learning and the development of new artificial intelligence algorithms for science. He is a Fellow of the Society of… Read more.