| Analysis On the concepts of nullity and full — ideas and new directions Suddhasattwa Das Mathematics and Statistics, Texas Tech University |
| Statistics Doubly Robust Conditional Independence Testing with Generative Neural Networks Yi Zhang Statistics, University of Illinois, Urbana-Champaign |
(arxiv link: https://arxiv.org/abs/2407.17694)
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* Meeting ID: 943 0383 4893 * Passcode: 057825
| Topology and Geometry A Higher Spin Statistics Theorem for Invertible Quantum Field Theories Lukas Müller Perimeter Institute for Theoretical Physics |
| Applied Mathematics and Machine Learning Modifying Metals to Promote Power Generation Michelle Pantoya Department of Mechanical Engineering, Texas Tech University |
Biography. Dr. Michelle Pantoya received her PhD from the University of California, Davis in 1999 and joined the faculty in the Mechanical Engineering Department at Texas Tech University in 2000. As the J. W. Wright Regents Endowed Chair Professor, her research focuses on studying fuel particle combustion in ways that can enhance our national safety and security. She has received many research and teaching awards including the US Presidential Early Career Award (PECASE) and the DoD Young Investigator Program Award and has over 220 archival publications on this topic. Dr. Pantoya is also the co-author of several children’s books introducing engineering to young kids (i.e., Engineering Elephants, Optimizing an Octopus & Designing Dandelions) and an advocate for elementary engineering education.
When: 4:00 pm (Lubbock's local time is GMT -6) Where: room Math 011 (Math Basement) ZOOM details:
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* Meeting ID: 979 1333 6658 * Passcode: Applied (Note the capital letter "A")
| Geometry, PDE and Mathematical Physics Magnetic curves in contact geometry Marian Ioan Munteanu Matematică, Universitatea Alexandru Ioan Cuza din Iaşi, Romania |
The dimension 3 is rather special, since it allows us to identify 2-forms with vector fields via the Hodge ⋆ operator and the volume form of the (oriented) manifold. Moreover, in dimension 3, one may define a cross product and therefore, the Lorentz equation may be written in an easier way.
The challenge is to solve the differential equation in order to find an explicit solution, meaning the explicit parametrization for the magnetic trajectories. Nevertheless, this is not always possible and, because of that, it is necessary to understand the behaviour of the solution.
Recent studies are done in 3-dimensional Sasakian manifolds, where the contact 2-form naturally defines a magnetic field. The solutions of the Lorentz equation, usually called contact magnetic trajectories, are often expressed in a concrete parametrization. It can be proved a reduction result for the codimension in a Sasakian space form, that is, essentially, we can reduce the study (of a magnetic curve in a Sasakian space form) to dimension 3. The geometry of magnetic trajectories have been recently studied in the z-sphere, in the Berger 3-sphere, in the Heisenberg group Nil3 and in SL(2,R), respectively.
Another important problem is the existence of closed curves which is a fascinating topic in dynamical systems. Periodic orbits of the contact magnetic fields on the unit 3-sphere and in the Berger 3-sphere were found in the last two decades and conditions for the periodicity have been obtained. A similar result has been recently given; it was proved that periodic contact magnetic curves in SL(2,R) can be quantized in the set of rational numbers.
The geometry of contact magnetic curves in SL(2,R) is much more beautiful. More precisely, it can be shown that every contact magnetic trajectory (of charge q) starting at the origin of SL(2,R) with initial velocity X and with charge q is the product of the homogeneous geodesic with initial velocity X and the charged Reeb flow exp(2qs\xi). Similar results are obtained for the Berger spheres as well.
This talk is based on several papers, mainly in collaboration with Prof. Jun-ichi Inoguchi (Japan).
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| Mathematics Education Math Circle Andrew Soto Levins Mathematics and Statistics, Texas Tech University |