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2:00pm - RH 340P - Logic Set Theory Brian Ransom - (UCI) The Boolean Prime Ideal Theorem in the First Cohen Model We state the dense-set Halpern-Lauchli theorem and sketch Harrington’s proof of the theorem. Harrington’s proof is then adapted to give a new proof of the Boolean Prime Ideal theorem in the first Cohen model. This method is flexible and is shown to admit two natural generalizations. First, it is applied to give a simpler proof of Pincus’ result that ZF+BPI+DC_\kappa does not imply choice. Second, it is applied to make progress towards the goal of proving BPI in iterations of symmetric extensions. Lastly, we show that this proof generalizes Stefanovic's theorem that the Halpern-Lauchli theorem can be derived from BPI in the Cohen model. |
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4:00pm to 5:00pm - RH 340N - Geometry and Topology Bianca Viray - (University of Washington) Algebraic points on curves The Mordell Conjecture (proved by Faltings in 1983) is a landmark result exemplifying the philosophy "Geometry controls arithmetic". It states that the genus of an algebraic curve, a purely topological invariant that can be computed over the complex numbers, determines whether the curve may have infinitely many rational points. However, it also implies that we can never hope to understand the arithmetic of a higher genus curve solely by studying its rational points over a fixed number field. In this talk, we will introduce the concepts of parametrized points and density degree sets and show how they, together with the Mordell-Lang conjecture (proved by Faltings in 1994), allow us to organize all algebraic points on a curve. |
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2:00pm to 3:00pm - RH 440R - Geometry and Topology Bianca Viray - (University of Washington) Swimming with the current: the impact of research atmosphere on mathematical progress Just as a current impacts the effort a swimmer must make, so too does the research atmosphere in a community or conference affect research output. In this talk, I will discuss various examples of this, both long-standing programs of others, and many examples that I have experienced or witnessed. In particular, I will discuss different branches of my research program and how their development was impacted by the atmosphere in conferences, seminars, and research communities. I also discuss what I have learned from times when my actions have created counter currents for others. Content note: This talk will include some descriptions of harassment. |
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3:00pm to 3:50pm - RH 306 - Analysis Edriss Titi - (University of Texas A&M) Is dispersion a stabilizing or destabilizing mechanism? In this talk, I will present a unified approach for the effect of fast rotation and dispersion as an averaging mechanism for regularizing and stabilizing certain evolution equations, such as the Euler, Navier-Stokes and Burgers equations. On the other hand, I will also present some results in which large dispersion acts as a destabilizing mechanism for the long-time dynamics of certain dissipative evolution equations, such as the Kuramoto-Sivashinsky equation. In addition, I will present some results concerning two- and three-dimensional turbulent flows with high Reynolds numbers in periodic domains, which exhibit enhanced dissipation mechanism due to large spatial average in the initial data--a phenomenon which is similar to the ``Landau-damping" effect.
This is a joint Analysis seminar and Nonlinear PDE seminar |
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3:00pm to 3:50pm - RH 306 - Nonlinear PDEs Edriss Titi - (University of Texas A&M) Is dispersion a stabilizing or destabilizing mechanism? In this talk, I will present a unified approach for the effect of fast rotation and dispersion as an averaging mechanism for regularizing and stabilizing certain evolution equations, such as the Euler, Navier-Stokes and Burgers equations. On the other hand, I will also present some results in which large dispersion acts as a destabilizing mechanism for the long-time dynamics of certain dissipative evolution equations, such as the Kuramoto-Sivashinsky equation. In addition, I will present some results concerning two- and three-dimensional turbulent flows with high Reynolds numbers in periodic domains, which exhibit enhanced dissipation mechanism due to large spatial average in the initial data--a phenomenon which is similar to the ``Landau-damping" effect.
This is a joint Analysis seminar and nonlinear PDE seminar |
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3:00pm to 4:00pm - Rowland Hall 510R - Combinatorics and Probability Daniel Bartl - (University of Vienna) Adapted optimal transport for stochastic processes I will discuss adapted transport theory and the adapted Wasserstein distance, which extend classical transport theory from probability measures to stochastic processes by incorporating the temporal flow of information. This adaptation addresses key limitations of classical transport when dealing with time-dependent data. I will highlight how, unlike other topologies for stochastic processes, the adapted Wasserstein distance ensures continuity for fundamental probabilistic operations, including the Doob decomposition, optimal stopping, and stochastic control. Additionally, I will explore how adapted transport preserves many desirable properties of classical transport theory, making it a powerful tool for analyzing stochastic systems. |
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9:00am to 9:50am - Zoom - Inverse Problems Thibault Lefeuvre - (Sorbonne University) The Holonomy and Spectral Inverse Problems for Connections |
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1:00pm to 1:50pm - RH 510R - Algebra Harold Polo - (UCI) Unique Factorization Semidomains and Their Localizations A semidomain is a subsemiring of an integral domain, and a unique factorization semidomain (UFS) is a semidomain in which every nonzero, nonunit element factors uniquely up to permutation of factors and multiplication by units. A UFS is said to be proper if it is not a unique factorization domain (UFD). In this talk, we explore the challenges and subtleties involved in constructing proper UFSs. We also investigate conditions under which the localization of a UFS preserves the unique factorization property. This presentation is based on joint work with Victor Gonzalez and Pedro Rodriguez. |
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3:00pm to 4:00pm - RH 306 - Number Theory Roberto Hernandez - (Emory Univeristy) Rational Points on a Family of Genus 3 Hyperelliptic Curves Let $C$ be a smooth projective curve of genus $g \geq 2$. By Faltings Theorem, we know that there are only finitely many rational points on $C$. We compute the rational points on a family of genus 3 hyperelliptic curves which are curves of the form $y^2 = f(x)$ where $f(x)$ is a polynomial of degree $2g+1$ or $2g+2$ via the method of Dem’janenko-Manin. |