seminars:anal
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| - | * **February 11th, Wednesday ** (4-5pm)\\ | ||
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| - | <WRAP box 80%> **//Abstract//**: | ||
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| - | * **February 18th, Wednesday ** (4-5pm)\\ | + | * **Tuesday, February 10 (Joint with Data Science Seminar) ** (12:15-1:15pm)\\ |
| - | \\ **//Speaker //**: | + | \\ **//Speaker //**: Dr. Yizeng Li (Department of Biomedical Engineering at Binghamton University) |
| - | \\ **//Topic//**: | + | \\ **//Topic//**: Multiphase Continuum Models for Cell Migration. |
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| - | <WRAP box 80%> **//Abstract//**: | + | <WRAP box 80%> **//Abstract//**: Cell migration is a fundamental process in physiology and disease, yet it poses challenging problems in multiscale modeling and continuum mechanics. Cell motility arises from the coupling of intracellular transport, active force generation, and evolving geometry. Cytoskeletal dynamics, in particular actin turnover and force production, provides a rich setting for mathematical analysis. In this talk, I will present a mathematical framework for mammalian cell motility based on multiphase continuum models with moving boundaries. The formulation incorporates fluid-structure interaction and active stresses to describe the coupled evolution of cytoskeletal flow and cell shape. The model predicts how migration efficiency depends on actin dynamics and geometric features of the cell. If time permits, I will also present a mechanical-electrical-chemical coupled model for water-driven cell motility induced by polarized membrane ion transport. This second framework highlights how transport processes and force balance together generate directed motion. |
| - | \\ | + | Biography of the speaker: Yizeng Li is an Assistant Professor in the Department of Biomedical Engineering at Binghamton University. She received MS from Mathematics and PhD from the Department of Mechanical Engineering at the University of Michigan-Ann Arbor. Afterwards, she was a postdoctoral researcher at Johns Hopkins University's Department of Mechanical Engineering and Institute for NanoBioTechnology. Her backgrounds are in theoretical mechanics and applied mathematics with applications to biophysics and mechanobiology. Li develops physiology-based mathematical models for cell motility, polarization, volume regulation, electro-homeostasis, signal transduction, and other biophysics problems. She also combines mathematical models with experimental data to explain non-intuitive cell biology phenomena. |
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| - | * **February 25th, Wednesday ** (4-5pm)\\ | + | |
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| - | * **March 4th, Wednesday ** (4-5pm)\\ | ||
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| - | * **March 11th, Wednesday ** (4-5pm)\\ | + | * **(Updated) March 19th, Thursday ** (4-5pm) \\ \\ |
| - | \\ **//Speaker //**: | + | **//Speaker//**: Zheng Sun (University of Alabama, Tuscaloosa)\\ |
| - | \\ **//Topic//**: | + | **//Topic//**: On a numerical artifact of solving shallow water equations with a discontinuous bottom |
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| - | * **March 18th, Wednesday ** (4-5pm) \\ \\ | + | |
| - | **//Speaker//**: Ziyao's visitor\\ | + | |
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| - | <WRAP box 80%> **//Abstract//**: | + | <WRAP box 80%> **//Abstract//**: The nonlinear shallow water equations are used to model the free surface flow in rivers and coastal areas for which the horizontal length scale is much greater than the vertical length scale. They have wide applications in oceanic sciences and hydraulic engineering. In this talk, we study a numerical artifact of solving the shallow water equations over a discontinuous riverbed. For various first-order methods, we report that the numerical solution will form a spurious spike in the numerical momentum at the discontinuous point of the bottom. This artifact will cause the convergence to a wrong solution in many test cases. We present a convergence analysis to show that this numerical artifact is caused by the numerical viscosity imposed at the discontinuous point. Motivated by our analysis, we propose a numerical fix which works for the nontransonic problems. |
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| * **March 25th, Wednesday ** (4-5pm) \\ \\ | * **March 25th, Wednesday ** (4-5pm) \\ \\ | ||
| **//Speaker//**: Yiming Zhao(Syracuse University) \\ | **//Speaker//**: Yiming Zhao(Syracuse University) \\ | ||
| - | **//Topic//**: TBD | + | **//Topic//**: $SL(n)$-invariant isoperimetric and Minkowski problems |
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| - | <WRAP box 80%> **//Abstract//**: | + | <WRAP box 80%> **//Abstract//**: In convex geometry, where convex bodies are the primary objects of study, a central goal is to discover geometric invariants and measures that can be used to recover or characterize their shapes. Two intertwined lines of research pursue this objective. Isoperimetric inequalities involving geometric invariants, including the classical isoperimetric inequality and the celebrated Brunn–Minkowski inequality, seek to identify special shapes as extremals. Minkowski problems, a family of problems originating in the work of Minkowski, aim to recover, sometimes uniquely, the shape of an arbitrary convex body by solving measure equations that, under additional but unnecessary smoothness assumptions, reduce to Monge–Ampère-type equations. In this talk, after giving some historical background, I will discuss recent joint work with Dongmeng Xi that continues this line of research through the study of integral affine surface area and radial mean bodies. |
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| * **April 1st, Wednesday ** (4-5pm) \\ \\ | * **April 1st, Wednesday ** (4-5pm) \\ \\ | ||
| - | **//Speaker//**: Spring Break \\ | + | **//Speaker//**: Spring Break (Binghamton University) \\ |
| - | **//Topic//**: | + | **//Topic//**: A lower bound on sleep duration under optimal conditions |
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| <WRAP box 80%> **//Abstract//**: | <WRAP box 80%> **//Abstract//**: | ||
| + | We show that in the absence of homework, sleep duration increases without bound. Applications to stress reduction are discussed. | ||
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| * **April 8th, Wednesday ** (4-5pm) \\ \\ | * **April 8th, Wednesday ** (4-5pm) \\ \\ | ||
| - | **//Speaker//**: \\ | + | **//Speaker//**: Gang Zhou (Binghamton University) \\ |
| - | **//Topic//**: | + | **//Topic//**: Exact characterizations for quantum conditional mutual information and some other entropies |
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| - | <WRAP box 80%> **//Abstract//**: | + | <WRAP box 80%> **//Abstract//**: I will present my latest results on quantum information theory. I will start with an introduction to the quantum theory for preparation, and then present the results. |
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| + | Lieb and Ruskai's strong subadditivity theorem, which shows that the conditional mutual information must be nonnegative, is fundamental in quantum theory. It has numerous applications, such as in quantum error correction. | ||
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| + | When the mutual information is zero, the Petz recovery map can be used to reconstruct the quantum channel. | ||
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| + | When the mutual information is small, one seeks to define an optimal recovery channel. To this end, a mathematical characterization of the mutual information is desirable. In my latest paper I provided an exact characterization of the mutual information, along with characterizations for other entropies. My controls are sharp, leaving no room for improvement, in the sense that I provided equalities, regardless of whether the mutual information (or remainder) is small or large. | ||
| + | I transformed the definitions of these entropies into a summation of explicitly constructed terms, and the definition of each term obviously demonstrates the desired positivity/convexity/concavity. The summation converges rapidly and absolutely in a chosen elementary norm. | ||
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| + | An exposition for the general public was provided by git.science and emailed to me, see the link https://gist.science/paper/2603.14650 | ||
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| - | * **April 15th, Wednesday, 4:00-5:00pm \\ \\ | + | * **April 15th, Wednesday,** 4:00-6:00pm (PhD Thesis Defense) \\ \\ |
| - | **//Speaker//**: \\ | + | **//Speaker//**: Brian Kirby(Binghamton University) \\ |
| - | **//Topic//**: | + | **//Topic//**: On Resolving the Singularities of the Reissner-Nordström Penrose Diagram via Method of Blow-Ups |
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| - | <WRAP box 80%> **//Abstract//**: | + | <WRAP box 80%> **//Abstract//**: The Penrose Diagram was first developed by Roger Penrose in the early 1960’s, taking an infinite spacetime and representing it in a concise diagram. This was first used to model the Schwartzchild spacetime metric, a black hole with no electric charge. The Penrose Diagram for the Reissner-Nordstrom metric was a result of the works of Brandon Carter, Stephen Hawking, and George Ellis, primarily in the late 1960’s to early 1970’s. These diagrams are still used today, primarily by physicists and astronomers to help better understand black holes, event horizons, and causality. This thesis focuses on better understanding the Penrose Diagram for the Reissner-Nordstrom metric. While work has been done recently to develop algorithms and explicitly construct these diagrams, current understanding of Penrose Diagrams works only on the interior of the diagrams, giving an incomplete picture of spacetime with infinitely many discontinuities with highly discontinuous behavior. In this thesis, we generalize the Reissner-Nordstrom metric and expand on its standard Penrose Diagram construction. Through the method of blow-ups of manifolds with corners, we resolve each singularity in the standard Penrose Diagram, and classify the asymptotic behavior of the metric at $r = 0$. In particular, we prove:\\ |
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| + | Theorem: Any Reissner-Nordstrom metric lifts to its blown-up Penrose Diagram to be a $C^{\infty}$ b-metric everywhere, up to and including the front faces, except at the $r = 0$ hypersurface, where it has an expansion of the form $r^{−2/3} F(r^{1/3})$.\\ | ||
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| + | The Thesis Committee members are: Paul Loya (Chair and Faculty Advisor), Emmett Wymann, Xiangjin Xu and Bruce White (Outside Examiner). | ||
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| * **April 22th, Wednesday ** (4-5pm) \\ \\ | * **April 22th, Wednesday ** (4-5pm) \\ \\ | ||
| - | **//Speaker//**: \\ | + | **//Speaker//**: Cancelled\\ |
| **//Topic//**: | **//Topic//**: | ||
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| * **May 6th, Wednesday ** (4-5pm) \\ \\ | * **May 6th, Wednesday ** (4-5pm) \\ \\ | ||
| - | **//Speaker//**: \\ | + | **//Speaker//**:Santiago Alzate (Binghamton University) \\ |
| - | **//Topic//**: | + | **//Topic//**: Masters thesis |
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seminars/anal.1770073281.txt · Last modified: 2026/02/02 18:01 by xxu